From 41314584371971eddc823e4bf131e5b9aa305718 Mon Sep 17 00:00:00 2001 From: Mattrixwv Date: Sat, 6 Jun 2020 17:29:24 -0400 Subject: [PATCH] Initial commit with existing files --- .gitignore | 2 + LICENSE | 165 ++++++++++++++++++++ Problem1.py | 58 +++++++ Problem10.py | 53 +++++++ Problem11.py | 157 +++++++++++++++++++ Problem12.py | 66 ++++++++ Problem13.py | 253 ++++++++++++++++++++++++++++++ Problem14.py | 80 ++++++++++ Problem15.py | 66 ++++++++ Problem16.py | 60 +++++++ Problem17.py | 173 +++++++++++++++++++++ Problem18.py | 139 +++++++++++++++++ Problem19.py | 162 +++++++++++++++++++ Problem2.py | 61 ++++++++ Problem20.py | 61 ++++++++ Problem21.py | 85 ++++++++++ Problem22.py | 432 +++++++++++++++++++++++++++++++++++++++++++++++++++ Problem23.py | 87 +++++++++++ Problem24.py | 53 +++++++ Problem25.py | 59 +++++++ Problem26.py | 84 ++++++++++ Problem27.py | 71 +++++++++ Problem28.py | 109 +++++++++++++ Problem29.py | 62 ++++++++ Problem3.py | 51 ++++++ Problem30.py | 76 +++++++++ Problem4.py | 63 ++++++++ Problem5.py | 69 ++++++++ Problem6.py | 56 +++++++ Problem67.py | 309 ++++++++++++++++++++++++++++++++++++ Problem7.py | 50 ++++++ Problem8.py | 85 ++++++++++ Problem9.py | 73 +++++++++ 33 files changed, 3430 insertions(+) create mode 100644 .gitignore create mode 100644 LICENSE create mode 100644 Problem1.py create mode 100644 Problem10.py create mode 100644 Problem11.py create mode 100644 Problem12.py create mode 100644 Problem13.py create mode 100644 Problem14.py create mode 100644 Problem15.py create mode 100644 Problem16.py create mode 100644 Problem17.py create mode 100644 Problem18.py create mode 100644 Problem19.py create mode 100644 Problem2.py create mode 100644 Problem20.py create mode 100644 Problem21.py create mode 100644 Problem22.py create mode 100644 Problem23.py create mode 100644 Problem24.py create mode 100644 Problem25.py create mode 100644 Problem26.py create mode 100644 Problem27.py create mode 100644 Problem28.py create mode 100644 Problem29.py create mode 100644 Problem3.py create mode 100644 Problem30.py create mode 100644 Problem4.py create mode 100644 Problem5.py create mode 100644 Problem6.py create mode 100644 Problem67.py create mode 100644 Problem7.py create mode 100644 Problem8.py create mode 100644 Problem9.py diff --git a/.gitignore b/.gitignore new file mode 100644 index 0000000..ca3b510 --- /dev/null +++ b/.gitignore @@ -0,0 +1,2 @@ +#Visual Studio Code +.vscode diff --git a/LICENSE b/LICENSE new file mode 100644 index 0000000..0a04128 --- /dev/null +++ b/LICENSE @@ -0,0 +1,165 @@ + GNU LESSER GENERAL PUBLIC LICENSE + Version 3, 29 June 2007 + + Copyright (C) 2007 Free Software Foundation, Inc. + Everyone is permitted to copy and distribute verbatim copies + of this license document, but changing it is not allowed. + + + This version of the GNU Lesser General Public License incorporates +the terms and conditions of version 3 of the GNU General Public +License, supplemented by the additional permissions listed below. + + 0. Additional Definitions. + + As used herein, "this License" refers to version 3 of the GNU Lesser +General Public License, and the "GNU GPL" refers to version 3 of the GNU +General Public License. + + "The Library" refers to a covered work governed by this License, +other than an Application or a Combined Work as defined below. + + An "Application" is any work that makes use of an interface provided +by the Library, but which is not otherwise based on the Library. +Defining a subclass of a class defined by the Library is deemed a mode +of using an interface provided by the Library. + + A "Combined Work" is a work produced by combining or linking an +Application with the Library. The particular version of the Library +with which the Combined Work was made is also called the "Linked +Version". + + The "Minimal Corresponding Source" for a Combined Work means the +Corresponding Source for the Combined Work, excluding any source code +for portions of the Combined Work that, considered in isolation, are +based on the Application, and not on the Linked Version. + + The "Corresponding Application Code" for a Combined Work means the +object code and/or source code for the Application, including any data +and utility programs needed for reproducing the Combined Work from the +Application, but excluding the System Libraries of the Combined Work. + + 1. Exception to Section 3 of the GNU GPL. + + You may convey a covered work under sections 3 and 4 of this License +without being bound by section 3 of the GNU GPL. + + 2. Conveying Modified Versions. + + If you modify a copy of the Library, and, in your modifications, a +facility refers to a function or data to be supplied by an Application +that uses the facility (other than as an argument passed when the +facility is invoked), then you may convey a copy of the modified +version: + + a) under this License, provided that you make a good faith effort to + ensure that, in the event an Application does not supply the + function or data, the facility still operates, and performs + whatever part of its purpose remains meaningful, or + + b) under the GNU GPL, with none of the additional permissions of + this License applicable to that copy. + + 3. Object Code Incorporating Material from Library Header Files. + + The object code form of an Application may incorporate material from +a header file that is part of the Library. You may convey such object +code under terms of your choice, provided that, if the incorporated +material is not limited to numerical parameters, data structure +layouts and accessors, or small macros, inline functions and templates +(ten or fewer lines in length), you do both of the following: + + a) Give prominent notice with each copy of the object code that the + Library is used in it and that the Library and its use are + covered by this License. + + b) Accompany the object code with a copy of the GNU GPL and this license + document. + + 4. Combined Works. + + You may convey a Combined Work under terms of your choice that, +taken together, effectively do not restrict modification of the +portions of the Library contained in the Combined Work and reverse +engineering for debugging such modifications, if you also do each of +the following: + + a) Give prominent notice with each copy of the Combined Work that + the Library is used in it and that the Library and its use are + covered by this License. + + b) Accompany the Combined Work with a copy of the GNU GPL and this license + document. + + c) For a Combined Work that displays copyright notices during + execution, include the copyright notice for the Library among + these notices, as well as a reference directing the user to the + copies of the GNU GPL and this license document. + + d) Do one of the following: + + 0) Convey the Minimal Corresponding Source under the terms of this + License, and the Corresponding Application Code in a form + suitable for, and under terms that permit, the user to + recombine or relink the Application with a modified version of + the Linked Version to produce a modified Combined Work, in the + manner specified by section 6 of the GNU GPL for conveying + Corresponding Source. + + 1) Use a suitable shared library mechanism for linking with the + Library. A suitable mechanism is one that (a) uses at run time + a copy of the Library already present on the user's computer + system, and (b) will operate properly with a modified version + of the Library that is interface-compatible with the Linked + Version. + + e) Provide Installation Information, but only if you would otherwise + be required to provide such information under section 6 of the + GNU GPL, and only to the extent that such information is + necessary to install and execute a modified version of the + Combined Work produced by recombining or relinking the + Application with a modified version of the Linked Version. (If + you use option 4d0, the Installation Information must accompany + the Minimal Corresponding Source and Corresponding Application + Code. If you use option 4d1, you must provide the Installation + Information in the manner specified by section 6 of the GNU GPL + for conveying Corresponding Source.) + + 5. Combined Libraries. + + You may place library facilities that are a work based on the +Library side by side in a single library together with other library +facilities that are not Applications and are not covered by this +License, and convey such a combined library under terms of your +choice, if you do both of the following: + + a) Accompany the combined library with a copy of the same work based + on the Library, uncombined with any other library facilities, + conveyed under the terms of this License. + + b) Give prominent notice with the combined library that part of it + is a work based on the Library, and explaining where to find the + accompanying uncombined form of the same work. + + 6. Revised Versions of the GNU Lesser General Public License. + + The Free Software Foundation may publish revised and/or new versions +of the GNU Lesser General Public License from time to time. Such new +versions will be similar in spirit to the present version, but may +differ in detail to address new problems or concerns. + + Each version is given a distinguishing version number. If the +Library as you received it specifies that a certain numbered version +of the GNU Lesser General Public License "or any later version" +applies to it, you have the option of following the terms and +conditions either of that published version or of any later version +published by the Free Software Foundation. If the Library as you +received it does not specify a version number of the GNU Lesser +General Public License, you may choose any version of the GNU Lesser +General Public License ever published by the Free Software Foundation. + + If the Library as you received it specifies that a proxy can decide +whether future versions of the GNU Lesser General Public License shall +apply, that proxy's public statement of acceptance of any version is +permanent authorization for you to choose that version for the +Library. diff --git a/Problem1.py b/Problem1.py new file mode 100644 index 0000000..7ad47e9 --- /dev/null +++ b/Problem1.py @@ -0,0 +1,58 @@ +#ProjectEuler/Python/Problem1.py +#Matthew Ellison +# Created: 01-26-19 +#Modified: 03-28-19 +#What is the sum of all the multiples of 3 or 5 that are less than 1000 +#Unless otherwise listed, all of my non-standard imports can be gotten from my pyClasses repository at https://bitbucket.org/Mattrixwv/pyClasses +""" + Copyright (C) 2019 Matthew Ellison + + This program is free software: you can redistribute it and/or modify + it under the terms of the GNU Lesser General Public License as published by + the Free Software Foundation, either version 3 of the License, or + (at your option) any later version. + + This program is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the + GNU Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public License + along with this program. If not, see . +""" + + +from Stopwatch import Stopwatch + + +def Problem1(): + #Setup your variables + fullSum = 0 #Holds the sum of all the correct numbers + + #Start at 3 and start counting up, checking if any of the numbers are divisible by 3 or 5 + #This method skips the problem of numbers that are divisible by both, like 15, being added twice + num = 3 + while(num < 1000): + if((num % 3) == 0): #3 Will be triggered more often, putting it first makes the algorithm more efficient + fullSum += num + elif((num % 5) == 0): + fullSum += num + num += 1 + + #Print the results + print("The sum of all the multiples of 3 or 5 is " + str(fullSum)) + + +#If you are running this file, automatically start the correct function +if(__name__ == "__main__"): + timer = Stopwatch() #Used to determine the algorithm's run time + timer.start() #Start the timer + Problem1() #Call the function that answers the problem + timer.stop() #Stop the timer + #Print the results of the timer + print("It took " + timer.getString() + " to run this algorithm") + +"""Results: +The sum of all the multiples of 3 or 5 is 233168 +It took 114.142 microseconds to run this algorithm +""" diff --git a/Problem10.py b/Problem10.py new file mode 100644 index 0000000..0e63a3b --- /dev/null +++ b/Problem10.py @@ -0,0 +1,53 @@ +#Project Euler/Python/Problem10.py +#Matthew Ellison +# Created: 01-30-19 +#Modified: 03-28-19 +#Find the sum of all the primes below two million +#Unless otherwise listed, all of my non-standard imports can be gotten from my pyClasses repository at https://bitbucket.org/Mattrixwv/pyClasses +""" + Copyright (C) 2019 Matthew Ellison + + This program is free software: you can redistribute it and/or modify + it under the terms of the GNU Lesser General Public License as published by + the Free Software Foundation, either version 3 of the License, or + (at your option) any later version. + + This program is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the + GNU Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public License + along with this program. If not, see . +""" + + +from Stopwatch import Stopwatch +from Algorithms import getPrimes + +__numberGreaterThanPrimes = 2000000 #Get all primes <= this number + + +def Problem10(): + #Get all of the primes < 2000000 + primes = getPrimes(__numberGreaterThanPrimes - 1) + + #Get the sum of the list + primeSum = sum(primes) + + #Print the results + print("The sum of all the prime numbers less than " + str(__numberGreaterThanPrimes) + " is " + str(primeSum)) + +#If you are running this file, automatically start the correct function +if __name__ == "__main__": + timer = Stopwatch() #Determines the algorithm's run time + timer.start() #Start the timer + Problem10() #Call the function that answers the question + timer.stop() #Stop the timer + #Print the results of the timer + print("It took " + timer.getString() + " to run this algorithm") + +"""Results: +The sum of all the prime numbers less than 2000000 is 142913828922 +It took 5.926 seconds to run this algorithm +""" diff --git a/Problem11.py b/Problem11.py new file mode 100644 index 0000000..5215ef1 --- /dev/null +++ b/Problem11.py @@ -0,0 +1,157 @@ +#ProjectEuler/Python/Problem11.py +#Matthew Ellison +# Created: 01-31-19 +#Modified: 03-28-19 +#What is the greatest product of four adjacent numbers in the same direction (up, down, left, right, or diagonally) in the 20×20 grid? +""" +08 02 22 97 38 15 00 40 00 75 04 05 07 78 52 12 50 77 91 08 +49 49 99 40 17 81 18 57 60 87 17 40 98 43 69 48 04 56 62 00 +81 49 31 73 55 79 14 29 93 71 40 67 53 88 30 03 49 13 36 65 +52 70 95 23 04 60 11 42 69 24 68 56 01 32 56 71 37 02 36 91 +22 31 16 71 51 67 63 89 41 92 36 54 22 40 40 28 66 33 13 80 +24 47 32 60 99 03 45 02 44 75 33 53 78 36 84 20 35 17 12 50 +32 98 81 28 64 23 67 10 26 38 40 67 59 54 70 66 18 38 64 70 +67 26 20 68 02 62 12 20 95 63 94 39 63 08 40 91 66 49 94 21 +24 55 58 05 66 73 99 26 97 17 78 78 96 83 14 88 34 89 63 72 +21 36 23 09 75 00 76 44 20 45 35 14 00 61 33 97 34 31 33 95 +78 17 53 28 22 75 31 67 15 94 03 80 04 62 16 14 09 53 56 92 +16 39 05 42 96 35 31 47 55 58 88 24 00 17 54 24 36 29 85 57 +86 56 00 48 35 71 89 07 05 44 44 37 44 60 21 58 51 54 17 58 +19 80 81 68 05 94 47 69 28 73 92 13 86 52 17 77 04 89 55 40 +04 52 08 83 97 35 99 16 07 97 57 32 16 26 26 79 33 27 98 66 +88 36 68 87 57 62 20 72 03 46 33 67 46 55 12 32 63 93 53 69 +04 42 16 73 38 25 39 11 24 94 72 18 08 46 29 32 40 62 76 36 +20 69 36 41 72 30 23 88 34 62 99 69 82 67 59 85 74 04 36 16 +20 73 35 29 78 31 90 01 74 31 49 71 48 86 81 16 23 57 05 54 +01 70 54 71 83 51 54 69 16 92 33 48 61 43 52 01 89 19 67 48 +""" +#Unless otherwise listed, all of my non-standard imports can be gotten from my pyClasses repository at https://bitbucket.org/Mattrixwv/pyClasses +""" + Copyright (C) 2019 Matthew Ellison + + This program is free software: you can redistribute it and/or modify + it under the terms of the GNU Lesser General Public License as published by + the Free Software Foundation, either version 3 of the License, or + (at your option) any later version. + + This program is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the + GNU Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public License + along with this program. If not, see . +""" + + +from Stopwatch import Stopwatch +from Algorithms import prod + +__grid = [[8, 2, 22, 97, 38, 15, 00, 40, 00, 75, 4, 5, 7, 78, 52, 12, 50, 77, 91, 8], + [49, 49, 99, 40, 17, 81, 18, 57, 60, 87, 17, 40, 98, 43, 69, 48, 4, 56, 62, 00], + [81, 49, 31, 73, 55, 79, 14, 29, 93, 71, 40, 67, 53, 88, 30, 3, 49, 13, 36, 65], + [52, 70, 95, 23, 4, 60, 11, 42, 69, 24, 68, 56, 1, 32, 56, 71, 37, 2, 36, 91], + [22, 31, 16, 71, 51, 67, 63, 89, 41, 92, 36, 54, 22, 40, 40, 28, 66, 33, 13, 80], + [24, 47, 32, 60, 99, 3, 45, 2, 44, 75, 33, 53, 78, 36, 84, 20, 35, 17, 12, 50], + [32, 98, 81, 28, 64, 23, 67, 10, 26, 38, 40, 67, 59, 54, 70, 66, 18, 38, 64, 70], + [67, 26, 20, 68, 2, 62, 12, 20, 95, 63, 94, 39, 63, 8, 40, 91, 66, 49, 94, 21], + [24, 55, 58, 5, 66, 73, 99, 26, 97, 17, 78, 78, 96, 83, 14, 88, 34, 89, 63, 72], + [21, 36, 23, 9, 75, 00, 76, 44, 20, 45, 35, 14, 00, 61, 33, 97, 34, 31, 33, 95], + [78, 17, 53, 28, 22, 75, 31, 67, 15, 94, 3, 80, 4, 62, 16, 14, 9, 53, 56, 92], + [16, 39, 5, 42, 96, 35, 31, 47, 55, 58, 88, 24, 00, 17, 54, 24, 36, 29, 85, 57], + [86, 56, 00, 48, 35, 71, 89, 7, 5, 44, 44, 37, 44, 60, 21, 58, 51, 54, 17, 58], + [19, 80, 81, 68, 5, 94, 47, 69, 28, 73, 92, 13, 86, 52, 17, 77, 4, 89, 55, 40], + [4, 52, 8, 83, 97, 35, 99, 16, 7, 97, 57, 32, 16, 26, 26, 79, 33, 27, 98, 66], + [88, 36, 68, 87, 57, 62, 20, 72, 3, 46, 33, 67, 46, 55, 12, 32, 63, 93, 53, 69], + [4, 42, 16, 73, 38, 25, 39, 11, 24, 94, 72, 18, 8, 46, 29, 32, 40, 62, 76, 36], + [20, 69, 36, 41, 72, 30, 23, 88, 34, 62, 99, 69, 82, 67, 59, 85, 74, 4, 36, 16], + [20, 73, 35, 29, 78, 31, 90, 1, 74, 31, 49, 71, 48, 86, 81, 16, 23, 57, 5, 54], + [1, 70, 54, 71, 83, 51, 54, 69, 16, 92, 33, 48, 61, 43, 52, 1, 89, 19, 67, 48]] + + +def Problem11(): + #Setup the variables + greatestNumbers = [0, 0, 0, 0] #Holds the numbers that give the greatest product + currentNumbers = [0, 0, 0, 0] #Holds the numbers that you are currently working with + row = 0 #Holds the row in the grid that you are currently working on + col = 0 #Holds the column in the grid that you are currently working on + + #Loop through every location in the grid + while(row < len(__grid)): #This loops through every row + col = 0 #Reset the column variable + while(col < len(__grid[row])): #This loops through every column + #Setup variables for knowing what direction you can move + moveLeft = False + moveRight = False + moveDown = False + + #Check which directions you will be able to move + if((col - 3) >= 0): + moveLeft = True + if((col + 3) < len(__grid[row])): + moveRight = True + if((row + 3) < 20): + moveDown = True + + #With these movements check for the greatest product of 4 adjacent numebrs + #Move Right + if moveRight: + currentNumbers[0] = __grid[row][col] + currentNumbers[1] = __grid[row][col + 1] + currentNumbers[2] = __grid[row][col + 2] + currentNumbers[3] = __grid[row][col + 3] + + if(prod(currentNumbers) > prod(greatestNumbers)): + greatestNumbers = currentNumbers.copy() + + #Move Down + if moveDown: + currentNumbers[0] = __grid[row][col] + currentNumbers[1] = __grid[row + 1][col] + currentNumbers[2] = __grid[row + 2][col] + currentNumbers[3] = __grid[row + 3][col] + + if(prod(currentNumbers) > prod(greatestNumbers)): + greatestNumbers = currentNumbers.copy() + + #Move Down & Left + if(moveDown and moveLeft): + currentNumbers[0] = __grid[row][col] + currentNumbers[1] = __grid[row + 1][col - 1] + currentNumbers[2] = __grid[row + 2][col - 2] + currentNumbers[3] = __grid[row + 3][col - 3] + + if(prod(currentNumbers) > prod(greatestNumbers)): + greatestNumbers = currentNumbers.copy() + + #Move Down & Right + if(moveDown and moveRight): + currentNumbers[0] = __grid[row][col] + currentNumbers[1] = __grid[row + 1][col + 1] + currentNumbers[2] = __grid[row + 2][col + 2] + currentNumbers[3] = __grid[row + 3][col + 3] + + if(prod(currentNumbers) > prod(greatestNumbers)): + greatestNumbers = currentNumbers.copy() + + #Move to the next column + col += 1 + #Move to the next row + row += 1 + + #Print the results + print("The greatest product of 3 numbers in a line is " + str(prod(greatestNumbers))) + +#If you are running this file, automatically start the correct function +if __name__ == "__main__": + timer = Stopwatch() #Determines the algorithm's run time + timer.start() #Start the timer + Problem11() #Call the function that answers the question + timer.stop() #Stop the timer + #Print the results of the timer + print("It took " + timer.getString() + " to run this algorithm") + +"""Results: +The greatest product of 3 numbers in a line is 70600674 +It took 1.162 milliseconds to run this algorithm +""" diff --git a/Problem12.py b/Problem12.py new file mode 100644 index 0000000..690b46e --- /dev/null +++ b/Problem12.py @@ -0,0 +1,66 @@ +#ProjectEuler/Python/Problem12.py +#Matthew Ellison +# Created: 01-31-19 +#Modified: 03-28-19 +#What is the value of the first triangle number to have over five hundred divisors? +#Unless otherwise listed, all of my non-standard imports can be gotten from my pyClasses repository at https://bitbucket.org/Mattrixwv/pyClasses +""" + Copyright (C) 2019 Matthew Ellison + + This program is free software: you can redistribute it and/or modify + it under the terms of the GNU Lesser General Public License as published by + the Free Software Foundation, either version 3 of the License, or + (at your option) any later version. + + This program is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the + GNU Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public License + along with this program. If not, see . +""" + + +from Stopwatch import Stopwatch +from Algorithms import getDivisors + +__goalDivisors = 500 #The number of divisors a number needs to reach + + +def Problem12(): + #Setup the variables + triangularNumber = 1 #Holds the triangular numbers + nextNumber = 2 #The next number to be added to the triangular number + foundNumber = False #A flag for when the triangular number has over __goalDivisors divisors + + #Start at the first triangular number and loop around, moving to the next, until you find one with the appropriate number of divisors + while((not foundNumber) and (triangularNumber > 0)): #Make sure you haven't caused an overflow and made trianularNumber negative + #See how many divisors this triangular number has + divisors = getDivisors(triangularNumber) + #If it did have enough raise a flag to stop the loop + if(len(divisors) > __goalDivisors): + foundNumber = True + else: + triangularNumber += nextNumber #Add the next number to continue the triangular sequence + nextNumber += 1 #Advance to the next number in the triangular sequence + + #Print the results + if(triangularNumber <= 0): + print("There was an error. Could not find a triangular number with " + str(__goalDivisors) + " divisors before overflow") + else: + print("The first triangular number with more than " + str(__goalDivisors) + " divisors is " + str(triangularNumber)) + +#If you are running this file, automatically start the correct function +if __name__ == "__main__": + timer = Stopwatch() #Determines the algorithm's run time + timer.start() #Start the timer + Problem12() #Call the function that answers the question + timer.stop() #Stop the timer + #Print the results of the timer + print("It took " + timer.getString() + " to run this algorithm") + +"""Results: +The first triangular number with more than 500 divisors is 76576500 +It took 2.898 seconds to run this algorithm +""" diff --git a/Problem13.py b/Problem13.py new file mode 100644 index 0000000..3ed91cf --- /dev/null +++ b/Problem13.py @@ -0,0 +1,253 @@ +#ProjectEuler/Python/Problem13.py +#Matthew Ellison +# Created: 01-31-19 +#Modified: 03-28-19 +#Work out the first ten digits of the sum of the following one-hundred 50-digit numbers +""" +37107287533902102798797998220837590246510135740250 +46376937677490009712648124896970078050417018260538 +74324986199524741059474233309513058123726617309629 +91942213363574161572522430563301811072406154908250 +23067588207539346171171980310421047513778063246676 +89261670696623633820136378418383684178734361726757 +28112879812849979408065481931592621691275889832738 +44274228917432520321923589422876796487670272189318 +47451445736001306439091167216856844588711603153276 +70386486105843025439939619828917593665686757934951 +62176457141856560629502157223196586755079324193331 +64906352462741904929101432445813822663347944758178 +92575867718337217661963751590579239728245598838407 +58203565325359399008402633568948830189458628227828 +80181199384826282014278194139940567587151170094390 +35398664372827112653829987240784473053190104293586 +86515506006295864861532075273371959191420517255829 +71693888707715466499115593487603532921714970056938 +54370070576826684624621495650076471787294438377604 +53282654108756828443191190634694037855217779295145 +36123272525000296071075082563815656710885258350721 +45876576172410976447339110607218265236877223636045 +17423706905851860660448207621209813287860733969412 +81142660418086830619328460811191061556940512689692 +51934325451728388641918047049293215058642563049483 +62467221648435076201727918039944693004732956340691 +15732444386908125794514089057706229429197107928209 +55037687525678773091862540744969844508330393682126 +18336384825330154686196124348767681297534375946515 +80386287592878490201521685554828717201219257766954 +78182833757993103614740356856449095527097864797581 +16726320100436897842553539920931837441497806860984 +48403098129077791799088218795327364475675590848030 +87086987551392711854517078544161852424320693150332 +59959406895756536782107074926966537676326235447210 +69793950679652694742597709739166693763042633987085 +41052684708299085211399427365734116182760315001271 +65378607361501080857009149939512557028198746004375 +35829035317434717326932123578154982629742552737307 +94953759765105305946966067683156574377167401875275 +88902802571733229619176668713819931811048770190271 +25267680276078003013678680992525463401061632866526 +36270218540497705585629946580636237993140746255962 +24074486908231174977792365466257246923322810917141 +91430288197103288597806669760892938638285025333403 +34413065578016127815921815005561868836468420090470 +23053081172816430487623791969842487255036638784583 +11487696932154902810424020138335124462181441773470 +63783299490636259666498587618221225225512486764533 +67720186971698544312419572409913959008952310058822 +95548255300263520781532296796249481641953868218774 +76085327132285723110424803456124867697064507995236 +37774242535411291684276865538926205024910326572967 +23701913275725675285653248258265463092207058596522 +29798860272258331913126375147341994889534765745501 +18495701454879288984856827726077713721403798879715 +38298203783031473527721580348144513491373226651381 +34829543829199918180278916522431027392251122869539 +40957953066405232632538044100059654939159879593635 +29746152185502371307642255121183693803580388584903 +41698116222072977186158236678424689157993532961922 +62467957194401269043877107275048102390895523597457 +23189706772547915061505504953922979530901129967519 +86188088225875314529584099251203829009407770775672 +11306739708304724483816533873502340845647058077308 +82959174767140363198008187129011875491310547126581 +97623331044818386269515456334926366572897563400500 +42846280183517070527831839425882145521227251250327 +55121603546981200581762165212827652751691296897789 +32238195734329339946437501907836945765883352399886 +75506164965184775180738168837861091527357929701337 +62177842752192623401942399639168044983993173312731 +32924185707147349566916674687634660915035914677504 +99518671430235219628894890102423325116913619626622 +73267460800591547471830798392868535206946944540724 +76841822524674417161514036427982273348055556214818 +97142617910342598647204516893989422179826088076852 +87783646182799346313767754307809363333018982642090 +10848802521674670883215120185883543223812876952786 +71329612474782464538636993009049310363619763878039 +62184073572399794223406235393808339651327408011116 +66627891981488087797941876876144230030984490851411 +60661826293682836764744779239180335110989069790714 +85786944089552990653640447425576083659976645795096 +66024396409905389607120198219976047599490197230297 +64913982680032973156037120041377903785566085089252 +16730939319872750275468906903707539413042652315011 +94809377245048795150954100921645863754710598436791 +78639167021187492431995700641917969777599028300699 +15368713711936614952811305876380278410754449733078 +40789923115535562561142322423255033685442488917353 +44889911501440648020369068063960672322193204149535 +41503128880339536053299340368006977710650566631954 +81234880673210146739058568557934581403627822703280 +82616570773948327592232845941706525094512325230608 +22918802058777319719839450180888072429661980811197 +77158542502016545090413245809786882778948721859617 +72107838435069186155435662884062257473692284509516 +20849603980134001723930671666823555245252804609722 +53503534226472524250874054075591789781264330331690 +""" +#Unless otherwise listed, all of my non-standard imports can be gotten from my pyClasses repository at https://bitbucket.org/Mattrixwv/pyClasses +""" + Copyright (C) 2019 Matthew Ellison + + This program is free software: you can redistribute it and/or modify + it under the terms of the GNU Lesser General Public License as published by + the Free Software Foundation, either version 3 of the License, or + (at your option) any later version. + + This program is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the + GNU Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public License + along with this program. If not, see . +""" + + +from Stopwatch import Stopwatch + +#The numbers that need to be summed +__numbers = [37107287533902102798797998220837590246510135740250, + 46376937677490009712648124896970078050417018260538, + 74324986199524741059474233309513058123726617309629, + 91942213363574161572522430563301811072406154908250, + 23067588207539346171171980310421047513778063246676, + 89261670696623633820136378418383684178734361726757, + 28112879812849979408065481931592621691275889832738, + 44274228917432520321923589422876796487670272189318, + 47451445736001306439091167216856844588711603153276, + 70386486105843025439939619828917593665686757934951, + 62176457141856560629502157223196586755079324193331, + 64906352462741904929101432445813822663347944758178, + 92575867718337217661963751590579239728245598838407, + 58203565325359399008402633568948830189458628227828, + 80181199384826282014278194139940567587151170094390, + 35398664372827112653829987240784473053190104293586, + 86515506006295864861532075273371959191420517255829, + 71693888707715466499115593487603532921714970056938, + 54370070576826684624621495650076471787294438377604, + 53282654108756828443191190634694037855217779295145, + 36123272525000296071075082563815656710885258350721, + 45876576172410976447339110607218265236877223636045, + 17423706905851860660448207621209813287860733969412, + 81142660418086830619328460811191061556940512689692, + 51934325451728388641918047049293215058642563049483, + 62467221648435076201727918039944693004732956340691, + 15732444386908125794514089057706229429197107928209, + 55037687525678773091862540744969844508330393682126, + 18336384825330154686196124348767681297534375946515, + 80386287592878490201521685554828717201219257766954, + 78182833757993103614740356856449095527097864797581, + 16726320100436897842553539920931837441497806860984, + 48403098129077791799088218795327364475675590848030, + 87086987551392711854517078544161852424320693150332, + 59959406895756536782107074926966537676326235447210, + 69793950679652694742597709739166693763042633987085, + 41052684708299085211399427365734116182760315001271, + 65378607361501080857009149939512557028198746004375, + 35829035317434717326932123578154982629742552737307, + 94953759765105305946966067683156574377167401875275, + 88902802571733229619176668713819931811048770190271, + 25267680276078003013678680992525463401061632866526, + 36270218540497705585629946580636237993140746255962, + 24074486908231174977792365466257246923322810917141, + 91430288197103288597806669760892938638285025333403, + 34413065578016127815921815005561868836468420090470, + 23053081172816430487623791969842487255036638784583, + 11487696932154902810424020138335124462181441773470, + 63783299490636259666498587618221225225512486764533, + 67720186971698544312419572409913959008952310058822, + 95548255300263520781532296796249481641953868218774, + 76085327132285723110424803456124867697064507995236, + 37774242535411291684276865538926205024910326572967, + 23701913275725675285653248258265463092207058596522, + 29798860272258331913126375147341994889534765745501, + 18495701454879288984856827726077713721403798879715, + 38298203783031473527721580348144513491373226651381, + 34829543829199918180278916522431027392251122869539, + 40957953066405232632538044100059654939159879593635, + 29746152185502371307642255121183693803580388584903, + 41698116222072977186158236678424689157993532961922, + 62467957194401269043877107275048102390895523597457, + 23189706772547915061505504953922979530901129967519, + 86188088225875314529584099251203829009407770775672, + 11306739708304724483816533873502340845647058077308, + 82959174767140363198008187129011875491310547126581, + 97623331044818386269515456334926366572897563400500, + 42846280183517070527831839425882145521227251250327, + 55121603546981200581762165212827652751691296897789, + 32238195734329339946437501907836945765883352399886, + 75506164965184775180738168837861091527357929701337, + 62177842752192623401942399639168044983993173312731, + 32924185707147349566916674687634660915035914677504, + 99518671430235219628894890102423325116913619626622, + 73267460800591547471830798392868535206946944540724, + 76841822524674417161514036427982273348055556214818, + 97142617910342598647204516893989422179826088076852, + 87783646182799346313767754307809363333018982642090, + 10848802521674670883215120185883543223812876952786, + 71329612474782464538636993009049310363619763878039, + 62184073572399794223406235393808339651327408011116, + 66627891981488087797941876876144230030984490851411, + 60661826293682836764744779239180335110989069790714, + 85786944089552990653640447425576083659976645795096, + 66024396409905389607120198219976047599490197230297, + 64913982680032973156037120041377903785566085089252, + 16730939319872750275468906903707539413042652315011, + 94809377245048795150954100921645863754710598436791, + 78639167021187492431995700641917969777599028300699, + 15368713711936614952811305876380278410754449733078, + 40789923115535562561142322423255033685442488917353, + 44889911501440648020369068063960672322193204149535, + 41503128880339536053299340368006977710650566631954, + 81234880673210146739058568557934581403627822703280, + 82616570773948327592232845941706525094512325230608, + 22918802058777319719839450180888072429661980811197, + 77158542502016545090413245809786882778948721859617, + 72107838435069186155435662884062257473692284509516, + 20849603980134001723930671666823555245252804609722, + 53503534226472524250874054075591789781264330331690] + + +def Problem13(): + #Get the sum of all of the numbers in the list + sumOfNums = sum(__numbers) + + #Print the results + print("The sum of all " + str(len(__numbers)) + " numbers is " + str(sumOfNums)) + print("The first 10 digits are: " + str(sumOfNums)[0:10]) + +#If you are running this file, automatically start the correct function +if __name__ == "__main__": + timer = Stopwatch() #Determines the algorithm's run time + timer.start() #Start the timer + Problem13() #Call the function that answers the question + timer.stop() #Stop the timer + #Print the results of the timer + print("It took " + timer.getString() + " to run this algorithm") + +"""Results: +The sum of all 100 numbers is 5537376230390876637302048746832985971773659831892672 +The first 10 digits are: 5537376230 +It took 23.015 microseconds to run this algorithm +""" diff --git a/Problem14.py b/Problem14.py new file mode 100644 index 0000000..1aa1ee4 --- /dev/null +++ b/Problem14.py @@ -0,0 +1,80 @@ +#ProjectEuler/Python/Problem14.py +#Matthew Ellison +# Created: 01-31-19 +#Modified: 03-28-19 +""" +The following iterative sequence is defined for the set of positive integers: +n → n/2 (n is even) +n → 3n + 1 (n is odd) +Which starting number, under one million, produces the longest chain? +""" +#Unless otherwise listed, all of my non-standard imports can be gotten from my pyClasses repository at https://bitbucket.org/Mattrixwv/pyClasses +""" + Copyright (C) 2019 Matthew Ellison + + This program is free software: you can redistribute it and/or modify + it under the terms of the GNU Lesser General Public License as published by + the Free Software Foundation, either version 3 of the License, or + (at your option) any later version. + + This program is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the + GNU Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public License + along with this program. If not, see . +""" + + +from Stopwatch import Stopwatch + +__topNum = 1000000 #The largest number that you will check against the chain + + +#This function returns a list of numbers created by the chain +def getChain(startNum: int) -> list: + #Put the starting number in the list + chain = [startNum] + + #Starting with the current number perform the correct opperations on the numbers until that number reaches 1 + while(startNum > 1): + #Determine if the number is odd or even and perform the correct operation and add the new number to the list + if((startNum % 2) == 0): + startNum /= 2 + else: + startNum = (3 * startNum) + 1 + #Add the new number to the chain + chain.append(startNum) + + #Return the list + return chain + +def Problem14(): + #Setup your variables + largestChain = [] #Holds the longest chain of numbers + + #Start at 1 and run up to 1000000, checking how long the chain is when started with each number + for startingNumber in range(1, __topNum): + currentChain = getChain(startingNumber) #Get the chain + #If the new chain is longer than the current longest chain replace it + if(len(currentChain) > len(largestChain)): + largestChain = currentChain.copy() + + #Print the results + print("The longest chain with a starting number < " + str(__topNum) + " is " + str(largestChain[0]) + " with a length of " + str(len(largestChain))) + + +#If you are running this file, automatically start the correct function +if __name__ == "__main__": + timer = Stopwatch() #Determines the algorithm's run time + timer.start() #Start the timer + Problem14() #Call the function that answers the question + timer.stop() #Stop the timer + #Print the results of the timer + print("It took " + timer.getString() + " to run this algorithm") + +"""Results: +The longest chain with a starting number < 1000000 is 837799 with a length of 525 +It took 28.893 seconds to run this algorithm +""" diff --git a/Problem15.py b/Problem15.py new file mode 100644 index 0000000..7ad650c --- /dev/null +++ b/Problem15.py @@ -0,0 +1,66 @@ +#ProjectEuler/Python/Problem15.py +#Matthew Ellison +# Created: 01-31-19 +#Modified: 03-28-19 +#How many routes from the top left corner to the bottom right corner are there through a 20×20 grid if you can only move right and down? +#Unless otherwise listed, all of my non-standard imports can be gotten from my pyClasses repository at https://bitbucket.org/Mattrixwv/pyClasses +#There must be a better way than this. This is untested. I let it run for about 14 hours and it still hadn't spit an answer out for me +#But it is programed exactly as I programmed the C++ solution, so the eventual answer should be correct +""" + Copyright (C) 2019 Matthew Ellison + + This program is free software: you can redistribute it and/or modify + it under the terms of the GNU Lesser General Public License as published by + the Free Software Foundation, either version 3 of the License, or + (at your option) any later version. + + This program is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the + GNU Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public License + along with this program. If not, see . +""" + + +from Stopwatch import Stopwatch + +__gridWidth = 20 #The height of the grid +__gridHeight = 20 #The width of the grid + + +def movement(currentX: int, currentY: int) -> int: + #Return 1 if you are at the finish location + if((currentX == __gridWidth) and (currentY == __gridHeight)): + return 1 + + numberMoves = 0 + #Otherwise move one right if you can and recurse + if(currentX < __gridWidth): + numberMoves = movement(currentX + 1, currentY) + + #Then move one down and recurse + if(currentY < __gridHeight): + numberMoves += movement(currentX, currentY + 1) + + return numberMoves + +def Problem15(): + #Start the recursion at the right location and catch what is returned + numberMoves = movement(0, 0) + #Print the results + print("The number of paths from 1 corner of a " + str(__gridWidth) + " x " + str(__gridHeight) + " grid to the opposite corner is " + str(numberMoves)) + +#If you are running this file, automatically start the correct function +if __name__ == "__main__": + timer = Stopwatch() #Determines the algorithm's run time + timer.start() #Start the timer + Problem15() #Call the function that answers the question + timer.stop() #Stop the timer + #Print the results of the timer + print("It took " + timer.getString() + " to run this algorithm") + +"""Results: + +""" diff --git a/Problem16.py b/Problem16.py new file mode 100644 index 0000000..428b37a --- /dev/null +++ b/Problem16.py @@ -0,0 +1,60 @@ +#Project Euler/Python/Problem16.py +#Matthew Ellison +# Created: 02-03-19 +#Modified: 03-28-19 +#What is the sum of the digits of the number 2^1000? +#Unless otherwise listed, all of my non-standard imports can be gotten from my pyClasses repository at https://bitbucket.org/Mattrixwv/pyClasses +""" + Copyright (C) 2019 Matthew Ellison + + This program is free software: you can redistribute it and/or modify + it under the terms of the GNU Lesser General Public License as published by + the Free Software Foundation, either version 3 of the License, or + (at your option) any later version. + + This program is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the + GNU Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public License + along with this program. If not, see . +""" + + +from Stopwatch import Stopwatch + + +def Problem16(): + #Setup the variables + sumOfNum = 0 #Holds the sum of the numbers + #Get the number + num = 2 ** 1000 + + #Change the number to a string + stringOfNum = str(num) + + #Step through the string one element at a time + for cnt in range(0, len(stringOfNum)): + #Change the character to an int and add it to the sum + sumOfNum += int(stringOfNum[cnt]) + + #Print the result + print("2^1000 = " + stringOfNum) + print("The sum of the digits is: " + str(sumOfNum)) + +#If you are running this file, automatically start the correct function +if __name__ == "__main__": + timer = Stopwatch() #Determines the algorithm's run time + timer.start() #Start the timer + Problem16() #Call the function that answers the question + timer.stop() #Stop the timer + #Print the results of the timer + print("It took " + timer.getString() + " to run this algorithm") + + +"""Results: +2^1000 = 10715086071862673209484250490600018105614048117055336074437503883703510511249361224931983788156958581275946729175531468251871452856923140435984577574698574803934567774824230985421074605062371141877954182153046474983581941267398767559165543946077062914571196477686542167660429831652624386837205668069376 +The sum of the digits is: 1366 +It took 86.206 microseconds to run this algorithm +""" diff --git a/Problem17.py b/Problem17.py new file mode 100644 index 0000000..a36dc10 --- /dev/null +++ b/Problem17.py @@ -0,0 +1,173 @@ +#ProjectEuler/Python/Problem17.py +#Matthew Ellison +# Created: 02-04-19 +#Modified: 03-28-19 +#If all the numbers from 1 to 1000 (one thousand) inclusive were written out in words, how many letters would be used? +#Unless otherwise listed, all of my non-standard imports can be gotten from my pyClasses repository at https://bitbucket.org/Mattrixwv/pyClasses +""" + Copyright (C) 2019 Matthew Ellison + + This program is free software: you can redistribute it and/or modify + it under the terms of the GNU Lesser General Public License as published by + the Free Software Foundation, either version 3 of the License, or + (at your option) any later version. + + This program is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the + GNU Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public License + along with this program. If not, see . +""" + + +from Stopwatch import Stopwatch +import math + +__startNum = 1 +__stopNum = 1000 + + +#This function only works for numbers -1,000,000 < num < 1,000,000 +def getStringFromNum(number: int) -> str: + numberString = "" + #Starting with the largest digit create a string based on the number passed in + #Check for negative + if(number < 0): + numberString += "negative " + + #Check if the number is zero + if(number == 0): + numberString += "zero" + + #Start with the thousands place + if((number / 1000) >= 1): + numberString += getStringFromNum(math.floor(number / 1000)) + numberString += " thousand" + number -= (math.floor(number / 1000) * 1000) + + #Check for hundreds place + if((number / 100) >= 1): + numberString += getStringFromNum(math.floor(number / 100)) + numberString += " hundred" + number -= (math.floor(number / 100) * 100) + + #Insert an and if there is need + if((numberString != "") and (number > 0)): + numberString += " and " + + #Check for tens place + if((number / 10) >= 2): + #For the tens you need to do something special + tensPlace = math.floor(number / 10) + if(tensPlace == 9): + numberString += "ninety" + elif(tensPlace == 8): + numberString += "eighty" + elif(tensPlace == 7): + numberString += "seventy" + elif(tensPlace == 6): + numberString += "sixty" + elif(tensPlace == 5): + numberString += "fifty" + elif(tensPlace == 4): + numberString += "forty" + elif(tensPlace == 3): + numberString += "thirty" + elif(tensPlace == 2): + numberString += "twenty" + number -= (tensPlace * 10) + #If there is something left in the number you will need a space to separate it + if(number > 0): + numberString += ' ' + #Check for teens + elif((number / 10) >= 1): + onesPlace = (number % 10) + if(onesPlace == 9): + numberString += "nineteen" + elif(onesPlace == 8): + numberString += "eighteen" + elif(onesPlace == 7): + numberString += "seventeen" + elif(onesPlace == 6): + numberString += "sixteen" + elif(onesPlace == 5): + numberString += "fifteen" + elif(onesPlace == 4): + numberString += "fourteen" + elif(onesPlace == 3): + numberString += "thirteen" + elif(onesPlace == 2): + numberString += "twelve" + elif(onesPlace == 1): + numberString += "eleven" + elif(onesPlace == 0): + numberString += "ten" + #If this if was hit number was used up + number = 0 + + #Check for ones place + if(number >= 1): + if(number == 9): + numberString += "nine" + elif(number == 8): + numberString += "eight" + elif(number == 7): + numberString += "seven" + elif(number == 6): + numberString += "six" + elif(number == 5): + numberString += "five" + elif(number == 4): + numberString += "four" + elif(number == 3): + numberString += "three" + elif(number == 2): + numberString += "two" + elif(number == 1): + numberString += "one" + #If this if was hit number was used up + number = 0 + + #Return the string + return numberString + + +def getNumberChars(number: str) -> int: + sumOfLetters = 0 + #Start at location 0 and count the number of letters, ignoring punctuation and whitespace + for location in range(0, len(number)): + tempString = number[location] + if(tempString.isalpha()): + sumOfLetters += 1 + + #Return the number + return sumOfLetters + + +def Problem17(): + sumOfLetters = 0 + #Start with 1 and increment + for num in range(__startNum, __stopNum + 1): + #Pass the number to a function that will create a string for the number + currentNumString = getStringFromNum(num) + #Pass the string to a function that will count the number of letters in a string, ignoring whitespace and punctuation and add the amount to the running tally + sumOfLetters += getNumberChars(currentNumString) + + #Print the results + print("The sum of all the letters in all the numbers " + str(__startNum) + '-' + str(__stopNum) + " is " + str(sumOfLetters)) + +#If you are running this file, automatically start the correct function +if __name__ == "__main__": + timer = Stopwatch() #Determines the algorithm's run time + timer.start() #Start the timer + Problem17() #Call the function that answers the question + timer.stop() #Stop the timer + #Print the results of the timer + print("It took " + timer.getString() + " to run this algorithm") + +"""Results: +The sum of all the letters in all the numbers 1-1000 is 21124 +It took 4.107 milliseconds to run this algorithm +""" diff --git a/Problem18.py b/Problem18.py new file mode 100644 index 0000000..0277097 --- /dev/null +++ b/Problem18.py @@ -0,0 +1,139 @@ +#ProjectEuler/Python/Problem18.py +#Matthew Ellison +# Created: 03-12-19 +#Modified: 03-28-19 +#Find the maximum total from top to bottom +""" +75 +95 64 +17 47 82 +18 35 87 10 +20 04 82 47 65 +19 01 23 75 03 34 +88 02 77 73 07 63 67 +99 65 04 28 06 16 70 92 +41 41 26 56 83 40 80 70 33 +41 48 72 33 47 32 37 16 94 29 +53 71 44 65 25 43 91 52 97 51 14 +70 11 33 28 77 73 17 78 39 68 17 57 +91 71 52 38 17 14 91 43 58 50 27 29 48 +63 66 04 68 89 53 67 30 73 16 69 87 40 31 +04 62 98 27 23 09 70 98 73 93 38 53 60 04 23 +""" +#Unless otherwise listed, all of my non-standard imports can be gotten from my pyClasses repository at https://bitbucket.org/Mattrixwv/pyClasses +""" + Copyright (C) 2019 Matthew Ellison + + This program is free software: you can redistribute it and/or modify + it under the terms of the GNU Lesser General Public License as published by + the Free Software Foundation, either version 3 of the License, or + (at your option) any later version. + + This program is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the + GNU Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public License + along with this program. If not, see . +""" + + +from Stopwatch import Stopwatch +from collections import namedtuple + + +location = namedtuple("location", "xLocation yLocation total fromRight") + +NUM_ROWS = 15 + + +def invert(listNum): + for rowCnt in range(0, NUM_ROWS): + for colCnt in range(0, len(listNum[rowCnt])): + listNum[rowCnt][colCnt] = 100 - listNum[rowCnt][colCnt] + +def removeIf(listNum: list, loc): + location = 0 + while(location < len(listNum)): + if((listNum[location].xLocation == loc.xLocation) and (listNum[location].yLocation == loc.yLocation)): + del listNum[location] + else: + location += 1 + +def Problem18(): + listNum = [[75], + [95, 64], + [17, 47, 82], + [18, 35, 87, 10], + [20, 4, 82, 47, 65], + [19, 1, 23, 75, 3, 34], + [88, 2, 77, 73, 7, 63, 67], + [99, 65, 4, 28, 6, 16, 70, 92], + [41, 41, 26, 56, 83, 40, 80, 70, 33], + [41, 48, 72, 33, 47, 32, 37, 16, 94, 29], + [53, 71, 44, 65, 25, 43, 91, 52, 97, 51, 14], + [70, 11, 33, 28, 77, 73, 17, 78, 39, 68, 17, 57], + [91, 71, 52, 38, 17, 14, 91, 43, 58, 50, 27, 29, 48], + [63, 66, 4, 68, 89, 53, 67, 30, 73, 16, 69, 87, 40, 31], + [ 4, 62, 98, 27, 23, 9, 70, 98, 73, 93, 38, 53, 60, 4, 23]] + + #Invert the list so that each element = 100 - element + invert(listNum) + + #Holds points we know are of the shortest route + foundPoints = [] + #Add the tip of the pyramid because everything has to go through that + foundPoints.append(location(0, 0, listNum[0][0], True)) + #Holds points that might be the shortest route + possiblePoints = [] + #Add the second row as possible points because everything must pass through the second row + possiblePoints.append(location(0, 1, (listNum[0][0] + listNum[1][0]), True)) + possiblePoints.append(location(1, 1, (listNum[0][0] + listNum[1][1]), False)) + foundBottom = False + + #Loop until you find the bottom + while(not foundBottom): + #Check which possible point gives us the lowest number. If more than one has the same number simply keep the first one + minLoc = possiblePoints[0] + for loc in possiblePoints: + if(loc.total < minLoc.total): + minLoc = loc + + #Remove it from the list of possible points + removeIf(possiblePoints, minLoc) + + foundPoints.append(minLoc) + + #Add to the list of possible points from the point we just found and + #If you are at the bottom raise the flag to end the program + xLoc = minLoc.xLocation + yLoc = minLoc.yLocation + 1 + if(yLoc >= NUM_ROWS): + foundBottom = True + else: + possiblePoints.append(location(xLoc, yLoc, minLoc.total + listNum[yLoc][xLoc], True)) + xLoc += 1 + possiblePoints.append(location(xLoc, yLoc, minLoc.total + listNum[yLoc][xLoc], False)) + + #Get the real total of the journey + actualTotal = ((100 * NUM_ROWS) - foundPoints[len(foundPoints) - 1].total) + + #Invert the list so it can be read again + invert(listNum) + + #Print the results + print("The value of the longest path is " + str(actualTotal)) + + +if __name__ == "__main__": + timer = Stopwatch() + timer.start() + Problem18() + timer.stop() + print("It took " + timer.getString() + " to run this algorithm") + +""" Results: +The value of the longest path is 1074 +It took 654.691 microseconds to run this algorithm +""" diff --git a/Problem19.py b/Problem19.py new file mode 100644 index 0000000..b977f8c --- /dev/null +++ b/Problem19.py @@ -0,0 +1,162 @@ +#ProjectEuler/Python/Problem19.py +#Matthew Ellison +# Created: 03-13-19 +#Modified: 03-28-19 +#How many Sundays fell on the first of the month during the twentieth century (1 Jan 1901 to 31 Dec 2000)? +""" +You are given the following information, but you may prefer to do some research for yourself. +1 Jan 1900 was a Monday. +Thirty days has September, +April, June and November. +All the rest have thirty-one, +Saving February alone, +Which has twenty-eight, rain or shine. +And on leap years, twenty-nine. +A leap year occurs on any year evenly divisible by 4, but not on a century unless it is divisible by 400. +""" +#Unless otherwise listed, all of my non-standard imports can be gotten from my pyClasses repository at https://bitbucket.org/Mattrixwv/pyClasses +""" + Copyright (C) 2019 Matthew Ellison + + This program is free software: you can redistribute it and/or modify + it under the terms of the GNU Lesser General Public License as published by + the Free Software Foundation, either version 3 of the License, or + (at your option) any later version. + + This program is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the + GNU Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public License + along with this program. If not, see . +""" + + +from Stopwatch import Stopwatch + + +class DAYS: + SUNDAY = 0 + MONDAY = 1 + TUESDAY = 2 + WEDNESDAY = 3 + THURSDAY = 4 + FRIDAY = 5 + SATURDAY = 6 + NUMBER_OF_DAYS = 7 + ERROR = 8 +START_YEAR = 1901 #The year we start counting sundays +END_YEAR = 2000 #The year we stop counting sundays + +#Return the day of the week that the date you pass into it is on +def getDay(month: int, day: int, year: int) -> DAYS: + #Make sure the numebrs are within propper bounds + if((month < 1) or (month > 12) or (day < 1) or (day > 31) or (year < 1)): + return DAYS.ERROR + + numDays = 0 #The number of days between 01-01-0001 and the date given + currentYear = 1 + currentMonth = 1 + currentDay = DAYS.SATURDAY + day -= 1 + + #Add the correct number of days for every year + while(currentYear < year): + if(isLeapYear(currentYear)): + numDays += 366 + else: + numDays += 365 + currentYear += 1 + #Add the correct number of days for eveyr month + while(currentMonth < month): + #February + if(currentMonth == 2): + if(isLeapYear(currentYear)): + numDays += 29 + else: + numDays += 28 + elif((currentMonth == 1) or (currentMonth == 3) or (currentMonth == 5) or (currentMonth == 7) or (currentMonth == 8) or (currentMonth == 10) or (currentMonth == 12)): + numDays += 31 + #For 30 day months + else: + numDays += 30 + currentMonth += 1 + #Account for the weird year of 1752 + if(year > 1752): + numDays -= 11 + elif(year == 1752): + if(month > 9): + numDays -= 11 + elif(month == 9): + if(day >= 14): + numDays -= 11 + #Days 3-13 were skipped that year + elif((day > 2) and (day < 14)): + return DAYS.ERROR + #Add the correct number of days for every day + numDays += day + + currentDay += numDays + currentDay = currentDay % DAYS.NUMBER_OF_DAYS + if(currentDay == DAYS.SUNDAY): + return DAYS.SUNDAY + elif(currentDay == DAYS.MONDAY): + return DAYS.MONDAY + elif(currentDay == DAYS.TUESDAY): + return DAYS.TUESDAY + elif(currentDay == DAYS.WEDNESDAY): + return DAYS.WEDNESDAY + elif(currentDay == DAYS.THURSDAY): + return DAYS.THURSDAY + elif(currentDay == DAYS.FRIDAY): + return DAYS.FRIDAY + elif(currentDay == DAYS.SATURDAY): + return DAYS.SATURDAY + else: + return DAYS.ERROR + +#Returns true if the year passed to it is a leap year +def isLeapYear(year: int) -> bool: + if(year < 1): + return False + elif((year % 100) == 0): + #This rule only applies at and after 1800 + if(year <= 1700): + return True + elif((year % 400) == 0): + return True + elif((year % 4) == 0): + return True + return False + +def Problem19(): + totalSundays = 0 #Keep track of the number of sundays + + #Run for all years from start to end + for year in range(START_YEAR, END_YEAR + 1): + #Run for all months in the year + for month in range(1, 13): + day = getDay(month, 1, year) + if(day == DAYS.ERROR): + print("There was an error with the day") + return + elif(day == DAYS.SUNDAY): + totalSundays += 1 + + #Print the results + print("There are " + str(totalSundays) + " Sundays that landed on the first of the month from " + str(START_YEAR) + " to " + str(END_YEAR)) + + +#Run automatically if the script was called stand alone +if __name__ == "__main__": + timer = Stopwatch() + timer.start() + Problem19() + timer.stop() + print("It took " + timer.getString() + " to run this algorithm") + +""" Results: +There are 171 Sundays that landed on the first of the month from 1901 to 2000 +It took 724.930 milliseconds to run this algorithm +""" diff --git a/Problem2.py b/Problem2.py new file mode 100644 index 0000000..e5302c9 --- /dev/null +++ b/Problem2.py @@ -0,0 +1,61 @@ +#ProjectEuler/Python/Problem2.py +#Matthew Ellison +# Created: 01-26-19 +#Modified: 03-28-19 +#The sum of the even Fibonacci numbers less than 4,000,000 +#Unless otherwise listed, all of my non-standard imports can be gotten from my pyClasses repository at https://bitbucket.org/Mattrixwv/pyClasses +""" + Copyright (C) 2019 Matthew Ellison + + This program is free software: you can redistribute it and/or modify + it under the terms of the GNU Lesser General Public License as published by + the Free Software Foundation, either version 3 of the License, or + (at your option) any later version. + + This program is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the + GNU Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public License + along with this program. If not, see . +""" + + +from Stopwatch import Stopwatch +from Algorithms import getAllFib + +__topNumber = 4000000 + + +def Problem2(): + #Setup your variables + fibSum = 0 #Holds the sum of the Fibonacci numbers + fibNums = [] #An array that holds the Fibonacci numbers + + #Get all of the fibonacci numbers + fibNums = getAllFib(__topNumber - 1) #Send it - 1 because it is < __topNumber + + #Determine if each number is odd or even + for num in fibNums: + #If it is even add it to the running sum + if((num % 2) == 0): + fibSum += num + + #Print the results + print("The sum of all even Fibonacci numbers less than " + str(__topNumber) + " is " + str(fibSum)) + + +#If you are running this file, automatically start the correct function +if __name__ == '__main__': + timer = Stopwatch() #Use to determine the algorithm's run time + timer.start() #Start the timer + Problem2() #Call the function that answers the question + timer.stop() #Stop the timer + #Print the results of the timer + print("It took " + timer.getString() + " to run this algorithm") + +"""Results: +The sum of all even Fibonacci numbers less than 4000000 is 4613732 +It took 27.621 microseconds to run this algorithm +""" diff --git a/Problem20.py b/Problem20.py new file mode 100644 index 0000000..556fb3a --- /dev/null +++ b/Problem20.py @@ -0,0 +1,61 @@ +#ProjectEuler/Python/Problem20.py +#Matthew Ellison +# Created: 03-14-19 +#Modified: 03-28-19 +#What is the sum of the digits of 100! +#Unless otherwise listed, all of my non-standard imports can be gotten from my pyClasses repository at https://bitbucket.org/Mattrixwv/pyClasses +""" + Copyright (C) 2019 Matthew Ellison + + This program is free software: you can redistribute it and/or modify + it under the terms of the GNU Lesser General Public License as published by + the Free Software Foundation, either version 3 of the License, or + (at your option) any later version. + + This program is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the + GNU Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public License + along with this program. If not, see . +""" + + +from Stopwatch import Stopwatch + +__TOP_NUM = 100 #The number that you are trying to find the factorial of + + +def Problem20(): + num = 1 #Holds the number being calculated + sumOfNum = 0 #Holds the sum of the digits of num + + #Run through every number from 1 to 100 and multiply it by the current num to get 100! + for cnt in range(1, __TOP_NUM + 1): + num *= cnt + + #Get a string of the number because it is easier to pull appart the individual charaters for the sum + numString = str(num) + #Run through every character in the string, convert it back to an integer and add it to the running sum + for char in numString: + sumOfNum += int(char) + + #Print the results + print("100! = " + numString) + print("The sum of the digits is: " + str(sumOfNum)) + + +#This starts the correct function if called directly +if __name__ == "__main__": + timer = Stopwatch() + timer.start() + Problem20() + timer.stop() + print("It took " + timer.getString() + " to run this algorithm") + +""" Results: +100! = 93326215443944152681699238856266700490715968264381621468592963895217599993229915608941463976156518286253697920827223758251185210916864000000000000000000000000 +The sum of the digits is: 648 +It took 99.670 microseconds to run this algorithm +""" diff --git a/Problem21.py b/Problem21.py new file mode 100644 index 0000000..f035572 --- /dev/null +++ b/Problem21.py @@ -0,0 +1,85 @@ +#ProjectEuler/Python/Problem21.py +#Matthew Ellison +# Created: 03-18-19 +#Modified: 03-28-19 +#Evaluate the sum of all the amicable numbers under 10000 +#Unless otherwise listed, all of my non-standard imports can be gotten from my pyClasses repository at https://bitbucket.org/Mattrixwv/pyClasses +""" + Copyright (C) 2019 Matthew Ellison + + This program is free software: you can redistribute it and/or modify + it under the terms of the GNU Lesser General Public License as published by + the Free Software Foundation, either version 3 of the License, or + (at your option) any later version. + + This program is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the + GNU Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public License + along with this program. If not, see . +""" + + +from Stopwatch import Stopwatch +import Algorithms + +__limit = 10000 #The top number that will be evaluated + + +def Problem21(): + #Setup the variables + divisorSum = [] #Holds the sum of the divisors of the subscript number + divisorSum.append(0) #Start with a 0 in the [0] location + + #Generate the divisors of all the numbers < 10000, get their sum, and add it to the list + for cnt in range(1, __limit): + divisors = Algorithms.getDivisors(cnt) #Get all the divisors of a number + if(len(divisors) > 1): + divisors.pop() #Remove the last entry because it will be the number itself + divisorSum.append(int(sum(divisors))) + #Check every sum of divisors in the list for a matching sum + amicable = [] + for cnt in range(1, len(divisorSum)): + currentSum = divisorSum[cnt] + #If the sum is greater than the number of divisors then it is impossible to be amicable. Skip the number and continue + if(currentSum >= len(divisorSum)): + continue + #We know that divisorSum[cnt] == currentSum, so if divisorSum[currentSum] == cnt we found an amicable number + if(divisorSum[currentSum] == cnt): + #A number can't be amicable with itself + if(currentSum == cnt): + continue + #Add the number to the amicable vector + amicable.append(cnt) + + #Print the results + print("All amicable numbers less than 10000 are") + for num in amicable: + print(str(num)) + print("The sum of all of these amicable numbers is " + str(sum(amicable))) + +#Run the correct function if this script is called stand along +if __name__ == "__main__": + timer = Stopwatch() + timer.start() + Problem21() + timer.stop() + print("It took " + timer.getString() + " to run this algorithm") + +""" Results: +All amicable numbers less than 10000 are +220 +284 +1184 +1210 +2620 +2924 +5020 +5564 +6232 +6368 +The sum of all of these amicable numbers is 31626 +It took 59.496 milliseconds to run this algorithm +""" diff --git a/Problem22.py b/Problem22.py new file mode 100644 index 0000000..bdbd468 --- /dev/null +++ b/Problem22.py @@ -0,0 +1,432 @@ +#ProjectEuler/Python/Problem22.py +#Matthew Ellison +# Created: 03-20-19 +#Modified: 03-28-19 +#What is the total of all the name scores in the file? +#Unless otherwise listed, all of my non-standard imports can be gotten from my pyClasses repository at https://bitbucket.org/Mattrixwv/pyClasses +""" + Copyright (C) 2019 Matthew Ellison + + This program is free software: you can redistribute it and/or modify + it under the terms of the GNU Lesser General Public License as published by + the Free Software Foundation, either version 3 of the License, or + (at your option) any later version. + + This program is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the + GNU Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public License + along with this program. If not, see . +""" + + +from Stopwatch import Stopwatch +import Algorithms + + +__NAMES = ["MARY","PATRICIA","LINDA","BARBARA","ELIZABETH","JENNIFER","MARIA","SUSAN","MARGARET","DOROTHY","LISA","NANCY","KAREN", + "BETTY","HELEN","SANDRA","DONNA","CAROL","RUTH","SHARON","MICHELLE","LAURA","SARAH","KIMBERLY","DEBORAH","JESSICA","SHIRLEY", + "CYNTHIA","ANGELA","MELISSA","BRENDA","AMY","ANNA","REBECCA","VIRGINIA","KATHLEEN","PAMELA","MARTHA","DEBRA","AMANDA","STEPHANIE", + "CAROLYN","CHRISTINE","MARIE","JANET","CATHERINE","FRANCES","ANN","JOYCE","DIANE","ALICE","JULIE","HEATHER","TERESA","DORIS", + "GLORIA","EVELYN","JEAN","CHERYL","MILDRED","KATHERINE","JOAN","ASHLEY","JUDITH","ROSE","JANICE","KELLY","NICOLE","JUDY", + "CHRISTINA","KATHY","THERESA","BEVERLY","DENISE","TAMMY","IRENE","JANE","LORI","RACHEL","MARILYN","ANDREA","KATHRYN","LOUISE", + "SARA","ANNE","JACQUELINE","WANDA","BONNIE","JULIA","RUBY","LOIS","TINA","PHYLLIS","NORMA","PAULA","DIANA","ANNIE","LILLIAN", + "EMILY","ROBIN","PEGGY","CRYSTAL","GLADYS","RITA","DAWN","CONNIE","FLORENCE","TRACY","EDNA","TIFFANY","CARMEN","ROSA","CINDY", + "GRACE","WENDY","VICTORIA","EDITH","KIM","SHERRY","SYLVIA","JOSEPHINE","THELMA","SHANNON","SHEILA","ETHEL","ELLEN","ELAINE", + "MARJORIE","CARRIE","CHARLOTTE","MONICA","ESTHER","PAULINE","EMMA","JUANITA","ANITA","RHONDA","HAZEL","AMBER","EVA","DEBBIE", + "APRIL","LESLIE","CLARA","LUCILLE","JAMIE","JOANNE","ELEANOR","VALERIE","DANIELLE","MEGAN","ALICIA","SUZANNE","MICHELE","GAIL", + "BERTHA","DARLENE","VERONICA","JILL","ERIN","GERALDINE","LAUREN","CATHY","JOANN","LORRAINE","LYNN","SALLY","REGINA","ERICA", + "BEATRICE","DOLORES","BERNICE","AUDREY","YVONNE","ANNETTE","JUNE","SAMANTHA","MARION","DANA","STACY","ANA","RENEE","IDA","VIVIAN", + "ROBERTA","HOLLY","BRITTANY","MELANIE","LORETTA","YOLANDA","JEANETTE","LAURIE","KATIE","KRISTEN","VANESSA","ALMA","SUE","ELSIE", + "BETH","JEANNE","VICKI","CARLA","TARA","ROSEMARY","EILEEN","TERRI","GERTRUDE","LUCY","TONYA","ELLA","STACEY","WILMA","GINA", + "KRISTIN","JESSIE","NATALIE","AGNES","VERA","WILLIE","CHARLENE","BESSIE","DELORES","MELINDA","PEARL","ARLENE","MAUREEN","COLLEEN", + "ALLISON","TAMARA","JOY","GEORGIA","CONSTANCE","LILLIE","CLAUDIA","JACKIE","MARCIA","TANYA","NELLIE","MINNIE","MARLENE","HEIDI", + "GLENDA","LYDIA","VIOLA","COURTNEY","MARIAN","STELLA","CAROLINE","DORA","JO","VICKIE","MATTIE","TERRY","MAXINE","IRMA","MABEL", + "MARSHA","MYRTLE","LENA","CHRISTY","DEANNA","PATSY","HILDA","GWENDOLYN","JENNIE","NORA","MARGIE","NINA","CASSANDRA","LEAH","PENNY", + "KAY","PRISCILLA","NAOMI","CAROLE","BRANDY","OLGA","BILLIE","DIANNE","TRACEY","LEONA","JENNY","FELICIA","SONIA","MIRIAM","VELMA", + "BECKY","BOBBIE","VIOLET","KRISTINA","TONI","MISTY","MAE","SHELLY","DAISY","RAMONA","SHERRI","ERIKA","KATRINA","CLAIRE","LINDSEY", + "LINDSAY","GENEVA","GUADALUPE","BELINDA","MARGARITA","SHERYL","CORA","FAYE","ADA","NATASHA","SABRINA","ISABEL","MARGUERITE", + "HATTIE","HARRIET","MOLLY","CECILIA","KRISTI","BRANDI","BLANCHE","SANDY","ROSIE","JOANNA","IRIS","EUNICE","ANGIE","INEZ","LYNDA", + "MADELINE","AMELIA","ALBERTA","GENEVIEVE","MONIQUE","JODI","JANIE","MAGGIE","KAYLA","SONYA","JAN","LEE","KRISTINE","CANDACE", + "FANNIE","MARYANN","OPAL","ALISON","YVETTE","MELODY","LUZ","SUSIE","OLIVIA","FLORA","SHELLEY","KRISTY","MAMIE","LULA","LOLA", + "VERNA","BEULAH","ANTOINETTE","CANDICE","JUANA","JEANNETTE","PAM","KELLI","HANNAH","WHITNEY","BRIDGET","KARLA","CELIA","LATOYA", + "PATTY","SHELIA","GAYLE","DELLA","VICKY","LYNNE","SHERI","MARIANNE","KARA","JACQUELYN","ERMA","BLANCA","MYRA","LETICIA","PAT", + "KRISTA","ROXANNE","ANGELICA","JOHNNIE","ROBYN","FRANCIS","ADRIENNE","ROSALIE","ALEXANDRA","BROOKE","BETHANY","SADIE","BERNADETTE", + "TRACI","JODY","KENDRA","JASMINE","NICHOLE","RACHAEL","CHELSEA","MABLE","ERNESTINE","MURIEL","MARCELLA","ELENA","KRYSTAL", + "ANGELINA","NADINE","KARI","ESTELLE","DIANNA","PAULETTE","LORA","MONA","DOREEN","ROSEMARIE","ANGEL","DESIREE","ANTONIA","HOPE", + "GINGER","JANIS","BETSY","CHRISTIE","FREDA","MERCEDES","MEREDITH","LYNETTE","TERI","CRISTINA","EULA","LEIGH","MEGHAN","SOPHIA", + "ELOISE","ROCHELLE","GRETCHEN","CECELIA","RAQUEL","HENRIETTA","ALYSSA","JANA","KELLEY","GWEN","KERRY","JENNA","TRICIA","LAVERNE", + "OLIVE","ALEXIS","TASHA","SILVIA","ELVIRA","CASEY","DELIA","SOPHIE","KATE","PATTI","LORENA","KELLIE","SONJA","LILA","LANA","DARLA", + "MAY","MINDY","ESSIE","MANDY","LORENE","ELSA","JOSEFINA","JEANNIE","MIRANDA","DIXIE","LUCIA","MARTA","FAITH","LELA","JOHANNA", + "SHARI","CAMILLE","TAMI","SHAWNA","ELISA","EBONY","MELBA","ORA","NETTIE","TABITHA","OLLIE","JAIME","WINIFRED","KRISTIE","MARINA", + "ALISHA","AIMEE","RENA","MYRNA","MARLA","TAMMIE","LATASHA","BONITA","PATRICE","RONDA","SHERRIE","ADDIE","FRANCINE","DELORIS", + "STACIE","ADRIANA","CHERI","SHELBY","ABIGAIL","CELESTE","JEWEL","CARA","ADELE","REBEKAH","LUCINDA","DORTHY","CHRIS","EFFIE", + "TRINA","REBA","SHAWN","SALLIE","AURORA","LENORA","ETTA","LOTTIE","KERRI","TRISHA","NIKKI","ESTELLA","FRANCISCA","JOSIE","TRACIE", + "MARISSA","KARIN","BRITTNEY","JANELLE","LOURDES","LAUREL","HELENE","FERN","ELVA","CORINNE","KELSEY","INA","BETTIE","ELISABETH", + "AIDA","CAITLIN","INGRID","IVA","EUGENIA","CHRISTA","GOLDIE","CASSIE","MAUDE","JENIFER","THERESE","FRANKIE","DENA","LORNA", + "JANETTE","LATONYA","CANDY","MORGAN","CONSUELO","TAMIKA","ROSETTA","DEBORA","CHERIE","POLLY","DINA","JEWELL","FAY","JILLIAN", + "DOROTHEA","NELL","TRUDY","ESPERANZA","PATRICA","KIMBERLEY","SHANNA","HELENA","CAROLINA","CLEO","STEFANIE","ROSARIO","OLA", + "JANINE","MOLLIE","LUPE","ALISA","LOU","MARIBEL","SUSANNE","BETTE","SUSANA","ELISE","CECILE","ISABELLE","LESLEY","JOCELYN", + "PAIGE","JONI","RACHELLE","LEOLA","DAPHNE","ALTA","ESTER","PETRA","GRACIELA","IMOGENE","JOLENE","KEISHA","LACEY","GLENNA", + "GABRIELA","KERI","URSULA","LIZZIE","KIRSTEN","SHANA","ADELINE","MAYRA","JAYNE","JACLYN","GRACIE","SONDRA","CARMELA","MARISA", + "ROSALIND","CHARITY","TONIA","BEATRIZ","MARISOL","CLARICE","JEANINE","SHEENA","ANGELINE","FRIEDA","LILY","ROBBIE","SHAUNA", + "MILLIE","CLAUDETTE","CATHLEEN","ANGELIA","GABRIELLE","AUTUMN","KATHARINE","SUMMER","JODIE","STACI","LEA","CHRISTI","JIMMIE", + "JUSTINE","ELMA","LUELLA","MARGRET","DOMINIQUE","SOCORRO","RENE","MARTINA","MARGO","MAVIS","CALLIE","BOBBI","MARITZA","LUCILE", + "LEANNE","JEANNINE","DEANA","AILEEN","LORIE","LADONNA","WILLA","MANUELA","GALE","SELMA","DOLLY","SYBIL","ABBY","LARA","DALE", + "IVY","DEE","WINNIE","MARCY","LUISA","JERI","MAGDALENA","OFELIA","MEAGAN","AUDRA","MATILDA","LEILA","CORNELIA","BIANCA","SIMONE", + "BETTYE","RANDI","VIRGIE","LATISHA","BARBRA","GEORGINA","ELIZA","LEANN","BRIDGETTE","RHODA","HALEY","ADELA","NOLA","BERNADINE", + "FLOSSIE","ILA","GRETA","RUTHIE","NELDA","MINERVA","LILLY","TERRIE","LETHA","HILARY","ESTELA","VALARIE","BRIANNA","ROSALYN", + "EARLINE","CATALINA","AVA","MIA","CLARISSA","LIDIA","CORRINE","ALEXANDRIA","CONCEPCION","TIA","SHARRON","RAE","DONA","ERICKA", + "JAMI","ELNORA","CHANDRA","LENORE","NEVA","MARYLOU","MELISA","TABATHA","SERENA","AVIS","ALLIE","SOFIA","JEANIE","ODESSA","NANNIE", + "HARRIETT","LORAINE","PENELOPE","MILAGROS","EMILIA","BENITA","ALLYSON","ASHLEE","TANIA","TOMMIE","ESMERALDA","KARINA","EVE", + "PEARLIE","ZELMA","MALINDA","NOREEN","TAMEKA","SAUNDRA","HILLARY","AMIE","ALTHEA","ROSALINDA","JORDAN","LILIA","ALANA","GAY", + "CLARE","ALEJANDRA","ELINOR","MICHAEL","LORRIE","JERRI","DARCY","EARNESTINE","CARMELLA","TAYLOR","NOEMI","MARCIE","LIZA", + "ANNABELLE","LOUISA","EARLENE","MALLORY","CARLENE","NITA","SELENA","TANISHA","KATY","JULIANNE","JOHN","LAKISHA","EDWINA", + "MARICELA","MARGERY","KENYA","DOLLIE","ROXIE","ROSLYN","KATHRINE","NANETTE","CHARMAINE","LAVONNE","ILENE","KRIS","TAMMI", + "SUZETTE","CORINE","KAYE","JERRY","MERLE","CHRYSTAL","LINA","DEANNE","LILIAN","JULIANA","ALINE","LUANN","KASEY","MARYANNE", + "EVANGELINE","COLETTE","MELVA","LAWANDA","YESENIA","NADIA","MADGE","KATHIE","EDDIE","OPHELIA","VALERIA","NONA","MITZI","MARI", + "GEORGETTE","CLAUDINE","FRAN","ALISSA","ROSEANN","LAKEISHA","SUSANNA","REVA","DEIDRE","CHASITY","SHEREE","CARLY","JAMES","ELVIA", + "ALYCE","DEIRDRE","GENA","BRIANA","ARACELI","KATELYN","ROSANNE","WENDI","TESSA","BERTA","MARVA","IMELDA","MARIETTA","MARCI", + "LEONOR","ARLINE","SASHA","MADELYN","JANNA","JULIETTE","DEENA","AURELIA","JOSEFA","AUGUSTA","LILIANA","YOUNG","CHRISTIAN", + "LESSIE","AMALIA","SAVANNAH","ANASTASIA","VILMA","NATALIA","ROSELLA","LYNNETTE","CORINA","ALFREDA","LEANNA","CAREY","AMPARO", + "COLEEN","TAMRA","AISHA","WILDA","KARYN","CHERRY","QUEEN","MAURA","MAI","EVANGELINA","ROSANNA","HALLIE","ERNA","ENID","MARIANA", + "LACY","JULIET","JACKLYN","FREIDA","MADELEINE","MARA","HESTER","CATHRYN","LELIA","CASANDRA","BRIDGETT","ANGELITA","JANNIE", + "DIONNE","ANNMARIE","KATINA","BERYL","PHOEBE","MILLICENT","KATHERYN","DIANN","CARISSA","MARYELLEN","LIZ","LAURI","HELGA","GILDA", + "ADRIAN","RHEA","MARQUITA","HOLLIE","TISHA","TAMERA","ANGELIQUE","FRANCESCA","BRITNEY","KAITLIN","LOLITA","FLORINE","ROWENA", + "REYNA","TWILA","FANNY","JANELL","INES","CONCETTA","BERTIE","ALBA","BRIGITTE","ALYSON","VONDA","PANSY","ELBA","NOELLE","LETITIA", + "KITTY","DEANN","BRANDIE","LOUELLA","LETA","FELECIA","SHARLENE","LESA","BEVERLEY","ROBERT","ISABELLA","HERMINIA","TERRA","CELINA", + "TORI","OCTAVIA","JADE","DENICE","GERMAINE","SIERRA","MICHELL","CORTNEY","NELLY","DORETHA","SYDNEY","DEIDRA","MONIKA","LASHONDA", + "JUDI","CHELSEY","ANTIONETTE","MARGOT","BOBBY","ADELAIDE","NAN","LEEANN","ELISHA","DESSIE","LIBBY","KATHI","GAYLA","LATANYA", + "MINA","MELLISA","KIMBERLEE","JASMIN","RENAE","ZELDA","ELDA","MA","JUSTINA","GUSSIE","EMILIE","CAMILLA","ABBIE","ROCIO","KAITLYN", + "JESSE","EDYTHE","ASHLEIGH","SELINA","LAKESHA","GERI","ALLENE","PAMALA","MICHAELA","DAYNA","CARYN","ROSALIA","SUN","JACQULINE", + "REBECA","MARYBETH","KRYSTLE","IOLA","DOTTIE","BENNIE","BELLE","AUBREY","GRISELDA","ERNESTINA","ELIDA","ADRIANNE","DEMETRIA", + "DELMA","CHONG","JAQUELINE","DESTINY","ARLEEN","VIRGINA","RETHA","FATIMA","TILLIE","ELEANORE","CARI","TREVA","BIRDIE","WILHELMINA", + "ROSALEE","MAURINE","LATRICE","YONG","JENA","TARYN","ELIA","DEBBY","MAUDIE","JEANNA","DELILAH","CATRINA","SHONDA","HORTENCIA", + "THEODORA","TERESITA","ROBBIN","DANETTE","MARYJANE","FREDDIE","DELPHINE","BRIANNE","NILDA","DANNA","CINDI","BESS","IONA","HANNA", + "ARIEL","WINONA","VIDA","ROSITA","MARIANNA","WILLIAM","RACHEAL","GUILLERMINA","ELOISA","CELESTINE","CAREN","MALISSA","LONA", + "CHANTEL","SHELLIE","MARISELA","LEORA","AGATHA","SOLEDAD","MIGDALIA","IVETTE","CHRISTEN","ATHENA","JANEL","CHLOE","VEDA","PATTIE", + "TESSIE","TERA","MARILYNN","LUCRETIA","KARRIE","DINAH","DANIELA","ALECIA","ADELINA","VERNICE","SHIELA","PORTIA","MERRY","LASHAWN", + "DEVON","DARA","TAWANA","OMA","VERDA","CHRISTIN","ALENE","ZELLA","SANDI","RAFAELA","MAYA","KIRA","CANDIDA","ALVINA","SUZAN", + "SHAYLA","LYN","LETTIE","ALVA","SAMATHA","ORALIA","MATILDE","MADONNA","LARISSA","VESTA","RENITA","INDIA","DELOIS","SHANDA", + "PHILLIS","LORRI","ERLINDA","CRUZ","CATHRINE","BARB","ZOE","ISABELL","IONE","GISELA","CHARLIE","VALENCIA","ROXANNA","MAYME", + "KISHA","ELLIE","MELLISSA","DORRIS","DALIA","BELLA","ANNETTA","ZOILA","RETA","REINA","LAURETTA","KYLIE","CHRISTAL","PILAR", + "CHARLA","ELISSA","TIFFANI","TANA","PAULINA","LEOTA","BREANNA","JAYME","CARMEL","VERNELL","TOMASA","MANDI","DOMINGA","SANTA", + "MELODIE","LURA","ALEXA","TAMELA","RYAN","MIRNA","KERRIE","VENUS","NOEL","FELICITA","CRISTY","CARMELITA","BERNIECE","ANNEMARIE", + "TIARA","ROSEANNE","MISSY","CORI","ROXANA","PRICILLA","KRISTAL","JUNG","ELYSE","HAYDEE","ALETHA","BETTINA","MARGE","GILLIAN", + "FILOMENA","CHARLES","ZENAIDA","HARRIETTE","CARIDAD","VADA","UNA","ARETHA","PEARLINE","MARJORY","MARCELA","FLOR","EVETTE", + "ELOUISE","ALINA","TRINIDAD","DAVID","DAMARIS","CATHARINE","CARROLL","BELVA","NAKIA","MARLENA","LUANNE","LORINE","KARON","DORENE", + "DANITA","BRENNA","TATIANA","SAMMIE","LOUANN","LOREN","JULIANNA","ANDRIA","PHILOMENA","LUCILA","LEONORA","DOVIE","ROMONA","MIMI", + "JACQUELIN","GAYE","TONJA","MISTI","JOE","GENE","CHASTITY","STACIA","ROXANN","MICAELA","NIKITA","MEI","VELDA","MARLYS","JOHNNA", + "AURA","LAVERN","IVONNE","HAYLEY","NICKI","MAJORIE","HERLINDA","GEORGE","ALPHA","YADIRA","PERLA","GREGORIA","DANIEL","ANTONETTE", + "SHELLI","MOZELLE","MARIAH","JOELLE","CORDELIA","JOSETTE","CHIQUITA","TRISTA","LOUIS","LAQUITA","GEORGIANA","CANDI","SHANON", + "LONNIE","HILDEGARD","CECIL","VALENTINA","STEPHANY","MAGDA","KAROL","GERRY","GABRIELLA","TIANA","ROMA","RICHELLE","RAY", + "PRINCESS","OLETA","JACQUE","IDELLA","ALAINA","SUZANNA","JOVITA","BLAIR","TOSHA","RAVEN","NEREIDA","MARLYN","KYLA","JOSEPH", + "DELFINA","TENA","STEPHENIE","SABINA","NATHALIE","MARCELLE","GERTIE","DARLEEN","THEA","SHARONDA","SHANTEL","BELEN","VENESSA", + "ROSALINA","ONA","GENOVEVA","COREY","CLEMENTINE","ROSALBA","RENATE","RENATA","MI","IVORY","GEORGIANNA","FLOY","DORCAS","ARIANA", + "TYRA","THEDA","MARIAM","JULI","JESICA","DONNIE","VIKKI","VERLA","ROSELYN","MELVINA","JANNETTE","GINNY","DEBRAH","CORRIE","ASIA", + "VIOLETA","MYRTIS","LATRICIA","COLLETTE","CHARLEEN","ANISSA","VIVIANA","TWYLA","PRECIOUS","NEDRA","LATONIA","LAN","HELLEN", + "FABIOLA","ANNAMARIE","ADELL","SHARYN","CHANTAL","NIKI","MAUD","LIZETTE","LINDY","KIA","KESHA","JEANA","DANELLE","CHARLINE", + "CHANEL","CARROL","VALORIE","LIA","DORTHA","CRISTAL","SUNNY","LEONE","LEILANI","GERRI","DEBI","ANDRA","KESHIA","IMA","EULALIA", + "EASTER","DULCE","NATIVIDAD","LINNIE","KAMI","GEORGIE","CATINA","BROOK","ALDA","WINNIFRED","SHARLA","RUTHANN","MEAGHAN", + "MAGDALENE","LISSETTE","ADELAIDA","VENITA","TRENA","SHIRLENE","SHAMEKA","ELIZEBETH","DIAN","SHANTA","MICKEY","LATOSHA","CARLOTTA", + "WINDY","SOON","ROSINA","MARIANN","LEISA","JONNIE","DAWNA","CATHIE","BILLY","ASTRID","SIDNEY","LAUREEN","JANEEN","HOLLI","FAWN", + "VICKEY","TERESSA","SHANTE","RUBYE","MARCELINA","CHANDA","CARY","TERESE","SCARLETT","MARTY","MARNIE","LULU","LISETTE","JENIFFER", + "ELENOR","DORINDA","DONITA","CARMAN","BERNITA","ALTAGRACIA","ALETA","ADRIANNA","ZORAIDA","RONNIE","NICOLA","LYNDSEY","KENDALL", + "JANINA","CHRISSY","AMI","STARLA","PHYLIS","PHUONG","KYRA","CHARISSE","BLANCH","SANJUANITA","RONA","NANCI","MARILEE","MARANDA", + "CORY","BRIGETTE","SANJUANA","MARITA","KASSANDRA","JOYCELYN","IRA","FELIPA","CHELSIE","BONNY","MIREYA","LORENZA","KYONG","ILEANA", + "CANDELARIA","TONY","TOBY","SHERIE","OK","MARK","LUCIE","LEATRICE","LAKESHIA","GERDA","EDIE","BAMBI","MARYLIN","LAVON","HORTENSE", + "GARNET","EVIE","TRESSA","SHAYNA","LAVINA","KYUNG","JEANETTA","SHERRILL","SHARA","PHYLISS","MITTIE","ANABEL","ALESIA","THUY", + "TAWANDA","RICHARD","JOANIE","TIFFANIE","LASHANDA","KARISSA","ENRIQUETA","DARIA","DANIELLA","CORINNA","ALANNA","ABBEY","ROXANE", + "ROSEANNA","MAGNOLIA","LIDA","KYLE","JOELLEN","ERA","CORAL","CARLEEN","TRESA","PEGGIE","NOVELLA","NILA","MAYBELLE","JENELLE", + "CARINA","NOVA","MELINA","MARQUERITE","MARGARETTE","JOSEPHINA","EVONNE","DEVIN","CINTHIA","ALBINA","TOYA","TAWNYA","SHERITA", + "SANTOS","MYRIAM","LIZABETH","LISE","KEELY","JENNI","GISELLE","CHERYLE","ARDITH","ARDIS","ALESHA","ADRIANE","SHAINA","LINNEA", + "KAROLYN","HONG","FLORIDA","FELISHA","DORI","DARCI","ARTIE","ARMIDA","ZOLA","XIOMARA","VERGIE","SHAMIKA","NENA","NANNETTE","MAXIE", + "LOVIE","JEANE","JAIMIE","INGE","FARRAH","ELAINA","CAITLYN","STARR","FELICITAS","CHERLY","CARYL","YOLONDA","YASMIN","TEENA", + "PRUDENCE","PENNIE","NYDIA","MACKENZIE","ORPHA","MARVEL","LIZBETH","LAURETTE","JERRIE","HERMELINDA","CAROLEE","TIERRA","MIRIAN", + "META","MELONY","KORI","JENNETTE","JAMILA","ENA","ANH","YOSHIKO","SUSANNAH","SALINA","RHIANNON","JOLEEN","CRISTINE","ASHTON", + "ARACELY","TOMEKA","SHALONDA","MARTI","LACIE","KALA","JADA","ILSE","HAILEY","BRITTANI","ZONA","SYBLE","SHERRYL","RANDY","NIDIA", + "MARLO","KANDICE","KANDI","DEB","DEAN","AMERICA","ALYCIA","TOMMY","RONNA","NORENE","MERCY","JOSE","INGEBORG","GIOVANNA","GEMMA", + "CHRISTEL","AUDRY","ZORA","VITA","VAN","TRISH","STEPHAINE","SHIRLEE","SHANIKA","MELONIE","MAZIE","JAZMIN","INGA","HOA","HETTIE", + "GERALYN","FONDA","ESTRELLA","ADELLA","SU","SARITA","RINA","MILISSA","MARIBETH","GOLDA","EVON","ETHELYN","ENEDINA","CHERISE", + "CHANA","VELVA","TAWANNA","SADE","MIRTA","LI","KARIE","JACINTA","ELNA","DAVINA","CIERRA","ASHLIE","ALBERTHA","TANESHA","STEPHANI", + "NELLE","MINDI","LU","LORINDA","LARUE","FLORENE","DEMETRA","DEDRA","CIARA","CHANTELLE","ASHLY","SUZY","ROSALVA","NOELIA","LYDA", + "LEATHA","KRYSTYNA","KRISTAN","KARRI","DARLINE","DARCIE","CINDA","CHEYENNE","CHERRIE","AWILDA","ALMEDA","ROLANDA","LANETTE", + "JERILYN","GISELE","EVALYN","CYNDI","CLETA","CARIN","ZINA","ZENA","VELIA","TANIKA","PAUL","CHARISSA","THOMAS","TALIA","MARGARETE", + "LAVONDA","KAYLEE","KATHLENE","JONNA","IRENA","ILONA","IDALIA","CANDIS","CANDANCE","BRANDEE","ANITRA","ALIDA","SIGRID","NICOLETTE", + "MARYJO","LINETTE","HEDWIG","CHRISTIANA","CASSIDY","ALEXIA","TRESSIE","MODESTA","LUPITA","LITA","GLADIS","EVELIA","DAVIDA", + "CHERRI","CECILY","ASHELY","ANNABEL","AGUSTINA","WANITA","SHIRLY","ROSAURA","HULDA","EUN","BAILEY","YETTA","VERONA","THOMASINA", + "SIBYL","SHANNAN","MECHELLE","LUE","LEANDRA","LANI","KYLEE","KANDY","JOLYNN","FERNE","EBONI","CORENE","ALYSIA","ZULA","NADA", + "MOIRA","LYNDSAY","LORRETTA","JUAN","JAMMIE","HORTENSIA","GAYNELL","CAMERON","ADRIA","VINA","VICENTA","TANGELA","STEPHINE", + "NORINE","NELLA","LIANA","LESLEE","KIMBERELY","ILIANA","GLORY","FELICA","EMOGENE","ELFRIEDE","EDEN","EARTHA","CARMA","BEA","OCIE", + "MARRY","LENNIE","KIARA","JACALYN","CARLOTA","ARIELLE","YU","STAR","OTILIA","KIRSTIN","KACEY","JOHNETTA","JOEY","JOETTA", + "JERALDINE","JAUNITA","ELANA","DORTHEA","CAMI","AMADA","ADELIA","VERNITA","TAMAR","SIOBHAN","RENEA","RASHIDA","OUIDA","ODELL", + "NILSA","MERYL","KRISTYN","JULIETA","DANICA","BREANNE","AUREA","ANGLEA","SHERRON","ODETTE","MALIA","LORELEI","LIN","LEESA", + "KENNA","KATHLYN","FIONA","CHARLETTE","SUZIE","SHANTELL","SABRA","RACQUEL","MYONG","MIRA","MARTINE","LUCIENNE","LAVADA","JULIANN", + "JOHNIE","ELVERA","DELPHIA","CLAIR","CHRISTIANE","CHAROLETTE","CARRI","AUGUSTINE","ASHA","ANGELLA","PAOLA","NINFA","LEDA","LAI", + "EDA","SUNSHINE","STEFANI","SHANELL","PALMA","MACHELLE","LISSA","KECIA","KATHRYNE","KARLENE","JULISSA","JETTIE","JENNIFFER","HUI", + "CORRINA","CHRISTOPHER","CAROLANN","ALENA","TESS","ROSARIA","MYRTICE","MARYLEE","LIANE","KENYATTA","JUDIE","JANEY","IN","ELMIRA", + "ELDORA","DENNA","CRISTI","CATHI","ZAIDA","VONNIE","VIVA","VERNIE","ROSALINE","MARIELA","LUCIANA","LESLI","KARAN","FELICE", + "DENEEN","ADINA","WYNONA","TARSHA","SHERON","SHASTA","SHANITA","SHANI","SHANDRA","RANDA","PINKIE","PARIS","NELIDA","MARILOU", + "LYLA","LAURENE","LACI","JOI","JANENE","DOROTHA","DANIELE","DANI","CAROLYNN","CARLYN","BERENICE","AYESHA","ANNELIESE","ALETHEA", + "THERSA","TAMIKO","RUFINA","OLIVA","MOZELL","MARYLYN","MADISON","KRISTIAN","KATHYRN","KASANDRA","KANDACE","JANAE","GABRIEL", + "DOMENICA","DEBBRA","DANNIELLE","CHUN","BUFFY","BARBIE","ARCELIA","AJA","ZENOBIA","SHAREN","SHAREE","PATRICK","PAGE","MY", + "LAVINIA","KUM","KACIE","JACKELINE","HUONG","FELISA","EMELIA","ELEANORA","CYTHIA","CRISTIN","CLYDE","CLARIBEL","CARON", + "ANASTACIA","ZULMA","ZANDRA","YOKO","TENISHA","SUSANN","SHERILYN","SHAY","SHAWANDA","SABINE","ROMANA","MATHILDA","LINSEY", + "KEIKO","JOANA","ISELA","GRETTA","GEORGETTA","EUGENIE","DUSTY","DESIRAE","DELORA","CORAZON","ANTONINA","ANIKA","WILLENE","TRACEE", + "TAMATHA","REGAN","NICHELLE","MICKIE","MAEGAN","LUANA","LANITA","KELSIE","EDELMIRA","BREE","AFTON","TEODORA","TAMIE","SHENA", + "MEG","LINH","KELI","KACI","DANYELLE","BRITT","ARLETTE","ALBERTINE","ADELLE","TIFFINY","STORMY","SIMONA","NUMBERS","NICOLASA", + "NICHOL","NIA","NAKISHA","MEE","MAIRA","LOREEN","KIZZY","JOHNNY","JAY","FALLON","CHRISTENE","BOBBYE","ANTHONY","YING","VINCENZA", + "TANJA","RUBIE","RONI","QUEENIE","MARGARETT","KIMBERLI","IRMGARD","IDELL","HILMA","EVELINA","ESTA","EMILEE","DENNISE","DANIA", + "CARL","CARIE","ANTONIO","WAI","SANG","RISA","RIKKI","PARTICIA","MUI","MASAKO","MARIO","LUVENIA","LOREE","LONI","LIEN","KEVIN", + "GIGI","FLORENCIA","DORIAN","DENITA","DALLAS","CHI","BILLYE","ALEXANDER","TOMIKA","SHARITA","RANA","NIKOLE","NEOMA","MARGARITE", + "MADALYN","LUCINA","LAILA","KALI","JENETTE","GABRIELE","EVELYNE","ELENORA","CLEMENTINA","ALEJANDRINA","ZULEMA","VIOLETTE", + "VANNESSA","THRESA","RETTA","PIA","PATIENCE","NOELLA","NICKIE","JONELL","DELTA","CHUNG","CHAYA","CAMELIA","BETHEL","ANYA", + "ANDREW","THANH","SUZANN","SPRING","SHU","MILA","LILLA","LAVERNA","KEESHA","KATTIE","GIA","GEORGENE","EVELINE","ESTELL","ELIZBETH", + "VIVIENNE","VALLIE","TRUDIE","STEPHANE","MICHEL","MAGALY","MADIE","KENYETTA","KARREN","JANETTA","HERMINE","HARMONY","DRUCILLA", + "DEBBI","CELESTINA","CANDIE","BRITNI","BECKIE","AMINA","ZITA","YUN","YOLANDE","VIVIEN","VERNETTA","TRUDI","SOMMER","PEARLE", + "PATRINA","OSSIE","NICOLLE","LOYCE","LETTY","LARISA","KATHARINA","JOSELYN","JONELLE","JENELL","IESHA","HEIDE","FLORINDA", + "FLORENTINA","FLO","ELODIA","DORINE","BRUNILDA","BRIGID","ASHLI","ARDELLA","TWANA","THU","TARAH","SUNG","SHEA","SHAVON","SHANE", + "SERINA","RAYNA","RAMONITA","NGA","MARGURITE","LUCRECIA","KOURTNEY","KATI","JESUS","JESENIA","DIAMOND","CRISTA","AYANA","ALICA", + "ALIA","VINNIE","SUELLEN","ROMELIA","RACHELL","PIPER","OLYMPIA","MICHIKO","KATHALEEN","JOLIE","JESSI","JANESSA","HANA","HA", + "ELEASE","CARLETTA","BRITANY","SHONA","SALOME","ROSAMOND","REGENA","RAINA","NGOC","NELIA","LOUVENIA","LESIA","LATRINA","LATICIA", + "LARHONDA","JINA","JACKI","HOLLIS","HOLLEY","EMMY","DEEANN","CORETTA","ARNETTA","VELVET","THALIA","SHANICE","NETA","MIKKI","MICKI", + "LONNA","LEANA","LASHUNDA","KILEY","JOYE","JACQULYN","IGNACIA","HYUN","HIROKO","HENRY","HENRIETTE","ELAYNE","DELINDA","DARNELL", + "DAHLIA","COREEN","CONSUELA","CONCHITA","CELINE","BABETTE","AYANNA","ANETTE","ALBERTINA","SKYE","SHAWNEE","SHANEKA","QUIANA", + "PAMELIA","MIN","MERRI","MERLENE","MARGIT","KIESHA","KIERA","KAYLENE","JODEE","JENISE","ERLENE","EMMIE","ELSE","DARYL","DALILA", + "DAISEY","CODY","CASIE","BELIA","BABARA","VERSIE","VANESA","SHELBA","SHAWNDA","SAM","NORMAN","NIKIA","NAOMA","MARNA","MARGERET", + "MADALINE","LAWANA","KINDRA","JUTTA","JAZMINE","JANETT","HANNELORE","GLENDORA","GERTRUD","GARNETT","FREEDA","FREDERICA","FLORANCE", + "FLAVIA","DENNIS","CARLINE","BEVERLEE","ANJANETTE","VALDA","TRINITY","TAMALA","STEVIE","SHONNA","SHA","SARINA","ONEIDA","MICAH", + "MERILYN","MARLEEN","LURLINE","LENNA","KATHERIN","JIN","JENI","HAE","GRACIA","GLADY","FARAH","ERIC","ENOLA","EMA","DOMINQUE", + "DEVONA","DELANA","CECILA","CAPRICE","ALYSHA","ALI","ALETHIA","VENA","THERESIA","TAWNY","SONG","SHAKIRA","SAMARA","SACHIKO", + "RACHELE","PAMELLA","NICKY","MARNI","MARIEL","MAREN","MALISA","LIGIA","LERA","LATORIA","LARAE","KIMBER","KATHERN","KAREY", + "JENNEFER","JANETH","HALINA","FREDIA","DELISA","DEBROAH","CIERA","CHIN","ANGELIKA","ANDREE","ALTHA","YEN","VIVAN","TERRESA", + "TANNA","SUK","SUDIE","SOO","SIGNE","SALENA","RONNI","REBBECCA","MYRTIE","MCKENZIE","MALIKA","MAIDA","LOAN","LEONARDA","KAYLEIGH", + "FRANCE","ETHYL","ELLYN","DAYLE","CAMMIE","BRITTNI","BIRGIT","AVELINA","ASUNCION","ARIANNA","AKIKO","VENICE","TYESHA","TONIE", + "TIESHA","TAKISHA","STEFFANIE","SINDY","SANTANA","MEGHANN","MANDA","MACIE","LADY","KELLYE","KELLEE","JOSLYN","JASON","INGER", + "INDIRA","GLINDA","GLENNIS","FERNANDA","FAUSTINA","ENEIDA","ELICIA","DOT","DIGNA","DELL","ARLETTA","ANDRE","WILLIA","TAMMARA", + "TABETHA","SHERRELL","SARI","REFUGIO","REBBECA","PAULETTA","NIEVES","NATOSHA","NAKITA","MAMMIE","KENISHA","KAZUKO","KASSIE", + "GARY","EARLEAN","DAPHINE","CORLISS","CLOTILDE","CAROLYNE","BERNETTA","AUGUSTINA","AUDREA","ANNIS","ANNABELL","YAN","TENNILLE", + "TAMICA","SELENE","SEAN","ROSANA","REGENIA","QIANA","MARKITA","MACY","LEEANNE","LAURINE","KYM","JESSENIA","JANITA","GEORGINE", + "GENIE","EMIKO","ELVIE","DEANDRA","DAGMAR","CORIE","COLLEN","CHERISH","ROMAINE","PORSHA","PEARLENE","MICHELINE","MERNA","MARGORIE", + "MARGARETTA","LORE","KENNETH","JENINE","HERMINA","FREDERICKA","ELKE","DRUSILLA","DORATHY","DIONE","DESIRE","CELENA","BRIGIDA", + "ANGELES","ALLEGRA","THEO","TAMEKIA","SYNTHIA","STEPHEN","SOOK","SLYVIA","ROSANN","REATHA","RAYE","MARQUETTA","MARGART","LING", + "LAYLA","KYMBERLY","KIANA","KAYLEEN","KATLYN","KARMEN","JOELLA","IRINA","EMELDA","ELENI","DETRA","CLEMMIE","CHERYLL","CHANTELL", + "CATHEY","ARNITA","ARLA","ANGLE","ANGELIC","ALYSE","ZOFIA","THOMASINE","TENNIE","SON","SHERLY","SHERLEY","SHARYL","REMEDIOS", + "PETRINA","NICKOLE","MYUNG","MYRLE","MOZELLA","LOUANNE","LISHA","LATIA","LANE","KRYSTA","JULIENNE","JOEL","JEANENE","JACQUALINE", + "ISAURA","GWENDA","EARLEEN","DONALD","CLEOPATRA","CARLIE","AUDIE","ANTONIETTA","ALISE","ALEX","VERDELL","VAL","TYLER","TOMOKO", + "THAO","TALISHA","STEVEN","SO","SHEMIKA","SHAUN","SCARLET","SAVANNA","SANTINA","ROSIA","RAEANN","ODILIA","NANA","MINNA","MAGAN", + "LYNELLE","LE","KARMA","JOEANN","IVANA","INELL","ILANA","HYE","HONEY","HEE","GUDRUN","FRANK","DREAMA","CRISSY","CHANTE", + "CARMELINA","ARVILLA","ARTHUR","ANNAMAE","ALVERA","ALEIDA","AARON","YEE","YANIRA","VANDA","TIANNA","TAM","STEFANIA","SHIRA", + "PERRY","NICOL","NANCIE","MONSERRATE","MINH","MELYNDA","MELANY","MATTHEW","LOVELLA","LAURE","KIRBY","KACY","JACQUELYNN","HYON", + "GERTHA","FRANCISCO","ELIANA","CHRISTENA","CHRISTEEN","CHARISE","CATERINA","CARLEY","CANDYCE","ARLENA","AMMIE","YANG","WILLETTE", + "VANITA","TUYET","TINY","SYREETA","SILVA","SCOTT","RONALD","PENNEY","NYLA","MICHAL","MAURICE","MARYAM","MARYA","MAGEN","LUDIE", + "LOMA","LIVIA","LANELL","KIMBERLIE","JULEE","DONETTA","DIEDRA","DENISHA","DEANE","DAWNE","CLARINE","CHERRYL","BRONWYN","BRANDON", + "ALLA","VALERY","TONDA","SUEANN","SORAYA","SHOSHANA","SHELA","SHARLEEN","SHANELLE","NERISSA","MICHEAL","MERIDITH","MELLIE","MAYE", + "MAPLE","MAGARET","LUIS","LILI","LEONILA","LEONIE","LEEANNA","LAVONIA","LAVERA","KRISTEL","KATHEY","KATHE","JUSTIN","JULIAN", + "JIMMY","JANN","ILDA","HILDRED","HILDEGARDE","GENIA","FUMIKO","EVELIN","ERMELINDA","ELLY","DUNG","DOLORIS","DIONNA","DANAE", + "BERNEICE","ANNICE","ALIX","VERENA","VERDIE","TRISTAN","SHAWNNA","SHAWANA","SHAUNNA","ROZELLA","RANDEE","RANAE","MILAGRO", + "LYNELL","LUISE","LOUIE","LOIDA","LISBETH","KARLEEN","JUNITA","JONA","ISIS","HYACINTH","HEDY","GWENN","ETHELENE","ERLINE", + "EDWARD","DONYA","DOMONIQUE","DELICIA","DANNETTE","CICELY","BRANDA","BLYTHE","BETHANN","ASHLYN","ANNALEE","ALLINE","YUKO","VELLA", + "TRANG","TOWANDA","TESHA","SHERLYN","NARCISA","MIGUELINA","MERI","MAYBELL","MARLANA","MARGUERITA","MADLYN","LUNA","LORY", + "LORIANN","LIBERTY","LEONORE","LEIGHANN","LAURICE","LATESHA","LARONDA","KATRICE","KASIE","KARL","KALEY","JADWIGA","GLENNIE", + "GEARLDINE","FRANCINA","EPIFANIA","DYAN","DORIE","DIEDRE","DENESE","DEMETRICE","DELENA","DARBY","CRISTIE","CLEORA","CATARINA", + "CARISA","BERNIE","BARBERA","ALMETA","TRULA","TEREASA","SOLANGE","SHEILAH","SHAVONNE","SANORA","ROCHELL","MATHILDE","MARGARETA", + "MAIA","LYNSEY","LAWANNA","LAUNA","KENA","KEENA","KATIA","JAMEY","GLYNDA","GAYLENE","ELVINA","ELANOR","DANUTA","DANIKA","CRISTEN", + "CORDIE","COLETTA","CLARITA","CARMON","BRYNN","AZUCENA","AUNDREA","ANGELE","YI","WALTER","VERLIE","VERLENE","TAMESHA","SILVANA", + "SEBRINA","SAMIRA","REDA","RAYLENE","PENNI","PANDORA","NORAH","NOMA","MIREILLE","MELISSIA","MARYALICE","LARAINE","KIMBERY", + "KARYL","KARINE","KAM","JOLANDA","JOHANA","JESUSA","JALEESA","JAE","JACQUELYNE","IRISH","ILUMINADA","HILARIA","HANH","GENNIE", + "FRANCIE","FLORETTA","EXIE","EDDA","DREMA","DELPHA","BEV","BARBAR","ASSUNTA","ARDELL","ANNALISA","ALISIA","YUKIKO","YOLANDO", + "WONDA","WEI","WALTRAUD","VETA","TEQUILA","TEMEKA","TAMEIKA","SHIRLEEN","SHENITA","PIEDAD","OZELLA","MIRTHA","MARILU","KIMIKO", + "JULIANE","JENICE","JEN","JANAY","JACQUILINE","HILDE","FE","FAE","EVAN","EUGENE","ELOIS","ECHO","DEVORAH","CHAU","BRINDA", + "BETSEY","ARMINDA","ARACELIS","APRYL","ANNETT","ALISHIA","VEOLA","USHA","TOSHIKO","THEOLA","TASHIA","TALITHA","SHERY","RUDY", + "RENETTA","REIKO","RASHEEDA","OMEGA","OBDULIA","MIKA","MELAINE","MEGGAN","MARTIN","MARLEN","MARGET","MARCELINE","MANA","MAGDALEN", + "LIBRADA","LEZLIE","LEXIE","LATASHIA","LASANDRA","KELLE","ISIDRA","ISA","INOCENCIA","GWYN","FRANCOISE","ERMINIA","ERINN","DIMPLE", + "DEVORA","CRISELDA","ARMANDA","ARIE","ARIANE","ANGELO","ANGELENA","ALLEN","ALIZA","ADRIENE","ADALINE","XOCHITL","TWANNA","TRAN", + "TOMIKO","TAMISHA","TAISHA","SUSY","SIU","RUTHA","ROXY","RHONA","RAYMOND","OTHA","NORIKO","NATASHIA","MERRIE","MELVIN","MARINDA", + "MARIKO","MARGERT","LORIS","LIZZETTE","LEISHA","KAILA","KA","JOANNIE","JERRICA","JENE","JANNET","JANEE","JACINDA","HERTA", + "ELENORE","DORETTA","DELAINE","DANIELL","CLAUDIE","CHINA","BRITTA","APOLONIA","AMBERLY","ALEASE","YURI","YUK","WEN","WANETA", + "UTE","TOMI","SHARRI","SANDIE","ROSELLE","REYNALDA","RAGUEL","PHYLICIA","PATRIA","OLIMPIA","ODELIA","MITZIE","MITCHELL","MISS", + "MINDA","MIGNON","MICA","MENDY","MARIVEL","MAILE","LYNETTA","LAVETTE","LAURYN","LATRISHA","LAKIESHA","KIERSTEN","KARY","JOSPHINE", + "JOLYN","JETTA","JANISE","JACQUIE","IVELISSE","GLYNIS","GIANNA","GAYNELLE","EMERALD","DEMETRIUS","DANYELL","DANILLE","DACIA", + "CORALEE","CHER","CEOLA","BRETT","BELL","ARIANNE","ALESHIA","YUNG","WILLIEMAE","TROY","TRINH","THORA","TAI","SVETLANA","SHERIKA", + "SHEMEKA","SHAUNDA","ROSELINE","RICKI","MELDA","MALLIE","LAVONNA","LATINA","LARRY","LAQUANDA","LALA","LACHELLE","KLARA","KANDIS", + "JOHNA","JEANMARIE","JAYE","HANG","GRAYCE","GERTUDE","EMERITA","EBONIE","CLORINDA","CHING","CHERY","CAROLA","BREANN","BLOSSOM", + "BERNARDINE","BECKI","ARLETHA","ARGELIA","ARA","ALITA","YULANDA","YON","YESSENIA","TOBI","TASIA","SYLVIE","SHIRL","SHIRELY", + "SHERIDAN","SHELLA","SHANTELLE","SACHA","ROYCE","REBECKA","REAGAN","PROVIDENCIA","PAULENE","MISHA","MIKI","MARLINE","MARICA", + "LORITA","LATOYIA","LASONYA","KERSTIN","KENDA","KEITHA","KATHRIN","JAYMIE","JACK","GRICELDA","GINETTE","ERYN","ELINA","ELFRIEDA", + "DANYEL","CHEREE","CHANELLE","BARRIE","AVERY","AURORE","ANNAMARIA","ALLEEN","AILENE","AIDE","YASMINE","VASHTI","VALENTINE", + "TREASA","TORY","TIFFANEY","SHERYLL","SHARIE","SHANAE","SAU","RAISA","PA","NEDA","MITSUKO","MIRELLA","MILDA","MARYANNA","MARAGRET", + "MABELLE","LUETTA","LORINA","LETISHA","LATARSHA","LANELLE","LAJUANA","KRISSY","KARLY","KARENA","JON","JESSIKA","JERICA","JEANELLE", + "JANUARY","JALISA","JACELYN","IZOLA","IVEY","GREGORY","EUNA","ETHA","DREW","DOMITILA","DOMINICA","DAINA","CREOLA","CARLI","CAMIE", + "BUNNY","BRITTNY","ASHANTI","ANISHA","ALEEN","ADAH","YASUKO","WINTER","VIKI","VALRIE","TONA","TINISHA","THI","TERISA","TATUM", + "TANEKA","SIMONNE","SHALANDA","SERITA","RESSIE","REFUGIA","PAZ","OLENE","NA","MERRILL","MARGHERITA","MANDIE","MAN","MAIRE", + "LYNDIA","LUCI","LORRIANE","LORETA","LEONIA","LAVONA","LASHAWNDA","LAKIA","KYOKO","KRYSTINA","KRYSTEN","KENIA","KELSI","JUDE", + "JEANICE","ISOBEL","GEORGIANN","GENNY","FELICIDAD","EILENE","DEON","DELOISE","DEEDEE","DANNIE","CONCEPTION","CLORA","CHERILYN", + "CHANG","CALANDRA","BERRY","ARMANDINA","ANISA","ULA","TIMOTHY","TIERA","THERESSA","STEPHANIA","SIMA","SHYLA","SHONTA","SHERA", + "SHAQUITA","SHALA","SAMMY","ROSSANA","NOHEMI","NERY","MORIAH","MELITA","MELIDA","MELANI","MARYLYNN","MARISHA","MARIETTE","MALORIE", + "MADELENE","LUDIVINA","LORIA","LORETTE","LORALEE","LIANNE","LEON","LAVENIA","LAURINDA","LASHON","KIT","KIMI","KEILA","KATELYNN", + "KAI","JONE","JOANE","JI","JAYNA","JANELLA","JA","HUE","HERTHA","FRANCENE","ELINORE","DESPINA","DELSIE","DEEDRA","CLEMENCIA", + "CARRY","CAROLIN","CARLOS","BULAH","BRITTANIE","BOK","BLONDELL","BIBI","BEAULAH","BEATA","ANNITA","AGRIPINA","VIRGEN","VALENE", + "UN","TWANDA","TOMMYE","TOI","TARRA","TARI","TAMMERA","SHAKIA","SADYE","RUTHANNE","ROCHEL","RIVKA","PURA","NENITA","NATISHA", + "MING","MERRILEE","MELODEE","MARVIS","LUCILLA","LEENA","LAVETA","LARITA","LANIE","KEREN","ILEEN","GEORGEANN","GENNA","GENESIS", + "FRIDA","EWA","EUFEMIA","EMELY","ELA","EDYTH","DEONNA","DEADRA","DARLENA","CHANELL","CHAN","CATHERN","CASSONDRA","CASSAUNDRA", + "BERNARDA","BERNA","ARLINDA","ANAMARIA","ALBERT","WESLEY","VERTIE","VALERI","TORRI","TATYANA","STASIA","SHERISE","SHERILL", + "SEASON","SCOTTIE","SANDA","RUTHE","ROSY","ROBERTO","ROBBI","RANEE","QUYEN","PEARLY","PALMIRA","ONITA","NISHA","NIESHA","NIDA", + "NEVADA","NAM","MERLYN","MAYOLA","MARYLOUISE","MARYLAND","MARX","MARTH","MARGENE","MADELAINE","LONDA","LEONTINE","LEOMA","LEIA", + "LAWRENCE","LAURALEE","LANORA","LAKITA","KIYOKO","KETURAH","KATELIN","KAREEN","JONIE","JOHNETTE","JENEE","JEANETT","IZETTA", + "HIEDI","HEIKE","HASSIE","HAROLD","GIUSEPPINA","GEORGANN","FIDELA","FERNANDE","ELWANDA","ELLAMAE","ELIZ","DUSTI","DOTTY","CYNDY", + "CORALIE","CELESTA","ARGENTINA","ALVERTA","XENIA","WAVA","VANETTA","TORRIE","TASHINA","TANDY","TAMBRA","TAMA","STEPANIE","SHILA", + "SHAUNTA","SHARAN","SHANIQUA","SHAE","SETSUKO","SERAFINA","SANDEE","ROSAMARIA","PRISCILA","OLINDA","NADENE","MUOI","MICHELINA", + "MERCEDEZ","MARYROSE","MARIN","MARCENE","MAO","MAGALI","MAFALDA","LOGAN","LINN","LANNIE","KAYCE","KAROLINE","KAMILAH","KAMALA", + "JUSTA","JOLINE","JENNINE","JACQUETTA","IRAIDA","GERALD","GEORGEANNA","FRANCHESCA","FAIRY","EMELINE","ELANE","EHTEL","EARLIE", + "DULCIE","DALENE","CRIS","CLASSIE","CHERE","CHARIS","CAROYLN","CARMINA","CARITA","BRIAN","BETHANIE","AYAKO","ARICA","AN","ALYSA", + "ALESSANDRA","AKILAH","ADRIEN","ZETTA","YOULANDA","YELENA","YAHAIRA","XUAN","WENDOLYN","VICTOR","TIJUANA","TERRELL","TERINA", + "TERESIA","SUZI","SUNDAY","SHERELL","SHAVONDA","SHAUNTE","SHARDA","SHAKITA","SENA","RYANN","RUBI","RIVA","REGINIA","REA","RACHAL", + "PARTHENIA","PAMULA","MONNIE","MONET","MICHAELE","MELIA","MARINE","MALKA","MAISHA","LISANDRA","LEO","LEKISHA","LEAN","LAURENCE", + "LAKENDRA","KRYSTIN","KORTNEY","KIZZIE","KITTIE","KERA","KENDAL","KEMBERLY","KANISHA","JULENE","JULE","JOSHUA","JOHANNE","JEFFREY", + "JAMEE","HAN","HALLEY","GIDGET","GALINA","FREDRICKA","FLETA","FATIMAH","EUSEBIA","ELZA","ELEONORE","DORTHEY","DORIA","DONELLA", + "DINORAH","DELORSE","CLARETHA","CHRISTINIA","CHARLYN","BONG","BELKIS","AZZIE","ANDERA","AIKO","ADENA","YER","YAJAIRA","WAN", + "VANIA","ULRIKE","TOSHIA","TIFANY","STEFANY","SHIZUE","SHENIKA","SHAWANNA","SHAROLYN","SHARILYN","SHAQUANA","SHANTAY","SEE", + "ROZANNE","ROSELEE","RICKIE","REMONA","REANNA","RAELENE","QUINN","PHUNG","PETRONILA","NATACHA","NANCEY","MYRL","MIYOKO","MIESHA", + "MERIDETH","MARVELLA","MARQUITTA","MARHTA","MARCHELLE","LIZETH","LIBBIE","LAHOMA","LADAWN","KINA","KATHELEEN","KATHARYN","KARISA", + "KALEIGH","JUNIE","JULIEANN","JOHNSIE","JANEAN","JAIMEE","JACKQUELINE","HISAKO","HERMA","HELAINE","GWYNETH","GLENN","GITA", + "EUSTOLIA","EMELINA","ELIN","EDRIS","DONNETTE","DONNETTA","DIERDRE","DENAE","DARCEL","CLAUDE","CLARISA","CINDERELLA","CHIA", + "CHARLESETTA","CHARITA","CELSA","CASSY","CASSI","CARLEE","BRUNA","BRITTANEY","BRANDE","BILLI","BAO","ANTONETTA","ANGLA","ANGELYN", + "ANALISA","ALANE","WENONA","WENDIE","VERONIQUE","VANNESA","TOBIE","TEMPIE","SUMIKO","SULEMA","SPARKLE","SOMER","SHEBA","SHAYNE", + "SHARICE","SHANEL","SHALON","SAGE","ROY","ROSIO","ROSELIA","RENAY","REMA","REENA","PORSCHE","PING","PEG","OZIE","ORETHA","ORALEE", + "ODA","NU","NGAN","NAKESHA","MILLY","MARYBELLE","MARLIN","MARIS","MARGRETT","MARAGARET","MANIE","LURLENE","LILLIA","LIESELOTTE", + "LAVELLE","LASHAUNDA","LAKEESHA","KEITH","KAYCEE","KALYN","JOYA","JOETTE","JENAE","JANIECE","ILLA","GRISEL","GLAYDS","GENEVIE", + "GALA","FREDDA","FRED","ELMER","ELEONOR","DEBERA","DEANDREA","DAN","CORRINNE","CORDIA","CONTESSA","COLENE","CLEOTILDE","CHARLOTT", + "CHANTAY","CECILLE","BEATRIS","AZALEE","ARLEAN","ARDATH","ANJELICA","ANJA","ALFREDIA","ALEISHA","ADAM","ZADA","YUONNE","XIAO", + "WILLODEAN","WHITLEY","VENNIE","VANNA","TYISHA","TOVA","TORIE","TONISHA","TILDA","TIEN","TEMPLE","SIRENA","SHERRIL","SHANTI", + "SHAN","SENAIDA","SAMELLA","ROBBYN","RENDA","REITA","PHEBE","PAULITA","NOBUKO","NGUYET","NEOMI","MOON","MIKAELA","MELANIA", + "MAXIMINA","MARG","MAISIE","LYNNA","LILLI","LAYNE","LASHAUN","LAKENYA","LAEL","KIRSTIE","KATHLINE","KASHA","KARLYN","KARIMA", + "JOVAN","JOSEFINE","JENNELL","JACQUI","JACKELYN","HYO","HIEN","GRAZYNA","FLORRIE","FLORIA","ELEONORA","DWANA","DORLA","DONG", + "DELMY","DEJA","DEDE","DANN","CRYSTA","CLELIA","CLARIS","CLARENCE","CHIEKO","CHERLYN","CHERELLE","CHARMAIN","CHARA","CAMMY","BEE", + "ARNETTE","ARDELLE","ANNIKA","AMIEE","AMEE","ALLENA","YVONE","YUKI","YOSHIE","YEVETTE","YAEL","WILLETTA","VONCILE","VENETTA", + "TULA","TONETTE","TIMIKA","TEMIKA","TELMA","TEISHA","TAREN","TA","STACEE","SHIN","SHAWNTA","SATURNINA","RICARDA","POK","PASTY", + "ONIE","NUBIA","MORA","MIKE","MARIELLE","MARIELLA","MARIANELA","MARDELL","MANY","LUANNA","LOISE","LISABETH","LINDSY","LILLIANA", + "LILLIAM","LELAH","LEIGHA","LEANORA","LANG","KRISTEEN","KHALILAH","KEELEY","KANDRA","JUNKO","JOAQUINA","JERLENE","JANI","JAMIKA", + "JAME","HSIU","HERMILA","GOLDEN","GENEVIVE","EVIA","EUGENA","EMMALINE","ELFREDA","ELENE","DONETTE","DELCIE","DEEANNA","DARCEY", + "CUC","CLARINDA","CIRA","CHAE","CELINDA","CATHERYN","CATHERIN","CASIMIRA","CARMELIA","CAMELLIA","BREANA","BOBETTE","BERNARDINA", + "BEBE","BASILIA","ARLYNE","AMAL","ALAYNA","ZONIA","ZENIA","YURIKO","YAEKO","WYNELL","WILLOW","WILLENA","VERNIA","TU","TRAVIS", + "TORA","TERRILYN","TERICA","TENESHA","TAWNA","TAJUANA","TAINA","STEPHNIE","SONA","SOL","SINA","SHONDRA","SHIZUKO","SHERLENE", + "SHERICE","SHARIKA","ROSSIE","ROSENA","RORY","RIMA","RIA","RHEBA","RENNA","PETER","NATALYA","NANCEE","MELODI","MEDA","MAXIMA", + "MATHA","MARKETTA","MARICRUZ","MARCELENE","MALVINA","LUBA","LOUETTA","LEIDA","LECIA","LAURAN","LASHAWNA","LAINE","KHADIJAH", + "KATERINE","KASI","KALLIE","JULIETTA","JESUSITA","JESTINE","JESSIA","JEREMY","JEFFIE","JANYCE","ISADORA","GEORGIANNE","FIDELIA", + "EVITA","EURA","EULAH","ESTEFANA","ELSY","ELIZABET","ELADIA","DODIE","DION","DIA","DENISSE","DELORAS","DELILA","DAYSI","DAKOTA", + "CURTIS","CRYSTLE","CONCHA","COLBY","CLARETTA","CHU","CHRISTIA","CHARLSIE","CHARLENA","CARYLON","BETTYANN","ASLEY","ASHLEA", + "AMIRA","AI","AGUEDA","AGNUS","YUETTE","VINITA","VICTORINA","TYNISHA","TREENA","TOCCARA","TISH","THOMASENA","TEGAN","SOILA", + "SHILOH","SHENNA","SHARMAINE","SHANTAE","SHANDI","SEPTEMBER","SARAN","SARAI","SANA","SAMUEL","SALLEY","ROSETTE","ROLANDE","REGINE", + "OTELIA","OSCAR","OLEVIA","NICHOLLE","NECOLE","NAIDA","MYRTA","MYESHA","MITSUE","MINTA","MERTIE","MARGY","MAHALIA","MADALENE", + "LOVE","LOURA","LOREAN","LEWIS","LESHA","LEONIDA","LENITA","LAVONE","LASHELL","LASHANDRA","LAMONICA","KIMBRA","KATHERINA","KARRY", + "KANESHA","JULIO","JONG","JENEVA","JAQUELYN","HWA","GILMA","GHISLAINE","GERTRUDIS","FRANSISCA","FERMINA","ETTIE","ETSUKO","ELLIS", + "ELLAN","ELIDIA","EDRA","DORETHEA","DOREATHA","DENYSE","DENNY","DEETTA","DAINE","CYRSTAL","CORRIN","CAYLA","CARLITA","CAMILA", + "BURMA","BULA","BUENA","BLAKE","BARABARA","AVRIL","AUSTIN","ALAINE","ZANA","WILHEMINA","WANETTA","VIRGIL","VI","VERONIKA","VERNON", + "VERLINE","VASILIKI","TONITA","TISA","TEOFILA","TAYNA","TAUNYA","TANDRA","TAKAKO","SUNNI","SUANNE","SIXTA","SHARELL","SEEMA", + "RUSSELL","ROSENDA","ROBENA","RAYMONDE","PEI","PAMILA","OZELL","NEIDA","NEELY","MISTIE","MICHA","MERISSA","MAURITA","MARYLN", + "MARYETTA","MARSHALL","MARCELL","MALENA","MAKEDA","MADDIE","LOVETTA","LOURIE","LORRINE","LORILEE","LESTER","LAURENA","LASHAY", + "LARRAINE","LAREE","LACRESHA","KRISTLE","KRISHNA","KEVA","KEIRA","KAROLE","JOIE","JINNY","JEANNETTA","JAMA","HEIDY","GILBERTE", + "GEMA","FAVIOLA","EVELYNN","ENDA","ELLI","ELLENA","DIVINA","DAGNY","COLLENE","CODI","CINDIE","CHASSIDY","CHASIDY","CATRICE", + "CATHERINA","CASSEY","CAROLL","CARLENA","CANDRA","CALISTA","BRYANNA","BRITTENY","BEULA","BARI","AUDRIE","AUDRIA","ARDELIA", + "ANNELLE","ANGILA","ALONA","ALLYN","DOUGLAS","ROGER","JONATHAN","RALPH","NICHOLAS","BENJAMIN","BRUCE","HARRY","WAYNE","STEVE", + "HOWARD","ERNEST","PHILLIP","TODD","CRAIG","ALAN","PHILIP","EARL","DANNY","BRYAN","STANLEY","LEONARD","NATHAN","MANUEL","RODNEY", + "MARVIN","VINCENT","JEFFERY","JEFF","CHAD","JACOB","ALFRED","BRADLEY","HERBERT","FREDERICK","EDWIN","DON","RICKY","RANDALL", + "BARRY","BERNARD","LEROY","MARCUS","THEODORE","CLIFFORD","MIGUEL","JIM","TOM","CALVIN","BILL","LLOYD","DEREK","WARREN","DARRELL", + "JEROME","FLOYD","ALVIN","TIM","GORDON","GREG","JORGE","DUSTIN","PEDRO","DERRICK","ZACHARY","HERMAN","GLEN","HECTOR","RICARDO", + "RICK","BRENT","RAMON","GILBERT","MARC","REGINALD","RUBEN","NATHANIEL","RAFAEL","EDGAR","MILTON","RAUL","BEN","CHESTER","DUANE", + "FRANKLIN","BRAD","RON","ROLAND","ARNOLD","HARVEY","JARED","ERIK","DARRYL","NEIL","JAVIER","FERNANDO","CLINTON","TED","MATHEW", + "TYRONE","DARREN","LANCE","KURT","ALLAN","NELSON","GUY","CLAYTON","HUGH","MAX","DWAYNE","DWIGHT","ARMANDO","FELIX","EVERETT", + "IAN","WALLACE","KEN","BOB","ALFREDO","ALBERTO","DAVE","IVAN","BYRON","ISAAC","MORRIS","CLIFTON","WILLARD","ROSS","ANDY", + "SALVADOR","KIRK","SERGIO","SETH","KENT","TERRANCE","EDUARDO","TERRENCE","ENRIQUE","WADE","STUART","FREDRICK","ARTURO","ALEJANDRO", + "NICK","LUTHER","WENDELL","JEREMIAH","JULIUS","OTIS","TREVOR","OLIVER","LUKE","HOMER","GERARD","DOUG","KENNY","HUBERT","LYLE", + "MATT","ALFONSO","ORLANDO","REX","CARLTON","ERNESTO","NEAL","PABLO","LORENZO","OMAR","WILBUR","GRANT","HORACE","RODERICK", + "ABRAHAM","WILLIS","RICKEY","ANDRES","CESAR","JOHNATHAN","MALCOLM","RUDOLPH","DAMON","KELVIN","PRESTON","ALTON","ARCHIE","MARCO", + "WM","PETE","RANDOLPH","GARRY","GEOFFREY","JONATHON","FELIPE","GERARDO","ED","DOMINIC","DELBERT","COLIN","GUILLERMO","EARNEST", + "LUCAS","BENNY","SPENCER","RODOLFO","MYRON","EDMUND","GARRETT","SALVATORE","CEDRIC","LOWELL","GREGG","SHERMAN","WILSON", + "SYLVESTER","ROOSEVELT","ISRAEL","JERMAINE","FORREST","WILBERT","LELAND","SIMON","CLARK","IRVING","BRYANT","OWEN","RUFUS", + "WOODROW","KRISTOPHER","MACK","LEVI","MARCOS","GUSTAVO","JAKE","LIONEL","GILBERTO","CLINT","NICOLAS","ISMAEL","ORVILLE","ERVIN", + "DEWEY","AL","WILFRED","JOSH","HUGO","IGNACIO","CALEB","TOMAS","SHELDON","ERICK","STEWART","DOYLE","DARREL","ROGELIO","TERENCE", + "SANTIAGO","ALONZO","ELIAS","BERT","ELBERT","RAMIRO","CONRAD","NOAH","GRADY","PHIL","CORNELIUS","LAMAR","ROLANDO","CLAY","PERCY", + "DEXTER","BRADFORD","DARIN","AMOS","MOSES","IRVIN","SAUL","ROMAN","RANDAL","TIMMY","DARRIN","WINSTON","BRENDAN","ABEL","DOMINICK", + "BOYD","EMILIO","ELIJAH","DOMINGO","EMMETT","MARLON","EMANUEL","JERALD","EDMOND","EMIL","DEWAYNE","WILL","OTTO","TEDDY", + "REYNALDO","BRET","JESS","TRENT","HUMBERTO","EMMANUEL","STEPHAN","VICENTE","LAMONT","GARLAND","MILES","EFRAIN","HEATH","RODGER", + "HARLEY","ETHAN","ELDON","ROCKY","PIERRE","JUNIOR","FREDDY","ELI","BRYCE","ANTOINE","STERLING","CHASE","GROVER","ELTON", + "CLEVELAND","DYLAN","CHUCK","DAMIAN","REUBEN","STAN","AUGUST","LEONARDO","JASPER","RUSSEL","ERWIN","BENITO","HANS","MONTE", + "BLAINE","ERNIE","CURT","QUENTIN","AGUSTIN","MURRAY","JAMAL","ADOLFO","HARRISON","TYSON","BURTON","BRADY","ELLIOTT","WILFREDO", + "BART","JARROD","VANCE","DENIS","DAMIEN","JOAQUIN","HARLAN","DESMOND","ELLIOT","DARWIN","GREGORIO","BUDDY","XAVIER","KERMIT", + "ROSCOE","ESTEBAN","ANTON","SOLOMON","SCOTTY","NORBERT","ELVIN","WILLIAMS","NOLAN","ROD","QUINTON","HAL","BRAIN","ROB","ELWOOD", + "KENDRICK","DARIUS","MOISES","FIDEL","THADDEUS","CLIFF","MARCEL","JACKSON","RAPHAEL","BRYON","ARMAND","ALVARO","JEFFRY","DANE", + "JOESPH","THURMAN","NED","RUSTY","MONTY","FABIAN","REGGIE","MASON","GRAHAM","ISAIAH","VAUGHN","GUS","LOYD","DIEGO","ADOLPH", + "NORRIS","MILLARD","ROCCO","GONZALO","DERICK","RODRIGO","WILEY","RIGOBERTO","ALPHONSO","TY","NOE","VERN","REED","JEFFERSON", + "ELVIS","BERNARDO","MAURICIO","HIRAM","DONOVAN","BASIL","RILEY","NICKOLAS","MAYNARD","SCOT","VINCE","QUINCY","EDDY","SEBASTIAN", + "FEDERICO","ULYSSES","HERIBERTO","DONNELL","COLE","DAVIS","GAVIN","EMERY","WARD","ROMEO","JAYSON","DANTE","CLEMENT","COY", + "MAXWELL","JARVIS","BRUNO","ISSAC","DUDLEY","BROCK","SANFORD","CARMELO","BARNEY","NESTOR","STEFAN","DONNY","ART","LINWOOD","BEAU", + "WELDON","GALEN","ISIDRO","TRUMAN","DELMAR","JOHNATHON","SILAS","FREDERIC","DICK","IRWIN","MERLIN","CHARLEY","MARCELINO","HARRIS", + "CARLO","TRENTON","KURTIS","HUNTER","AURELIO","WINFRED","VITO","COLLIN","DENVER","CARTER","LEONEL","EMORY","PASQUALE","MOHAMMAD", + "MARIANO","DANIAL","LANDON","DIRK","BRANDEN","ADAN","BUFORD","GERMAN","WILMER","EMERSON","ZACHERY","FLETCHER","JACQUES","ERROL", + "DALTON","MONROE","JOSUE","EDWARDO","BOOKER","WILFORD","SONNY","SHELTON","CARSON","THERON","RAYMUNDO","DAREN","HOUSTON","ROBBY", + "LINCOLN","GENARO","BENNETT","OCTAVIO","CORNELL","HUNG","ARRON","ANTONY","HERSCHEL","GIOVANNI","GARTH","CYRUS","CYRIL","RONNY", + "LON","FREEMAN","DUNCAN","KENNITH","CARMINE","ERICH","CHADWICK","WILBURN","RUSS","REID","MYLES","ANDERSON","MORTON","JONAS", + "FOREST","MITCHEL","MERVIN","ZANE","RICH","JAMEL","LAZARO","ALPHONSE","RANDELL","MAJOR","JARRETT","BROOKS","ABDUL","LUCIANO", + "SEYMOUR","EUGENIO","MOHAMMED","VALENTIN","CHANCE","ARNULFO","LUCIEN","FERDINAND","THAD","EZRA","ALDO","RUBIN","ROYAL","MITCH", + "EARLE","ABE","WYATT","MARQUIS","LANNY","KAREEM","JAMAR","BORIS","ISIAH","EMILE","ELMO","ARON","LEOPOLDO","EVERETTE","JOSEF", + "ELOY","RODRICK","REINALDO","LUCIO","JERROD","WESTON","HERSHEL","BARTON","PARKER","LEMUEL","BURT","JULES","GIL","ELISEO","AHMAD", + "NIGEL","EFREN","ANTWAN","ALDEN","MARGARITO","COLEMAN","DINO","OSVALDO","LES","DEANDRE","NORMAND","KIETH","TREY","NORBERTO", + "NAPOLEON","JEROLD","FRITZ","ROSENDO","MILFORD","CHRISTOPER","ALFONZO","LYMAN","JOSIAH","BRANT","WILTON","RICO","JAMAAL","DEWITT", + "BRENTON","OLIN","FOSTER","FAUSTINO","CLAUDIO","JUDSON","GINO","EDGARDO","ALEC","TANNER","JARRED","DONN","TAD","PRINCE","PORFIRIO", + "ODIS","LENARD","CHAUNCEY","TOD","MEL","MARCELO","KORY","AUGUSTUS","KEVEN","HILARIO","BUD","SAL","ORVAL","MAURO","ZACHARIAH", + "OLEN","ANIBAL","MILO","JED","DILLON","AMADO","NEWTON","LENNY","RICHIE","HORACIO","BRICE","MOHAMED","DELMER","DARIO","REYES","MAC", + "JONAH","JERROLD","ROBT","HANK","RUPERT","ROLLAND","KENTON","DAMION","ANTONE","WALDO","FREDRIC","BRADLY","KIP","BURL","WALKER", + "TYREE","JEFFEREY","AHMED","WILLY","STANFORD","OREN","NOBLE","MOSHE","MIKEL","ENOCH","BRENDON","QUINTIN","JAMISON","FLORENCIO", + "DARRICK","TOBIAS","HASSAN","GIUSEPPE","DEMARCUS","CLETUS","TYRELL","LYNDON","KEENAN","WERNER","GERALDO","COLUMBUS","CHET", + "BERTRAM","MARKUS","HUEY","HILTON","DWAIN","DONTE","TYRON","OMER","ISAIAS","HIPOLITO","FERMIN","ADALBERTO","BO","BARRETT", + "TEODORO","MCKINLEY","MAXIMO","GARFIELD","RALEIGH","LAWERENCE","ABRAM","RASHAD","KING","EMMITT","DARON","SAMUAL","MIQUEL", + "EUSEBIO","DOMENIC","DARRON","BUSTER","WILBER","RENATO","JC","HOYT","HAYWOOD","EZEKIEL","CHAS","FLORENTINO","ELROY","CLEMENTE", + "ARDEN","NEVILLE","EDISON","DESHAWN","NATHANIAL","JORDON","DANILO","CLAUD","SHERWOOD","RAYMON","RAYFORD","CRISTOBAL","AMBROSE", + "TITUS","HYMAN","FELTON","EZEQUIEL","ERASMO","STANTON","LONNY","LEN","IKE","MILAN","LINO","JAROD","HERB","ANDREAS","WALTON", + "RHETT","PALMER","DOUGLASS","CORDELL","OSWALDO","ELLSWORTH","VIRGILIO","TONEY","NATHANAEL","DEL","BENEDICT","MOSE","JOHNSON", + "ISREAL","GARRET","FAUSTO","ASA","ARLEN","ZACK","WARNER","MODESTO","FRANCESCO","MANUAL","GAYLORD","GASTON","FILIBERTO","DEANGELO", + "MICHALE","GRANVILLE","WES","MALIK","ZACKARY","TUAN","ELDRIDGE","CRISTOPHER","CORTEZ","ANTIONE","MALCOM","LONG","KOREY","JOSPEH", + "COLTON","WAYLON","VON","HOSEA","SHAD","SANTO","RUDOLF","ROLF","REY","RENALDO","MARCELLUS","LUCIUS","KRISTOFER","BOYCE","BENTON", + "HAYDEN","HARLAND","ARNOLDO","RUEBEN","LEANDRO","KRAIG","JERRELL","JEROMY","HOBERT","CEDRICK","ARLIE","WINFORD","WALLY","LUIGI", + "KENETH","JACINTO","GRAIG","FRANKLYN","EDMUNDO","SID","PORTER","LEIF","JERAMY","BUCK","WILLIAN","VINCENZO","SHON","LYNWOOD","JERE", + "HAI","ELDEN","DORSEY","DARELL","BRODERICK","ALONSO"] + +def Problem22(): + #Setup the variables + sums = [] #Holds the score based on the sum of the characters in the name + prod = [] #Holds the score based on the sum of the characters and the location in alphabetical order + + #Sort all the names + __NAMES.sort() + #Step through every name adding up the values of the characters + for nameCnt in range(0, len(__NAMES)): + #Step through every character in the current name adding up the value of the characters + sums.append(0) + for charCnt in range(0, len(__NAMES[nameCnt])): + #A = 65 so subtracting 64 means A - 1. This will only work correctly if all letters are capitalized + sums[nameCnt] += (ord(__NAMES[nameCnt][charCnt]) - 64) + + #Get the product for all numbers + for cnt in range(0, len(sums)): + prod.append(sums[cnt] * (cnt + 1)) + + #Print the results + print("The answer to the question is " + str(sum(prod))) + + +#This ensures the correct function is called if this is called as a stand along script +if __name__ == "__main__": + timer = Stopwatch() + timer.start() + Problem22() + timer.stop() + print("It took " + timer.getString() + " to run this algorithm") + +""" Results: +The answer to the question is 871198282 +It took 9.206 milliseconds to run this algorithm +""" diff --git a/Problem23.py b/Problem23.py new file mode 100644 index 0000000..8e0fd06 --- /dev/null +++ b/Problem23.py @@ -0,0 +1,87 @@ +#ProjectEuler/Python/Problem23.py +#Matthew Ellison +# Created: 03-22-19 +#Modified: 03-28-19 +#Find the sum of all the positive integers which cannot be written as the sum of two abundant numbers +#All of my imports can be gotten from my pyClasses repository at https://bitbucket.org/Mattrixwv/pyClasses +""" + Copyright (C) 2019 Matthew Ellison + + This program is free software: you can redistribute it and/or modify + it under the terms of the GNU Lesser General Public License as published by + the Free Software Foundation, either version 3 of the License, or + (at your option) any later version. + + This program is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the + GNU Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public License + along with this program. If not, see . +""" + + +from Stopwatch import Stopwatch +import Algorithms + +__maxNum = 28123 + + +#A function that returns true if num can be created by adding two elements from abund and false if it cannot +def isSum(abund: list, num: int) -> bool: + sumOfNums = 0 + #Pick a number for the first part of the sum + for firstNum in range(0, len(abund)): + #Pick a number for the second part of the sum + for secondNum in range(0, len(abund)): + sumOfNums = abund[firstNum] + abund[secondNum] + if(sumOfNums == num): + return True + elif(sumOfNums > num): + break + #If you have run through the entire list and did not find a sum then it is false + return False + + +def Problem23(): + #Setup the variables + divisorSums = [] + #Make sure every element has a 0 in it's location + for cnt in range(0, __maxNum): + divisorSums.append(0) + + #Get the sum of the divisors of all numbers < __maxNum + for cnt in range(1, __maxNum): + div = Algorithms.getDivisors(cnt) + if(len(div) > 1): + div.remove(div[len(div) - 1]) + divisorSums[cnt] = sum(div) + + #Get the abundant numbers + abund = [] + for cnt in range(0, len(divisorSums)): + if(divisorSums[cnt] > cnt): + abund.append(cnt) + + #Check if each number can be the sum of 2 abundant numbers and add to the sum if no + sumOfNums = 0 + for cnt in range(1, __maxNum): + if(not isSum(abund, cnt)): + sumOfNums += cnt + + #Print the results + print("The answer is " + str(sumOfNums)) + + +if __name__ == "__main__": + timer = Stopwatch() + timer.start() + Problem23() + timer.stop() + print("It took " + timer.getString() + " to run this algorithm") + +""" Results: +The answer is 4179871 +It took 27.738 minutes to run this algorithm +""" diff --git a/Problem24.py b/Problem24.py new file mode 100644 index 0000000..b77852f --- /dev/null +++ b/Problem24.py @@ -0,0 +1,53 @@ +#ProjectEuler/Python/Problem24.py +#Matthew Ellison +# Created: 03-24-19 +#Modified: 03-28-19 +#What is the millionth lexicographic permutation of the digits 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9? +#Unless otherwise listed, all of my non-standard imports can be gotten from my pyClasses repository at https://bitbucket.org/Mattrixwv/pyClasses +""" + Copyright (C) 2019 Matthew Ellison + + This program is free software: you can redistribute it and/or modify + it under the terms of the GNU Lesser General Public License as published by + the Free Software Foundation, either version 3 of the License, or + (at your option) any later version. + + This program is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the + GNU Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public License + along with this program. If not, see . +""" + + +from Stopwatch import Stopwatch +import Algorithms + +__neededPerm = 1000000 #The number of the permutation that you need + + +def Problem24(): + #Setup the variables + nums = "0123456789" + + #Get all permutations of the string + permutations = Algorithms.getPermutations(nums) + + #Print the results + print("The 1 millionth permutation is " + str(permutations[__neededPerm - 1])) + + +#This calls the appropriate functions if the script is called stand alone +if __name__ == "__main__": + timer = Stopwatch() + timer.start() + Problem24() + timer.stop() + print("It took " + timer.getString() + " to run this algorithm") + +""" Results: +The 1 millionth permutation is 2783915460 +It took 7.363 seconds to run this algorithm +""" diff --git a/Problem25.py b/Problem25.py new file mode 100644 index 0000000..b1d9256 --- /dev/null +++ b/Problem25.py @@ -0,0 +1,59 @@ +#ProjectEuler/Python/Problem25.py +#Matthew Ellison +# Created: 03-25-19 +#Modified: 03-28-19 +#What is the index of the first term in the Fibonacci sequence to contain 1000 digits? +#Unless otherwise listed, all of my non-standard imports can be gotten from my pyClasses repository at https://bitbucket.org/Mattrixwv/pyClasses +""" + Copyright (C) 2019 Matthew Ellison + + This program is free software: you can redistribute it and/or modify + it under the terms of the GNU Lesser General Public License as published by + the Free Software Foundation, either version 3 of the License, or + (at your option) any later version. + + This program is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the + GNU Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public License + along with this program. If not, see . +""" + + +from Stopwatch import Stopwatch +import Algorithms + + +__numDigits = 1000 #The number of digits to calculate up to + + +def Problem25(): + #Setup the variables + number = 0 #The current Fibonacci number + index = 2 #The index of the just calculated Fibonacci number + + #Move through all Fibonacci numbers until you reach the one with at least __numDigits digits + while(len(str(number)) < __numDigits): + index += 1 #Increase the index number. Doing this at the beginning keeps the index correct at the end of the loop + number = Algorithms.getFib(index) #Calculate the number + + #Print the results + print("The first Fibonacci number with " + str(__numDigits) + " digits is " + str(number)) + print("Its index is " + str(index)) + + +#This runs the appropriate functions if the script is called by itself +if __name__ == "__main__": + timer = Stopwatch() + timer.start() + Problem25() + timer.stop() + print("It took " + timer.getString() + " to run this algorithm") + +""" Results: +The first Fibonacci number with 1000 digits is 1070066266382758936764980584457396885083683896632151665013235203375314520604694040621889147582489792657804694888177591957484336466672569959512996030461262748092482186144069433051234774442750273781753087579391666192149259186759553966422837148943113074699503439547001985432609723067290192870526447243726117715821825548491120525013201478612965931381792235559657452039506137551467837543229119602129934048260706175397706847068202895486902666185435124521900369480641357447470911707619766945691070098024393439617474103736912503231365532164773697023167755051595173518460579954919410967778373229665796581646513903488154256310184224190259846088000110186255550245493937113651657039447629584714548523425950428582425306083544435428212611008992863795048006894330309773217834864543113205765659868456288616808718693835297350643986297640660000723562917905207051164077614812491885830945940566688339109350944456576357666151619317753792891661581327159616877487983821820492520348473874384736771934512787029218636250627816 +Its index is 4782 +It took 4.216 seconds to run this algorithm +""" diff --git a/Problem26.py b/Problem26.py new file mode 100644 index 0000000..9b3bee6 --- /dev/null +++ b/Problem26.py @@ -0,0 +1,84 @@ +#ProjectEuler/Python/Problem26.py +#Matthew Ellison +# Created: 07-29-19 +#Modified: 08-02-19 +#Find the value of d < 1000 for which 1/d contains the longest recurring cycle in its decimal fraction part. +#Unless otherwise listed, all of my non-standard imports can be gotten from my pyClasses repository at https://bitbucket.org/Mattrixwv/pyClasses +""" + Copyright (C) 2019 Matthew Ellison + + This program is free software: you can redistribute it and/or modify + it under the terms of the GNU Lesser General Public License as published by + the Free Software Foundation, either version 3 of the License, or + (at your option) any later version. + + This program is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the + GNU Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public License + along with this program. If not, see . +""" + + +from Stopwatch import Stopwatch +import Algorithms + + +__topNumber = 999 #The largest denominator to be checked + + +def Problem26(): + longestCycle = 0 + longestNumber = 1 + #Start with 1/2 and find out how long the longest cycle is by checking the remainders + #Loop through every number from 2-999 and use it for the denominator + for denominator in range(2, __topNumber): + remainderList = [] #Holds the list of remainders + endFound = False #Holds whether we have found an end to the number (either a cycle or a 0 for remainder) + cycleFound = False #Holds whether a cycle was detected + numerator = 1 #The numerator that will be divided + while(not endFound): + #Get the remainder after the division + remainder = numerator % denominator + #Check if the remainder is 0 + #If it is set the flag + if(remainder == 0): + endFound = True + #Check if the remainder is in the list + #If it is in the list, set the appropriate flags + elif remainder in remainderList: + endFound = True + cycleFound = True + #Else add it to the list + else: + remainderList.append(remainder) + + #Multiply the remainder by 10 to continue finding the next remainder + numerator = remainder * 10 + #If a cycle was found check the size of the list against the largest cycle + if(cycleFound): + #If it is larger than the largest, set it as the new largest + if(len(remainderList) > longestCycle): + longestCycle = len(remainderList) + longestNumber = denominator + + #Print the results + print("The longest cycle is " + str(longestCycle) + " digits long") + print("It is started with the number " + str(longestNumber)) + + +#This calls the appropriate functions if the script is called stand along +if __name__ == "__main__": + timer = Stopwatch() + timer.start() + Problem26() + timer.stop() + print("It took " + timer.getString() + " to run this algorithm") + +""" Results: +The longest cycle is 982 digits long +It is started with the number 983 +It took 182.704 milliseconds to run this algorithm +""" diff --git a/Problem27.py b/Problem27.py new file mode 100644 index 0000000..06fa3f3 --- /dev/null +++ b/Problem27.py @@ -0,0 +1,71 @@ +#ProjectEuler/Python/Problem27.py +#Matthew Ellison +# Created: 09-15-19 +#Modified: 09-15-19 +#Find the product of the coefficients, |a| < 1000 and |b| <= 1000, for the quadratic expression that produces the maximum number of primes for consecutive values of n, starting with n=0. +#Unless otherwise listed, all of my non-standard imports can be gotten from my pyClasses repository at https://bitbucket.org/Mattrixwv/pyClasses +""" + Copyright (C) 2019 Matthew Ellison + + This program is free software: you can redistribute it and/or modify + it under the terms of the GNU Lesser General Public License as published by + the Free Software Foundation, either version 3 of the License, or + (at your option) any later version. + + This program is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the + GNU Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public License + along with this program. If not, see . +""" + + +from Stopwatch import Stopwatch +import Algorithms + + +def Problem27(): + #Setup the variables + topA = 0 #The A for the most n's generated + topB = 0 #The B for the most n's generated + topN = 0 #The most n's generated + primes = Algorithms.getPrimes(12000) #A list of all primes that could possibly be generated with this formula + + #Start with the lowest possible A and check all possibilities after that + for a in range(-999, 999): + #Start with the lowest possible B and check all possibilities after that + for b in range(-1000, 1000): + #Start with n=0 and check the formula to see how many primes you can get get with concecutive n's + n = 0 + quadratic = (n * n) + (a * n) + b + while(quadratic in primes): + n += 1 + quadratic = (n * n) + (a * n) + b + n -= 1 #Negate an n because the last formula failed + + #Set all the largest numbers if this created more primes than any other + if(n > topN): + topN = n + topB = b + topA = a + print("The greatest number of primes found is " + str(topN)) + print("It was found with A = " + str(topA) + ", B = " + str(topB)) + print("The product of A and B is " + str(topA * topB)) + + +#This calls the appropriate functions if the script is called stand alone +if __name__ == "__main__": + timer = Stopwatch() + timer.start() + Problem27() + timer.stop() + print("It took " + timer.getString() + " to run this algorithm") + +""" Results: +The greatest number of primes found is 70 +It was found with A = -61, B = 971 +The product of A and B is -59231 +It took 35.775 seconds to run this algorithm +""" diff --git a/Problem28.py b/Problem28.py new file mode 100644 index 0000000..d9068c3 --- /dev/null +++ b/Problem28.py @@ -0,0 +1,109 @@ +#ProjectEuler/Python/Problem28.py +#Matthew Ellison +# Created: 09-22-19 +#Modified: 09-22-19 +#What is the sum of the numbers on the diagonals in a 1001 by 1001 spiral formed by starting with the number 1 and moving to the right in a clockwise direction a 5 by 5 spiral +#Unless otherwise listed, all of my non-standard imports can be gotten from my pyClasses repository at https://bitbucket.org/Mattrixwv/pyClasses +""" + Copyright (C) 2019 Matthew Ellison + + This program is free software: you can redistribute it and/or modify + it under the terms of the GNU Lesser General Public License as published by + the Free Software Foundation, either version 3 of the License, or + (at your option) any later version. + + This program is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the + GNU Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public License + along with this program. If not, see . +""" + + +from Stopwatch import Stopwatch + + +def setupGrid() -> list: + #Setup the grid to be the right size and fill it with 0's + grid = [[0 for x in range(1001)] for y in range(1001)] + + finalLocation = False #A flag to indicate if the final location to be filled has been reached + currentNum = 1 #Set the number that is going to be put at each location + #Start with the middle location and set it correctly and advance the tracker to the next number + xLocation = 500 + yLocation = 500 + grid[yLocation][xLocation] = currentNum + currentNum += 1 + #Move right the first time + xLocation += 1 + #Move in a circular pattern until you reach the final location + while(not finalLocation): + #Move down until you reach a blank location on the left + while(grid[yLocation][xLocation - 1] != 0): + grid[yLocation][xLocation] = currentNum + currentNum += 1 + yLocation += 1 + + #Move left until you reach a blank location above + while(grid[yLocation - 1][xLocation] != 0): + grid[yLocation][xLocation] = currentNum + currentNum += 1 + xLocation -= 1 + + #Move up until you reach a blank location to the right + while(grid[yLocation][xLocation + 1] != 0): + grid[yLocation][xLocation] = currentNum + currentNum += 1 + yLocation -= 1 + + #Move right until you reach a blank location below + while(grid[yLocation + 1][xLocation] != 0): + grid[yLocation][xLocation] = currentNum + currentNum += 1 + xLocation += 1 + #Check if you are at the final location and break the loop if you are + if(xLocation == len(grid)): + finalLocation = True + break + return grid + +def findSum(grid: list) -> int: + sumOfDiagonals = 0 + leftSide = 0 + rightSide = len(grid) - 1 + row = 0 + while(row < len(grid)): + #This ensure the middle location is only counted once + if(leftSide == rightSide): + sumOfDiagonals += grid[row][leftSide] + else: + sumOfDiagonals += grid[row][leftSide] + sumOfDiagonals += grid[row][rightSide] + row += 1 + leftSide += 1 + rightSide -= 1 + return sumOfDiagonals + +def Problem28(): + #Setup the grid + grid = setupGrid() + #Find the sum of the diagonals in the grid + diagSum = findSum(grid) + + #Print the results + print("The sum of the diagonals in the given grid is " + str(diagSum)) + +#This calls the appropriate functions if the script is called stand alone +if __name__ == "__main__": + timer = Stopwatch() + timer.start() + Problem28() + timer.stop() + print("It took " + timer.getString() + " to run this algorithm") + +""" Results: +The sum of the diagonals in the given grid is 669171001 +It took 197.764 milliseconds to run this algorithm +""" diff --git a/Problem29.py b/Problem29.py new file mode 100644 index 0000000..0e142eb --- /dev/null +++ b/Problem29.py @@ -0,0 +1,62 @@ +#ProjectEuler/Python/Problem29.py +#Matthew Ellison +# Created: 10-10-19 +#Modified: 10-10-19 +#How many distinct terms are in the sequence generated by a^b for 2 <= a <= 100 and 2 <= b <= 100? +#Unless otherwise listed, all of my non-standard imports can be gotten from my pyClasses repository at https://bitbucket.org/Mattrixwv/pyClasses +""" + Copyright (C) 2019 Matthew Ellison + + This program is free software: you can redistribute it and/or modify + it under the terms of the GNU Lesser General Public License as published by + the Free Software Foundation, either version 3 of the License, or + (at your option) any later version. + + This program is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the + GNU Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public License + along with this program. If not, see . +""" + + +from Stopwatch import Stopwatch + + +#Setup the variables +__BOTTOM_A = 2 #The lowest possible value for A +__TOP_A = 100 #The highest possible value for A +__BOTTOM_B = 2 #The lowest possible value for B +__TOP_B = 100 #The highest possible value for B + + +def Problem29(): + unique = [] #This will hold all of the unique answers + + #Start with the first A and move towards the top + for currentA in range(__BOTTOM_A, __TOP_A + 1): + #Start with the first B and move towards the top + for currentB in range(__BOTTOM_B, __TOP_B + 1): + #Get the new number + currentNum = currentA ** currentB + #If the new number isn't in the list add it + if currentNum not in unique: + unique.append(currentNum) + + #Print the results + print("The number of unique values generated by a^b for " + str(__BOTTOM_A) + " <= a < = " + str(__TOP_A) + " and " + str(__BOTTOM_B) + " <= b <= " + str(__TOP_B) + " is " + str(len(unique))) + +#This calls the appropriate functions if the script is called stand alone +if __name__ == "__main__": + timer = Stopwatch() + timer.start() + Problem29() + timer.stop() + print("It took " + timer.getString() + " to run this algorithm") + +""" Results: +The number of unique values generated by a^b for 2 <= a < = 100 and 2 <= b <= 100 is 9183 +It took 304.630 milliseconds to run this algorithm +""" diff --git a/Problem3.py b/Problem3.py new file mode 100644 index 0000000..6797c5a --- /dev/null +++ b/Problem3.py @@ -0,0 +1,51 @@ +#ProjectEuler/Python/Problem3.py +#Matthew Ellison +# Created: 01-27-19 +#Modified: 03-28-19 +#The largest prime factor of 600851475143 +#Unless otherwise listed, all of my non-standard imports can be gotten from my pyClasses repository at https://bitbucket.org/Mattrixwv/pyClasses +""" + Copyright (C) 2019 Matthew Ellison + + This program is free software: you can redistribute it and/or modify + it under the terms of the GNU Lesser General Public License as published by + the Free Software Foundation, either version 3 of the License, or + (at your option) any later version. + + This program is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the + GNU Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public License + along with this program. If not, see . +""" + + +from Stopwatch import Stopwatch +from Algorithms import getFactors + +__targetNumber = 600851475143 + + +def Problem3(): + #Get the factors of the number + factors = getFactors(__targetNumber) + #The largest number will be the answer + #Print the results + print("The largest prime factor of " + str(__targetNumber) + " is " + str(factors[(len(factors) - 1)])) + + +#If you are running this file, automatically start the correct function +if __name__ == '__main__': + timer = Stopwatch() #Used to determine the algorithm's run time + timer.start() #Start the timer + Problem3() #Call the function that answers the question + timer.stop() #Stop the timer + #Print the results of the timer + print("It took " + timer.getString() + " to run this algorithm") + +"""Results: +The largest prime factor of 600851475143 is 6857 +It took 1.685 seconds to run this algorithm +""" diff --git a/Problem30.py b/Problem30.py new file mode 100644 index 0000000..8997680 --- /dev/null +++ b/Problem30.py @@ -0,0 +1,76 @@ +#ProjectEuler/Python/Problem30.py +#Matthew Ellison +# Created: 10-28-19 +#Modified: 10-28-19 +#Find the sum of all the numbers that can be written as the sum of the fifth powers of their digits. +#Unless otherwise listed, all of my non-standard imports can be gotten from my pyClasses repository at https://bitbucket.org/Mattrixwv/pyClasses +""" + Copyright (C) 2019 Matthew Ellison + + This program is free software: you can redistribute it and/or modify + it under the terms of the GNU Lesser General Public License as published by + the Free Software Foundation, either version 3 of the License, or + (at your option) any later version. + + This program is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the + GNU Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public License + along with this program. If not, see . +""" + + +from Stopwatch import Stopwatch + + +#Setup the variables +__TOP_NUM = 1000000 #This is the largest number that will be checked +__BOTTOM_NUM = 2 #Starts with 2 because 0 and 1 don't count +__POWER_RAISED = 5 #This is the power that the digits are raised to + + +#Returns a list with the individual digits of the number passed to it +def getDigits(num: int) -> list: + listOfDigits = [] #This list holds the individual digits of num + #The easiest way to get the individual digits of a number is by converting it to a string + digits = str(num) + #Start with the first digit, convert it to an integer, store it in the list, and move to the next digit + for cnt in range(0, len(digits)): + listOfDigits.append(int(digits[cnt])) + #Return the list of digits + return listOfDigits + +def Problem30(): + sumOfFifthNumbers = [] #This is a list of the numbers that are the sum of the fifth power of their digits + + #Start with the lowest number and increment until you reach the largest number + for currentNum in range(__BOTTOM_NUM, __TOP_NUM): + #Get the digits of the number + digits = getDigits(currentNum) + #Get the sum of the powers + sumOfPowers = 0 + for cnt in range(0, len(digits)): + sumOfPowers += digits[cnt]**__POWER_RAISED + #Check if the sum of the powers is the same as the number + #If it is add it to the list, otherwise continue to the next number + if(sumOfPowers == currentNum): + sumOfFifthNumbers.append(currentNum) + + #Print the results + print("The sum of all the numbers that can be written as the sum of the fifth powers of their digits is " + str(sum(sumOfFifthNumbers))) + + +#This calls the appropriate functions if the script is called stand alone +if __name__ == "__main__": + timer = Stopwatch() + timer.start() + Problem30() + timer.stop() + print("It took " + timer.getString() + " to run this algorithm") + +""" Results: +The sum of all the numbers that can be written as the sum of the fifth powers of their digits is 443839 +It took 3.284 seconds to run this algorithm +""" diff --git a/Problem4.py b/Problem4.py new file mode 100644 index 0000000..3cac34b --- /dev/null +++ b/Problem4.py @@ -0,0 +1,63 @@ +#ProjectEuler/Python/Problem4.py +#Matthew Ellison +# Created: 01-28-19 +#Modified: 03-28-19 +#Find the largest palindrome made from the product of two 3-digit numbers +#Unless otherwise listed, all of my non-standard imports can be gotten from my pyClasses repository at https://bitbucket.org/Mattrixwv/pyClasses +""" + Copyright (C) 2019 Matthew Ellison + + This program is free software: you can redistribute it and/or modify + it under the terms of the GNU Lesser General Public License as published by + the Free Software Foundation, either version 3 of the License, or + (at your option) any later version. + + This program is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the + GNU Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public License + along with this program. If not, see . +""" + + +from Stopwatch import Stopwatch + +__lowestNum = 100 +__highestNum = 1000 + + +def Problem4(): + #Setup the variables + palindromes = [] #Holds all of the palindromes + currentNum = 0 #Holds the product of the two numbers I am currently working on + + #Loop through every number from __lowestNum to __highestNum twice and multiply every number together + for num1 in range(__lowestNum, __highestNum + 1): + for num2 in range(num1, __highestNum + 1): #You can start at num1 because 100 * 101 == 101 * 100 + currentNum = num1 * num2 + #If the number is a palindrome add it to the list of palindromes, otherwise ignore it + #Using strings makes it easier to determine a palindrome + if(str(currentNum) == str(currentNum)[::-1]): + palindromes.append(currentNum) + + #Sort the palindromes so that the last element is the largest + palindromes.sort() + + #Print the results + print("The largest palindrome made from the product of two 3-digit numbers is " + str(palindromes[len(palindromes) - 1])) + +#If you are running this file, automatically start the correct function +if __name__ == '__main__': + timer = Stopwatch() #Determines the algorithm's run time + timer.start() #Start the timer + Problem4() #Call the function that answers the question + timer.stop() #Stop the timer + #Print the results of the timer + print("It took " + timer.getString() + " to run this algorithm") + +"""Results: +The largest palindrome made from the product of two 3-digit numbers is 906609 +It took 177.314 milliseconds to run this algorithm +""" diff --git a/Problem5.py b/Problem5.py new file mode 100644 index 0000000..f9b17cc --- /dev/null +++ b/Problem5.py @@ -0,0 +1,69 @@ +#ProjectEulter/Python/Project5.py +#Matthew Ellison +# Created: 01-28-19 +#Modified: 03-28-19 +#What is the smallest positive number that is evenly divisible by all of the numbers from 1 to 20? +#Unless otherwise listed, all of my non-standard imports can be gotten from my pyClasses repository at https://bitbucket.org/Mattrixwv/pyClasses +""" + Copyright (C) 2019 Matthew Ellison + + This program is free software: you can redistribute it and/or modify + it under the terms of the GNU Lesser General Public License as published by + the Free Software Foundation, either version 3 of the License, or + (at your option) any later version. + + This program is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the + GNU Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public License + along with this program. If not, see . +""" + + +from Stopwatch import Stopwatch + +__startNum = 1 +__stopNum = 20 + + +def Problem5(): + #Setup the variables + numFound = False #Holds whether we have found the divisible number yet + #Start at 20 and loop through all numbers until you find one that works + #It must be at least 20 to be divisible by 20 + num = 20 #Holds the number that you are currently checking against + while((not numFound) and (num > 0)): #Set an escape, just in case there is no answer and you overflow + #Set that you found the number to true, because you set this flag when you don't find it + numFound = True + #See if the current number is divisible by all numbers from 1 to 20 + for divisor in range(__startNum, __stopNum + 1): + #If it is not set a flag to move to the next possible number + if((num % divisor) != 0): + numFound = False + break + + #Increment the number by 2 to check the next one if you didn't find the number + if not numFound: + num += 2 + + #Print the results + if(num < 0): + print("There was an error: Could not find a number that fit the criteria") + else: + print("The smallest positive number that is evenly divisible by all numbers 1-20 is " + str(num)) + +#If you are running this file, automatically start the correct function +if __name__ == '__main__': + timer = Stopwatch() #Determines the algorithm's run time + timer.start() #Start the timer + Problem5() #Call the function that answers the question + timer.stop() #Stop the timer + #Print the results of the timer + print("It took " + timer.getString() + " to run this algorithm") + +"""Results: +The smallest positive number that is evenly divisible by all numbers 1-20 is 232792560 +It took 50.236 seconds to run this algorithm +""" \ No newline at end of file diff --git a/Problem6.py b/Problem6.py new file mode 100644 index 0000000..c2f3bc6 --- /dev/null +++ b/Problem6.py @@ -0,0 +1,56 @@ +#ProjectEuler/Python/Problem6.py +#Matthew Ellison +# Created: 01-28-19 +#Modified: 03-28-19 +#Find the difference between the sum of the squares of the first one hundred natural numbers and the square of the sum +#Unless otherwise listed, all of my non-standard imports can be gotten from my pyClasses repository at https://bitbucket.org/Mattrixwv/pyClasses +""" + Copyright (C) 2019 Matthew Ellison + + This program is free software: you can redistribute it and/or modify + it under the terms of the GNU Lesser General Public License as published by + the Free Software Foundation, either version 3 of the License, or + (at your option) any later version. + + This program is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the + GNU Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public License + along with this program. If not, see . +""" + + +from Stopwatch import Stopwatch #To time the algorithm + + +def Problem6(): + #Setup the variables + sumOfSquares = 0 #Holds the sum of the square of the numbers + squareOfSum = 0 #Holds the square of the sum of the numbers + + #Run through all numbers from 1-100 and add them to the approriate sums + for num in range(1, 101): + sumOfSquares += num * num #Get the sum of the squares of the first 100 natural numbers + squareOfSum += num #Get the sum of the first 100 natural numbers so you can square it later + + #Square the normal sum + squareOfSum *= squareOfSum + + #Print the result + print("The difference between the sum of the squares and the square of the sum of the numbers 1-100 is " + str(abs(sumOfSquares - squareOfSum))) + +#If you are running this file, automatically start the correct function +if __name__ == '__main__': + timer = Stopwatch() #Determines the algorithm's run time + timer.start() #Start the timer + Problem6() #Call the function that answers the question + timer.stop() #Stop the timer + #Print the results of the timer + print("It took " + timer.getString() + " to run this algorithm") + +"""Results: +The difference between the sum of the squares and the square of the sum of the numbers 1-100 is 25164150 +It took 24.384 microseconds to run this algorithm +""" diff --git a/Problem67.py b/Problem67.py new file mode 100644 index 0000000..fa3a448 --- /dev/null +++ b/Problem67.py @@ -0,0 +1,309 @@ +#ProjectEuler/Python/Problem67.py +#Matthew Ellison +# Created: 03-26-19 +#Modified: 03-28-19 +#Find the maximum total from top to bottom +""" +59 +73 41 +52 40 09 +26 53 06 34 +10 51 87 86 81 +61 95 66 57 25 68 +90 81 80 38 92 67 73 +30 28 51 76 81 18 75 44 +84 14 95 87 62 81 17 78 58 +21 46 71 58 02 79 62 39 31 09 +56 34 35 53 78 31 81 18 90 93 15 +78 53 04 21 84 93 32 13 97 11 37 51 +45 03 81 79 05 18 78 86 13 30 63 99 95 +39 87 96 28 03 38 42 17 82 87 58 07 22 57 +06 17 51 17 07 93 09 07 75 97 95 78 87 08 53 +67 66 59 60 88 99 94 65 55 77 55 34 27 53 78 28 +76 40 41 04 87 16 09 42 75 69 23 97 30 60 10 79 87 +12 10 44 26 21 36 32 84 98 60 13 12 36 16 63 31 91 35 +70 39 06 05 55 27 38 48 28 22 34 35 62 62 15 14 94 89 86 +66 56 68 84 96 21 34 34 34 81 62 40 65 54 62 05 98 03 02 60 +38 89 46 37 99 54 34 53 36 14 70 26 02 90 45 13 31 61 83 73 47 +36 10 63 96 60 49 41 05 37 42 14 58 84 93 96 17 09 43 05 43 06 59 +66 57 87 57 61 28 37 51 84 73 79 15 39 95 88 87 43 39 11 86 77 74 18 +54 42 05 79 30 49 99 73 46 37 50 02 45 09 54 52 27 95 27 65 19 45 26 45 +71 39 17 78 76 29 52 90 18 99 78 19 35 62 71 19 23 65 93 85 49 33 75 09 02 +33 24 47 61 60 55 32 88 57 55 91 54 46 57 07 77 98 52 80 99 24 25 46 78 79 05 +92 09 13 55 10 67 26 78 76 82 63 49 51 31 24 68 05 57 07 54 69 21 67 43 17 63 12 +24 59 06 08 98 74 66 26 61 60 13 03 09 09 24 30 71 08 88 70 72 70 29 90 11 82 41 34 +66 82 67 04 36 60 92 77 91 85 62 49 59 61 30 90 29 94 26 41 89 04 53 22 83 41 09 74 90 +48 28 26 37 28 52 77 26 51 32 18 98 79 36 62 13 17 08 19 54 89 29 73 68 42 14 08 16 70 37 +37 60 69 70 72 71 09 59 13 60 38 13 57 36 09 30 43 89 30 39 15 02 44 73 05 73 26 63 56 86 12 +55 55 85 50 62 99 84 77 28 85 03 21 27 22 19 26 82 69 54 04 13 07 85 14 01 15 70 59 89 95 10 19 +04 09 31 92 91 38 92 86 98 75 21 05 64 42 62 84 36 20 73 42 21 23 22 51 51 79 25 45 85 53 03 43 22 +75 63 02 49 14 12 89 14 60 78 92 16 44 82 38 30 72 11 46 52 90 27 08 65 78 03 85 41 57 79 39 52 33 48 +78 27 56 56 39 13 19 43 86 72 58 95 39 07 04 34 21 98 39 15 39 84 89 69 84 46 37 57 59 35 59 50 26 15 93 +42 89 36 27 78 91 24 11 17 41 05 94 07 69 51 96 03 96 47 90 90 45 91 20 50 56 10 32 36 49 04 53 85 92 25 65 +52 09 61 30 61 97 66 21 96 92 98 90 06 34 96 60 32 69 68 33 75 84 18 31 71 50 84 63 03 03 19 11 28 42 75 45 45 +61 31 61 68 96 34 49 39 05 71 76 59 62 67 06 47 96 99 34 21 32 47 52 07 71 60 42 72 94 56 82 83 84 40 94 87 82 46 +01 20 60 14 17 38 26 78 66 81 45 95 18 51 98 81 48 16 53 88 37 52 69 95 72 93 22 34 98 20 54 27 73 61 56 63 60 34 63 +93 42 94 83 47 61 27 51 79 79 45 01 44 73 31 70 83 42 88 25 53 51 30 15 65 94 80 44 61 84 12 77 02 62 02 65 94 42 14 94 +32 73 09 67 68 29 74 98 10 19 85 48 38 31 85 67 53 93 93 77 47 67 39 72 94 53 18 43 77 40 78 32 29 59 24 06 02 83 50 60 66 +32 01 44 30 16 51 15 81 98 15 10 62 86 79 50 62 45 60 70 38 31 85 65 61 64 06 69 84 14 22 56 43 09 48 66 69 83 91 60 40 36 61 +92 48 22 99 15 95 64 43 01 16 94 02 99 19 17 69 11 58 97 56 89 31 77 45 67 96 12 73 08 20 36 47 81 44 50 64 68 85 40 81 85 52 09 +91 35 92 45 32 84 62 15 19 64 21 66 06 01 52 80 62 59 12 25 88 28 91 50 40 16 22 99 92 79 87 51 21 77 74 77 07 42 38 42 74 83 02 05 +46 19 77 66 24 18 05 32 02 84 31 99 92 58 96 72 91 36 62 99 55 29 53 42 12 37 26 58 89 50 66 19 82 75 12 48 24 87 91 85 02 07 03 76 86 +99 98 84 93 07 17 33 61 92 20 66 60 24 66 40 30 67 05 37 29 24 96 03 27 70 62 13 04 45 47 59 88 43 20 66 15 46 92 30 04 71 66 78 70 53 99 +67 60 38 06 88 04 17 72 10 99 71 07 42 25 54 05 26 64 91 50 45 71 06 30 67 48 69 82 08 56 80 67 18 46 66 63 01 20 08 80 47 07 91 16 03 79 87 +18 54 78 49 80 48 77 40 68 23 60 88 58 80 33 57 11 69 55 53 64 02 94 49 60 92 16 35 81 21 82 96 25 24 96 18 02 05 49 03 50 77 06 32 84 27 18 38 +68 01 50 04 03 21 42 94 53 24 89 05 92 26 52 36 68 11 85 01 04 42 02 45 15 06 50 04 53 73 25 74 81 88 98 21 67 84 79 97 99 20 95 04 40 46 02 58 87 +94 10 02 78 88 52 21 03 88 60 06 53 49 71 20 91 12 65 07 49 21 22 11 41 58 99 36 16 09 48 17 24 52 36 23 15 72 16 84 56 02 99 43 76 81 71 29 39 49 17 +64 39 59 84 86 16 17 66 03 09 43 06 64 18 63 29 68 06 23 07 87 14 26 35 17 12 98 41 53 64 78 18 98 27 28 84 80 67 75 62 10 11 76 90 54 10 05 54 41 39 66 +43 83 18 37 32 31 52 29 95 47 08 76 35 11 04 53 35 43 34 10 52 57 12 36 20 39 40 55 78 44 07 31 38 26 08 15 56 88 86 01 52 62 10 24 32 05 60 65 53 28 57 99 +03 50 03 52 07 73 49 92 66 80 01 46 08 67 25 36 73 93 07 42 25 53 13 96 76 83 87 90 54 89 78 22 78 91 73 51 69 09 79 94 83 53 09 40 69 62 10 79 49 47 03 81 30 +71 54 73 33 51 76 59 54 79 37 56 45 84 17 62 21 98 69 41 95 65 24 39 37 62 03 24 48 54 64 46 82 71 78 33 67 09 16 96 68 52 74 79 68 32 21 13 78 96 60 09 69 20 36 +73 26 21 44 46 38 17 83 65 98 07 23 52 46 61 97 33 13 60 31 70 15 36 77 31 58 56 93 75 68 21 36 69 53 90 75 25 82 39 50 65 94 29 30 11 33 11 13 96 02 56 47 07 49 02 +76 46 73 30 10 20 60 70 14 56 34 26 37 39 48 24 55 76 84 91 39 86 95 61 50 14 53 93 64 67 37 31 10 84 42 70 48 20 10 72 60 61 84 79 69 65 99 73 89 25 85 48 92 56 97 16 +03 14 80 27 22 30 44 27 67 75 79 32 51 54 81 29 65 14 19 04 13 82 04 91 43 40 12 52 29 99 07 76 60 25 01 07 61 71 37 92 40 47 99 66 57 01 43 44 22 40 53 53 09 69 26 81 07 +49 80 56 90 93 87 47 13 75 28 87 23 72 79 32 18 27 20 28 10 37 59 21 18 70 04 79 96 03 31 45 71 81 06 14 18 17 05 31 50 92 79 23 47 09 39 47 91 43 54 69 47 42 95 62 46 32 85 +37 18 62 85 87 28 64 05 77 51 47 26 30 65 05 70 65 75 59 80 42 52 25 20 44 10 92 17 71 95 52 14 77 13 24 55 11 65 26 91 01 30 63 15 49 48 41 17 67 47 03 68 20 90 98 32 04 40 68 +90 51 58 60 06 55 23 68 05 19 76 94 82 36 96 43 38 90 87 28 33 83 05 17 70 83 96 93 06 04 78 47 80 06 23 84 75 23 87 72 99 14 50 98 92 38 90 64 61 58 76 94 36 66 87 80 51 35 61 38 +57 95 64 06 53 36 82 51 40 33 47 14 07 98 78 65 39 58 53 06 50 53 04 69 40 68 36 69 75 78 75 60 03 32 39 24 74 47 26 90 13 40 44 71 90 76 51 24 36 50 25 45 70 80 61 80 61 43 90 64 11 +18 29 86 56 68 42 79 10 42 44 30 12 96 18 23 18 52 59 02 99 67 46 60 86 43 38 55 17 44 93 42 21 55 14 47 34 55 16 49 24 23 29 96 51 55 10 46 53 27 92 27 46 63 57 30 65 43 27 21 20 24 83 +81 72 93 19 69 52 48 01 13 83 92 69 20 48 69 59 20 62 05 42 28 89 90 99 32 72 84 17 08 87 36 03 60 31 36 36 81 26 97 36 48 54 56 56 27 16 91 08 23 11 87 99 33 47 02 14 44 73 70 99 43 35 33 +90 56 61 86 56 12 70 59 63 32 01 15 81 47 71 76 95 32 65 80 54 70 34 51 40 45 33 04 64 55 78 68 88 47 31 47 68 87 03 84 23 44 89 72 35 08 31 76 63 26 90 85 96 67 65 91 19 14 17 86 04 71 32 95 +37 13 04 22 64 37 37 28 56 62 86 33 07 37 10 44 52 82 52 06 19 52 57 75 90 26 91 24 06 21 14 67 76 30 46 14 35 89 89 41 03 64 56 97 87 63 22 34 03 79 17 45 11 53 25 56 96 61 23 18 63 31 37 37 47 +77 23 26 70 72 76 77 04 28 64 71 69 14 85 96 54 95 48 06 62 99 83 86 77 97 75 71 66 30 19 57 90 33 01 60 61 14 12 90 99 32 77 56 41 18 14 87 49 10 14 90 64 18 50 21 74 14 16 88 05 45 73 82 47 74 44 +22 97 41 13 34 31 54 61 56 94 03 24 59 27 98 77 04 09 37 40 12 26 87 09 71 70 07 18 64 57 80 21 12 71 83 94 60 39 73 79 73 19 97 32 64 29 41 07 48 84 85 67 12 74 95 20 24 52 41 67 56 61 29 93 35 72 69 +72 23 63 66 01 11 07 30 52 56 95 16 65 26 83 90 50 74 60 18 16 48 43 77 37 11 99 98 30 94 91 26 62 73 45 12 87 73 47 27 01 88 66 99 21 41 95 80 02 53 23 32 61 48 32 43 43 83 14 66 95 91 19 81 80 67 25 88 +08 62 32 18 92 14 83 71 37 96 11 83 39 99 05 16 23 27 10 67 02 25 44 11 55 31 46 64 41 56 44 74 26 81 51 31 45 85 87 09 81 95 22 28 76 69 46 48 64 87 67 76 27 89 31 11 74 16 62 03 60 94 42 47 09 34 94 93 72 +56 18 90 18 42 17 42 32 14 86 06 53 33 95 99 35 29 15 44 20 49 59 25 54 34 59 84 21 23 54 35 90 78 16 93 13 37 88 54 19 86 67 68 55 66 84 65 42 98 37 87 56 33 28 58 38 28 38 66 27 52 21 81 15 08 22 97 32 85 27 +91 53 40 28 13 34 91 25 01 63 50 37 22 49 71 58 32 28 30 18 68 94 23 83 63 62 94 76 80 41 90 22 82 52 29 12 18 56 10 08 35 14 37 57 23 65 67 40 72 39 93 39 70 89 40 34 07 46 94 22 20 05 53 64 56 30 05 56 61 88 27 +23 95 11 12 37 69 68 24 66 10 87 70 43 50 75 07 62 41 83 58 95 93 89 79 45 39 02 22 05 22 95 43 62 11 68 29 17 40 26 44 25 71 87 16 70 85 19 25 59 94 90 41 41 80 61 70 55 60 84 33 95 76 42 63 15 09 03 40 38 12 03 32 +09 84 56 80 61 55 85 97 16 94 82 94 98 57 84 30 84 48 93 90 71 05 95 90 73 17 30 98 40 64 65 89 07 79 09 19 56 36 42 30 23 69 73 72 07 05 27 61 24 31 43 48 71 84 21 28 26 65 65 59 65 74 77 20 10 81 61 84 95 08 52 23 70 +47 81 28 09 98 51 67 64 35 51 59 36 92 82 77 65 80 24 72 53 22 07 27 10 21 28 30 22 48 82 80 48 56 20 14 43 18 25 50 95 90 31 77 08 09 48 44 80 90 22 93 45 82 17 13 96 25 26 08 73 34 99 06 49 24 06 83 51 40 14 15 10 25 01 +54 25 10 81 30 64 24 74 75 80 36 75 82 60 22 69 72 91 45 67 03 62 79 54 89 74 44 83 64 96 66 73 44 30 74 50 37 05 09 97 70 01 60 46 37 91 39 75 75 18 58 52 72 78 51 81 86 52 08 97 01 46 43 66 98 62 81 18 70 93 73 08 32 46 34 +96 80 82 07 59 71 92 53 19 20 88 66 03 26 26 10 24 27 50 82 94 73 63 08 51 33 22 45 19 13 58 33 90 15 22 50 36 13 55 06 35 47 82 52 33 61 36 27 28 46 98 14 73 20 73 32 16 26 80 53 47 66 76 38 94 45 02 01 22 52 47 96 64 58 52 39 +88 46 23 39 74 63 81 64 20 90 33 33 76 55 58 26 10 46 42 26 74 74 12 83 32 43 09 02 73 55 86 54 85 34 28 23 29 79 91 62 47 41 82 87 99 22 48 90 20 05 96 75 95 04 43 28 81 39 81 01 28 42 78 25 39 77 90 57 58 98 17 36 73 22 63 74 51 +29 39 74 94 95 78 64 24 38 86 63 87 93 06 70 92 22 16 80 64 29 52 20 27 23 50 14 13 87 15 72 96 81 22 08 49 72 30 70 24 79 31 16 64 59 21 89 34 96 91 48 76 43 53 88 01 57 80 23 81 90 79 58 01 80 87 17 99 86 90 72 63 32 69 14 28 88 69 +37 17 71 95 56 93 71 35 43 45 04 98 92 94 84 96 11 30 31 27 31 60 92 03 48 05 98 91 86 94 35 90 90 08 48 19 33 28 68 37 59 26 65 96 50 68 22 07 09 49 34 31 77 49 43 06 75 17 81 87 61 79 52 26 27 72 29 50 07 98 86 01 17 10 46 64 24 18 56 +51 30 25 94 88 85 79 91 40 33 63 84 49 67 98 92 15 26 75 19 82 05 18 78 65 93 61 48 91 43 59 41 70 51 22 15 92 81 67 91 46 98 11 11 65 31 66 10 98 65 83 21 05 56 05 98 73 67 46 74 69 34 08 30 05 52 07 98 32 95 30 94 65 50 24 63 28 81 99 57 +19 23 61 36 09 89 71 98 65 17 30 29 89 26 79 74 94 11 44 48 97 54 81 55 39 66 69 45 28 47 13 86 15 76 74 70 84 32 36 33 79 20 78 14 41 47 89 28 81 05 99 66 81 86 38 26 06 25 13 60 54 55 23 53 27 05 89 25 23 11 13 54 59 54 56 34 16 24 53 44 06 +13 40 57 72 21 15 60 08 04 19 11 98 34 45 09 97 86 71 03 15 56 19 15 44 97 31 90 04 87 87 76 08 12 30 24 62 84 28 12 85 82 53 99 52 13 94 06 65 97 86 09 50 94 68 69 74 30 67 87 94 63 07 78 27 80 36 69 41 06 92 32 78 37 82 30 05 18 87 99 72 19 99 +44 20 55 77 69 91 27 31 28 81 80 27 02 07 97 23 95 98 12 25 75 29 47 71 07 47 78 39 41 59 27 76 13 15 66 61 68 35 69 86 16 53 67 63 99 85 41 56 08 28 33 40 94 76 90 85 31 70 24 65 84 65 99 82 19 25 54 37 21 46 33 02 52 99 51 33 26 04 87 02 08 18 96 +54 42 61 45 91 06 64 79 80 82 32 16 83 63 42 49 19 78 65 97 40 42 14 61 49 34 04 18 25 98 59 30 82 72 26 88 54 36 21 75 03 88 99 53 46 51 55 78 22 94 34 40 68 87 84 25 30 76 25 08 92 84 42 61 40 38 09 99 40 23 29 39 46 55 10 90 35 84 56 70 63 23 91 39 +52 92 03 71 89 07 09 37 68 66 58 20 44 92 51 56 13 71 79 99 26 37 02 06 16 67 36 52 58 16 79 73 56 60 59 27 44 77 94 82 20 50 98 33 09 87 94 37 40 83 64 83 58 85 17 76 53 02 83 52 22 27 39 20 48 92 45 21 09 42 24 23 12 37 52 28 50 78 79 20 86 62 73 20 59 +54 96 80 15 91 90 99 70 10 09 58 90 93 50 81 99 54 38 36 10 30 11 35 84 16 45 82 18 11 97 36 43 96 79 97 65 40 48 23 19 17 31 64 52 65 65 37 32 65 76 99 79 34 65 79 27 55 33 03 01 33 27 61 28 66 08 04 70 49 46 48 83 01 45 19 96 13 81 14 21 31 79 93 85 50 05 +92 92 48 84 59 98 31 53 23 27 15 22 79 95 24 76 05 79 16 93 97 89 38 89 42 83 02 88 94 95 82 21 01 97 48 39 31 78 09 65 50 56 97 61 01 07 65 27 21 23 14 15 80 97 44 78 49 35 33 45 81 74 34 05 31 57 09 38 94 07 69 54 69 32 65 68 46 68 78 90 24 28 49 51 45 86 35 +41 63 89 76 87 31 86 09 46 14 87 82 22 29 47 16 13 10 70 72 82 95 48 64 58 43 13 75 42 69 21 12 67 13 64 85 58 23 98 09 37 76 05 22 31 12 66 50 29 99 86 72 45 25 10 28 19 06 90 43 29 31 67 79 46 25 74 14 97 35 76 37 65 46 23 82 06 22 30 76 93 66 94 17 96 13 20 72 +63 40 78 08 52 09 90 41 70 28 36 14 46 44 85 96 24 52 58 15 87 37 05 98 99 39 13 61 76 38 44 99 83 74 90 22 53 80 56 98 30 51 63 39 44 30 91 91 04 22 27 73 17 35 53 18 35 45 54 56 27 78 48 13 69 36 44 38 71 25 30 56 15 22 73 43 32 69 59 25 93 83 45 11 34 94 44 39 92 +12 36 56 88 13 96 16 12 55 54 11 47 19 78 17 17 68 81 77 51 42 55 99 85 66 27 81 79 93 42 65 61 69 74 14 01 18 56 12 01 58 37 91 22 42 66 83 25 19 04 96 41 25 45 18 69 96 88 36 93 10 12 98 32 44 83 83 04 72 91 04 27 73 07 34 37 71 60 59 31 01 54 54 44 96 93 83 36 04 45 +30 18 22 20 42 96 65 79 17 41 55 69 94 81 29 80 91 31 85 25 47 26 43 49 02 99 34 67 99 76 16 14 15 93 08 32 99 44 61 77 67 50 43 55 87 55 53 72 17 46 62 25 50 99 73 05 93 48 17 31 70 80 59 09 44 59 45 13 74 66 58 94 87 73 16 14 85 38 74 99 64 23 79 28 71 42 20 37 82 31 23 +51 96 39 65 46 71 56 13 29 68 53 86 45 33 51 49 12 91 21 21 76 85 02 17 98 15 46 12 60 21 88 30 92 83 44 59 42 50 27 88 46 86 94 73 45 54 23 24 14 10 94 21 20 34 23 51 04 83 99 75 90 63 60 16 22 33 83 70 11 32 10 50 29 30 83 46 11 05 31 17 86 42 49 01 44 63 28 60 07 78 95 40 +44 61 89 59 04 49 51 27 69 71 46 76 44 04 09 34 56 39 15 06 94 91 75 90 65 27 56 23 74 06 23 33 36 69 14 39 05 34 35 57 33 22 76 46 56 10 61 65 98 09 16 69 04 62 65 18 99 76 49 18 72 66 73 83 82 40 76 31 89 91 27 88 17 35 41 35 32 51 32 67 52 68 74 85 80 57 07 11 62 66 47 22 67 +65 37 19 97 26 17 16 24 24 17 50 37 64 82 24 36 32 11 68 34 69 31 32 89 79 93 96 68 49 90 14 23 04 04 67 99 81 74 70 74 36 96 68 09 64 39 88 35 54 89 96 58 66 27 88 97 32 14 06 35 78 20 71 06 85 66 57 02 58 91 72 05 29 56 73 48 86 52 09 93 22 57 79 42 12 01 31 68 17 59 63 76 07 77 +73 81 14 13 17 20 11 09 01 83 08 85 91 70 84 63 62 77 37 07 47 01 59 95 39 69 39 21 99 09 87 02 97 16 92 36 74 71 90 66 33 73 73 75 52 91 11 12 26 53 05 26 26 48 61 50 90 65 01 87 42 47 74 35 22 73 24 26 56 70 52 05 48 41 31 18 83 27 21 39 80 85 26 08 44 02 71 07 63 22 05 52 19 08 20 +17 25 21 11 72 93 33 49 64 23 53 82 03 13 91 65 85 02 40 05 42 31 77 42 05 36 06 54 04 58 07 76 87 83 25 57 66 12 74 33 85 37 74 32 20 69 03 97 91 68 82 44 19 14 89 28 85 85 80 53 34 87 58 98 88 78 48 65 98 40 11 57 10 67 70 81 60 79 74 72 97 59 79 47 30 20 54 80 89 91 14 05 33 36 79 39 +60 85 59 39 60 07 57 76 77 92 06 35 15 72 23 41 45 52 95 18 64 79 86 53 56 31 69 11 91 31 84 50 44 82 22 81 41 40 30 42 30 91 48 94 74 76 64 58 74 25 96 57 14 19 03 99 28 83 15 75 99 01 89 85 79 50 03 95 32 67 44 08 07 41 62 64 29 20 14 76 26 55 48 71 69 66 19 72 44 25 14 01 48 74 12 98 07 +64 66 84 24 18 16 27 48 20 14 47 69 30 86 48 40 23 16 61 21 51 50 26 47 35 33 91 28 78 64 43 68 04 79 51 08 19 60 52 95 06 68 46 86 35 97 27 58 04 65 30 58 99 12 12 75 91 39 50 31 42 64 70 04 46 07 98 73 98 93 37 89 77 91 64 71 64 65 66 21 78 62 81 74 42 20 83 70 73 95 78 45 92 27 34 53 71 15 +30 11 85 31 34 71 13 48 05 14 44 03 19 67 23 73 19 57 06 90 94 72 57 69 81 62 59 68 88 57 55 69 49 13 07 87 97 80 89 05 71 05 05 26 38 40 16 62 45 99 18 38 98 24 21 26 62 74 69 04 85 57 77 35 58 67 91 79 79 57 86 28 66 34 72 51 76 78 36 95 63 90 08 78 47 63 45 31 22 70 52 48 79 94 15 77 61 67 68 +23 33 44 81 80 92 93 75 94 88 23 61 39 76 22 03 28 94 32 06 49 65 41 34 18 23 08 47 62 60 03 63 33 13 80 52 31 54 73 43 70 26 16 69 57 87 83 31 03 93 70 81 47 95 77 44 29 68 39 51 56 59 63 07 25 70 07 77 43 53 64 03 94 42 95 39 18 01 66 21 16 97 20 50 90 16 70 10 95 69 29 06 25 61 41 26 15 59 63 35 +""" +#Unless otherwise listed, all of my non-standard imports can be gotten from my pyClasses repository at https://bitbucket.org/Mattrixwv/pyClasses +""" + Copyright (C) 2019 Matthew Ellison + + This program is free software: you can redistribute it and/or modify + it under the terms of the GNU Lesser General Public License as published by + the Free Software Foundation, either version 3 of the License, or + (at your option) any later version. + + This program is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the + GNU Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public License + along with this program. If not, see . +""" + + +from Stopwatch import Stopwatch +from collections import namedtuple + + +location = namedtuple("location", "xLocation yLocation total fromRight") + +NUM_ROWS = 100 + + +def invert(listNum): + for rowCnt in range(0, NUM_ROWS): + for colCnt in range(0, len(listNum[rowCnt])): + listNum[rowCnt][colCnt] = 100 - listNum[rowCnt][colCnt] + +def removeIf(listNum: list, loc): + location = 0 + while(location < len(listNum)): + if((listNum[location].xLocation == loc.xLocation) and (listNum[location].yLocation == loc.yLocation)): + del listNum[location] + else: + location += 1 + +def Problem67(): + listNum = [[59], + [73, 41], + [52, 40, 9], + [26, 53, 6, 34], + [10, 51, 87, 86, 81], + [61, 95, 66, 57, 25, 68], + [90, 81, 80, 38, 92, 67, 73], + [30, 28, 51, 76, 81, 18, 75, 44], + [84, 14, 95, 87, 62, 81, 17, 78, 58], + [21, 46, 71, 58, 2, 79, 62, 39, 31, 9], + [56, 34, 35, 53, 78, 31, 81, 18, 90, 93, 15], + [78, 53, 4, 21, 84, 93, 32, 13, 97, 11, 37, 51], + [45, 3, 81, 79, 5, 18, 78, 86, 13, 30, 63, 99, 95], + [39, 87, 96, 28, 3, 38, 42, 17, 82, 87, 58, 7, 22, 57], + [ 6, 17, 51, 17, 7, 93, 9, 7, 75, 97, 95, 78, 87, 8, 53], + [67, 66, 59, 60, 88, 99, 94, 65, 55, 77, 55, 34, 27, 53, 78, 28], + [76, 40, 41, 4, 87, 16, 9, 42, 75, 69, 23, 97, 30, 60, 10, 79, 87], + [12, 10, 44, 26, 21, 36, 32, 84, 98, 60, 13, 12, 36, 16, 63, 31, 91, 35], + [70, 39, 6, 5, 55, 27, 38, 48, 28, 22, 34, 35, 62, 62, 15, 14, 94, 89, 86], + [66, 56, 68, 84, 96, 21, 34, 34, 34, 81, 62, 40, 65, 54, 62, 5, 98, 3, 2, 60], + [38, 89, 46, 37, 99, 54, 34, 53, 36, 14, 70, 26, 2, 90, 45, 13, 31, 61, 83, 73, 47], + [36, 10, 63, 96, 60, 49, 41, 5, 37, 42, 14, 58, 84, 93, 96, 17, 9, 43, 5, 43, 6, 59], + [66, 57, 87, 57, 61, 28, 37, 51, 84, 73, 79, 15, 39, 95, 88, 87, 43, 39, 11, 86, 77, 74, 18], + [54, 42, 5, 79, 30, 49, 99, 73, 46, 37, 50, 2, 45, 9, 54, 52, 27, 95, 27, 65, 19, 45, 26, 45], + [71, 39, 17, 78, 76, 29, 52, 90, 18, 99, 78, 19, 35, 62, 71, 19, 23, 65, 93, 85, 49, 33, 75, 9, 2], + [33, 24, 47, 61, 60, 55, 32, 88, 57, 55, 91, 54, 46, 57, 7, 77, 98, 52, 80, 99, 24, 25, 46, 78, 79, 5], + [92, 9, 13, 55, 10, 67, 26, 78, 76, 82, 63, 49, 51, 31, 24, 68, 5, 57, 7, 54, 69, 21, 67, 43, 17, 63, 12], + [24, 59, 6, 8, 98, 74, 66, 26, 61, 60, 13, 3, 9, 9, 24, 30, 71, 8, 88, 70, 72, 70, 29, 90, 11, 82, 41, 34], + [66, 82, 67, 4, 36, 60, 92, 77, 91, 85, 62, 49, 59, 61, 30, 90, 29, 94, 26, 41, 89, 4, 53, 22, 83, 41, 9, 74, 90], + [48, 28, 26, 37, 28, 52, 77, 26, 51, 32, 18, 98, 79, 36, 62, 13, 17, 8, 19, 54, 89, 29, 73, 68, 42, 14, 8, 16, 70, 37], + [37, 60, 69, 70, 72, 71, 9, 59, 13, 60, 38, 13, 57, 36, 9, 30, 43, 89, 30, 39, 15, 2, 44, 73, 5, 73, 26, 63, 56, 86, 12], + [55, 55, 85, 50, 62, 99, 84, 77, 28, 85, 3, 21, 27, 22, 19, 26, 82, 69, 54, 4, 13, 7, 85, 14, 1, 15, 70, 59, 89, 95, 10, 19], + [ 4, 9, 31, 92, 91, 38, 92, 86, 98, 75, 21, 5, 64, 42, 62, 84, 36, 20, 73, 42, 21, 23, 22, 51, 51, 79, 25, 45, 85, 53, 3, 43, 22], + [75, 63, 2, 49, 14, 12, 89, 14, 60, 78, 92, 16, 44, 82, 38, 30, 72, 11, 46, 52, 90, 27, 8, 65, 78, 3, 85, 41, 57, 79, 39, 52, 33, 48], + [78, 27, 56, 56, 39, 13, 19, 43, 86, 72, 58, 95, 39, 7, 4, 34, 21, 98, 39, 15, 39, 84, 89, 69, 84, 46, 37, 57, 59, 35, 59, 50, 26, 15, 93], + [42, 89, 36, 27, 78, 91, 24, 11, 17, 41, 5, 94, 7, 69, 51, 96, 3, 96, 47, 90, 90, 45, 91, 20, 50, 56, 10, 32, 36, 49, 4, 53, 85, 92, 25, 65], + [52, 9, 61, 30, 61, 97, 66, 21, 96, 92, 98, 90, 6, 34, 96, 60, 32, 69, 68, 33, 75, 84, 18, 31, 71, 50, 84, 63, 3, 3, 19, 11, 28, 42, 75, 45, 45], + [61, 31, 61, 68, 96, 34, 49, 39, 5, 71, 76, 59, 62, 67, 6, 47, 96, 99, 34, 21, 32, 47, 52, 7, 71, 60, 42, 72, 94, 56, 82, 83, 84, 40, 94, 87, 82, 46], + [ 1, 20, 60, 14, 17, 38, 26, 78, 66, 81, 45, 95, 18, 51, 98, 81, 48, 16, 53, 88, 37, 52, 69, 95, 72, 93, 22, 34, 98, 20, 54, 27, 73, 61, 56, 63, 60, 34, 63], + [93, 42, 94, 83, 47, 61, 27, 51, 79, 79, 45, 1, 44, 73, 31, 70, 83, 42, 88, 25, 53, 51, 30, 15, 65, 94, 80, 44, 61, 84, 12, 77, 2, 62, 2, 65, 94, 42, 14, 94], + [32, 73, 9, 67, 68, 29, 74, 98, 10, 19, 85, 48, 38, 31, 85, 67, 53, 93, 93, 77, 47, 67, 39, 72, 94, 53, 18, 43, 77, 40, 78, 32, 29, 59, 24, 6, 2, 83, 50, 60, 66], + [32, 1, 44, 30, 16, 51, 15, 81, 98, 15, 10, 62, 86, 79, 50, 62, 45, 60, 70, 38, 31, 85, 65, 61, 64, 6, 69, 84, 14, 22, 56, 43, 9, 48, 66, 69, 83, 91, 60, 40, 36, 61], + [92, 48, 22, 99, 15, 95, 64, 43, 1, 16, 94, 2, 99, 19, 17, 69, 11, 58, 97, 56, 89, 31, 77, 45, 67, 96, 12, 73, 8, 20, 36, 47, 81, 44, 50, 64, 68, 85, 40, 81, 85, 52, 9], + [91, 35, 92, 45, 32, 84, 62, 15, 19, 64, 21, 66, 6, 1, 52, 80, 62, 59, 12, 25, 88, 28, 91, 50, 40, 16, 22, 99, 92, 79, 87, 51, 21, 77, 74, 77, 7, 42, 38, 42, 74, 83, 2, 5], + [46, 19, 77, 66, 24, 18, 5, 32, 2, 84, 31, 99, 92, 58, 96, 72, 91, 36, 62, 99, 55, 29, 53, 42, 12, 37, 26, 58, 89, 50, 66, 19, 82, 75, 12, 48, 24, 87, 91, 85, 2, 7, 3, 76, 86], + [99, 98, 84, 93, 7, 17, 33, 61, 92, 20, 66, 60, 24, 66, 40, 30, 67, 5, 37, 29, 24, 96, 3, 27, 70, 62, 13, 4, 45, 47, 59, 88, 43, 20, 66, 15, 46, 92, 30, 4, 71, 66, 78, 70, 53, 99], + [67, 60, 38, 6, 88, 4, 17, 72, 10, 99, 71, 7, 42, 25, 54, 5, 26, 64, 91, 50, 45, 71, 6, 30, 67, 48, 69, 82, 8, 56, 80, 67, 18, 46, 66, 63, 1, 20, 8, 80, 47, 7, 91, 16, 3, 79, 87], + [18, 54, 78, 49, 80, 48, 77, 40, 68, 23, 60, 88, 58, 80, 33, 57, 11, 69, 55, 53, 64, 2, 94, 49, 60, 92, 16, 35, 81, 21, 82, 96, 25, 24, 96, 18, 2, 5, 49, 3, 50, 77, 6, 32, 84, 27, 18, 38], + [68, 1, 50, 4, 3, 21, 42, 94, 53, 24, 89, 5, 92, 26, 52, 36, 68, 11, 85, 1, 4, 42, 2, 45, 15, 6, 50, 4, 53, 73, 25, 74, 81, 88, 98, 21, 67, 84, 79, 97, 99, 20, 95, 4, 40, 46, 2, 58, 87], + [94, 10, 2, 78, 88, 52, 21, 3, 88, 60, 6, 53, 49, 71, 20, 91, 12, 65, 7, 49, 21, 22, 11, 41, 58, 99, 36, 16, 9, 48, 17, 24, 52, 36, 23, 15, 72, 16, 84, 56, 2, 99, 43, 76, 81, 71, 29, 39, 49, 17], + [64, 39, 59, 84, 86, 16, 17, 66, 3, 9, 43, 6, 64, 18, 63, 29, 68, 6, 23, 7, 87, 14, 26, 35, 17, 12, 98, 41, 53, 64, 78, 18, 98, 27, 28, 84, 80, 67, 75, 62, 10, 11, 76, 90, 54, 10, 5, 54, 41, 39, 66], + [43, 83, 18, 37, 32, 31, 52, 29, 95, 47, 8, 76, 35, 11, 4, 53, 35, 43, 34, 10, 52, 57, 12, 36, 20, 39, 40, 55, 78, 44, 7, 31, 38, 26, 8, 15, 56, 88, 86, 1, 52, 62, 10, 24, 32, 5, 60, 65, 53, 28, 57, 99], + [ 3, 50, 3, 52, 7, 73, 49, 92, 66, 80, 1, 46, 8, 67, 25, 36, 73, 93, 7, 42, 25, 53, 13, 96, 76, 83, 87, 90, 54, 89, 78, 22, 78, 91, 73, 51, 69, 9, 79, 94, 83, 53, 9, 40, 69, 62, 10, 79, 49, 47, 3, 81, 30], + [71, 54, 73, 33, 51, 76, 59, 54, 79, 37, 56, 45, 84, 17, 62, 21, 98, 69, 41, 95, 65, 24, 39, 37, 62, 3, 24, 48, 54, 64, 46, 82, 71, 78, 33, 67, 9, 16, 96, 68, 52, 74, 79, 68, 32, 21, 13, 78, 96, 60, 9, 69, 20, 36], + [73, 26, 21, 44, 46, 38, 17, 83, 65, 98, 7, 23, 52, 46, 61, 97, 33, 13, 60, 31, 70, 15, 36, 77, 31, 58, 56, 93, 75, 68, 21, 36, 69, 53, 90, 75, 25, 82, 39, 50, 65, 94, 29, 30, 11, 33, 11, 13, 96, 2, 56, 47, 7, 49, 2], + [76, 46, 73, 30, 10, 20, 60, 70, 14, 56, 34, 26, 37, 39, 48, 24, 55, 76, 84, 91, 39, 86, 95, 61, 50, 14, 53, 93, 64, 67, 37, 31, 10, 84, 42, 70, 48, 20, 10, 72, 60, 61, 84, 79, 69, 65, 99, 73, 89, 25, 85, 48, 92, 56, 97, 16], + [ 3, 14, 80, 27, 22, 30, 44, 27, 67, 75, 79, 32, 51, 54, 81, 29, 65, 14, 19, 4, 13, 82, 4, 91, 43, 40, 12, 52, 29, 99, 7, 76, 60, 25, 1, 7, 61, 71, 37, 92, 40, 47, 99, 66, 57, 1, 43, 44, 22, 40, 53, 53, 9, 69, 26, 81, 7], + [49, 80, 56, 90, 93, 87, 47, 13, 75, 28, 87, 23, 72, 79, 32, 18, 27, 20, 28, 10, 37, 59, 21, 18, 70, 4, 79, 96, 3, 31, 45, 71, 81, 6, 14, 18, 17, 5, 31, 50, 92, 79, 23, 47, 9, 39, 47, 91, 43, 54, 69, 47, 42, 95, 62, 46, 32, 85], + [37, 18, 62, 85, 87, 28, 64, 5, 77, 51, 47, 26, 30, 65, 5, 70, 65, 75, 59, 80, 42, 52, 25, 20, 44, 10, 92, 17, 71, 95, 52, 14, 77, 13, 24, 55, 11, 65, 26, 91, 1, 30, 63, 15, 49, 48, 41, 17, 67, 47, 3, 68, 20, 90, 98, 32, 4, 40, 68], + [90, 51, 58, 60, 6, 55, 23, 68, 5, 19, 76, 94, 82, 36, 96, 43, 38, 90, 87, 28, 33, 83, 5, 17, 70, 83, 96, 93, 6, 4, 78, 47, 80, 6, 23, 84, 75, 23, 87, 72, 99, 14, 50, 98, 92, 38, 90, 64, 61, 58, 76, 94, 36, 66, 87, 80, 51, 35, 61, 38], + [57, 95, 64, 6, 53, 36, 82, 51, 40, 33, 47, 14, 7, 98, 78, 65, 39, 58, 53, 6, 50, 53, 4, 69, 40, 68, 36, 69, 75, 78, 75, 60, 3, 32, 39, 24, 74, 47, 26, 90, 13, 40, 44, 71, 90, 76, 51, 24, 36, 50, 25, 45, 70, 80, 61, 80, 61, 43, 90, 64, 11], + [18, 29, 86, 56, 68, 42, 79, 10, 42, 44, 30, 12, 96, 18, 23, 18, 52, 59, 2, 99, 67, 46, 60, 86, 43, 38, 55, 17, 44, 93, 42, 21, 55, 14, 47, 34, 55, 16, 49, 24, 23, 29, 96, 51, 55, 10, 46, 53, 27, 92, 27, 46, 63, 57, 30, 65, 43, 27, 21, 20, 24, 83], + [81, 72, 93, 19, 69, 52, 48, 1, 13, 83, 92, 69, 20, 48, 69, 59, 20, 62, 5, 42, 28, 89, 90, 99, 32, 72, 84, 17, 8, 87, 36, 3, 60, 31, 36, 36, 81, 26, 97, 36, 48, 54, 56, 56, 27, 16, 91, 8, 23, 11, 87, 99, 33, 47, 2, 14, 44, 73, 70, 99, 43, 35, 33], + [90, 56, 61, 86, 56, 12, 70, 59, 63, 32, 1, 15, 81, 47, 71, 76, 95, 32, 65, 80, 54, 70, 34, 51, 40, 45, 33, 4, 64, 55, 78, 68, 88, 47, 31, 47, 68, 87, 3, 84, 23, 44, 89, 72, 35, 8, 31, 76, 63, 26, 90, 85, 96, 67, 65, 91, 19, 14, 17, 86, 4, 71, 32, 95], + [37, 13, 4, 22, 64, 37, 37, 28, 56, 62, 86, 33, 7, 37, 10, 44, 52, 82, 52, 6, 19, 52, 57, 75, 90, 26, 91, 24, 6, 21, 14, 67, 76, 30, 46, 14, 35, 89, 89, 41, 3, 64, 56, 97, 87, 63, 22, 34, 3, 79, 17, 45, 11, 53, 25, 56, 96, 61, 23, 18, 63, 31, 37, 37, 47], + [77, 23, 26, 70, 72, 76, 77, 4, 28, 64, 71, 69, 14, 85, 96, 54, 95, 48, 6, 62, 99, 83, 86, 77, 97, 75, 71, 66, 30, 19, 57, 90, 33, 1, 60, 61, 14, 12, 90, 99, 32, 77, 56, 41, 18, 14, 87, 49, 10, 14, 90, 64, 18, 50, 21, 74, 14, 16, 88, 5, 45, 73, 82, 47, 74, 44], + [22, 97, 41, 13, 34, 31, 54, 61, 56, 94, 3, 24, 59, 27, 98, 77, 4, 9, 37, 40, 12, 26, 87, 9, 71, 70, 7, 18, 64, 57, 80, 21, 12, 71, 83, 94, 60, 39, 73, 79, 73, 19, 97, 32, 64, 29, 41, 7, 48, 84, 85, 67, 12, 74, 95, 20, 24, 52, 41, 67, 56, 61, 29, 93, 35, 72, 69], + [72, 23, 63, 66, 1, 11, 7, 30, 52, 56, 95, 16, 65, 26, 83, 90, 50, 74, 60, 18, 16, 48, 43, 77, 37, 11, 99, 98, 30, 94, 91, 26, 62, 73, 45, 12, 87, 73, 47, 27, 1, 88, 66, 99, 21, 41, 95, 80, 2, 53, 23, 32, 61, 48, 32, 43, 43, 83, 14, 66, 95, 91, 19, 81, 80, 67, 25, 88], + [ 8, 62, 32, 18, 92, 14, 83, 71, 37, 96, 11, 83, 39, 99, 5, 16, 23, 27, 10, 67, 2, 25, 44, 11, 55, 31, 46, 64, 41, 56, 44, 74, 26, 81, 51, 31, 45, 85, 87, 9, 81, 95, 22, 28, 76, 69, 46, 48, 64, 87, 67, 76, 27, 89, 31, 11, 74, 16, 62, 3, 60, 94, 42, 47, 9, 34, 94, 93, 72], + [56, 18, 90, 18, 42, 17, 42, 32, 14, 86, 6, 53, 33, 95, 99, 35, 29, 15, 44, 20, 49, 59, 25, 54, 34, 59, 84, 21, 23, 54, 35, 90, 78, 16, 93, 13, 37, 88, 54, 19, 86, 67, 68, 55, 66, 84, 65, 42, 98, 37, 87, 56, 33, 28, 58, 38, 28, 38, 66, 27, 52, 21, 81, 15, 8, 22, 97, 32, 85, 27], + [91, 53, 40, 28, 13, 34, 91, 25, 1, 63, 50, 37, 22, 49, 71, 58, 32, 28, 30, 18, 68, 94, 23, 83, 63, 62, 94, 76, 80, 41, 90, 22, 82, 52, 29, 12, 18, 56, 10, 8, 35, 14, 37, 57, 23, 65, 67, 40, 72, 39, 93, 39, 70, 89, 40, 34, 7, 46, 94, 22, 20, 5, 53, 64, 56, 30, 5, 56, 61, 88, 27], + [23, 95, 11, 12, 37, 69, 68, 24, 66, 10, 87, 70, 43, 50, 75, 7, 62, 41, 83, 58, 95, 93, 89, 79, 45, 39, 2, 22, 5, 22, 95, 43, 62, 11, 68, 29, 17, 40, 26, 44, 25, 71, 87, 16, 70, 85, 19, 25, 59, 94, 90, 41, 41, 80, 61, 70, 55, 60, 84, 33, 95, 76, 42, 63, 15, 9, 3, 40, 38, 12, 3, 32], + [ 9, 84, 56, 80, 61, 55, 85, 97, 16, 94, 82, 94, 98, 57, 84, 30, 84, 48, 93, 90, 71, 5, 95, 90, 73, 17, 30, 98, 40, 64, 65, 89, 7, 79, 9, 19, 56, 36, 42, 30, 23, 69, 73, 72, 7, 5, 27, 61, 24, 31, 43, 48, 71, 84, 21, 28, 26, 65, 65, 59, 65, 74, 77, 20, 10, 81, 61, 84, 95, 8, 52, 23, 70], + [47, 81, 28, 9, 98, 51, 67, 64, 35, 51, 59, 36, 92, 82, 77, 65, 80, 24, 72, 53, 22, 7, 27, 10, 21, 28, 30, 22, 48, 82, 80, 48, 56, 20, 14, 43, 18, 25, 50, 95, 90, 31, 77, 8, 9, 48, 44, 80, 90, 22, 93, 45, 82, 17, 13, 96, 25, 26, 8, 73, 34, 99, 6, 49, 24, 6, 83, 51, 40, 14, 15, 10, 25, 1], + [54, 25, 10, 81, 30, 64, 24, 74, 75, 80, 36, 75, 82, 60, 22, 69, 72, 91, 45, 67, 3, 62, 79, 54, 89, 74, 44, 83, 64, 96, 66, 73, 44, 30, 74, 50, 37, 5, 9, 97, 70, 1, 60, 46, 37, 91, 39, 75, 75, 18, 58, 52, 72, 78, 51, 81, 86, 52, 8, 97, 1, 46, 43, 66, 98, 62, 81, 18, 70, 93, 73, 8, 32, 46, 34], + [96, 80, 82, 7, 59, 71, 92, 53, 19, 20, 88, 66, 3, 26, 26, 10, 24, 27, 50, 82, 94, 73, 63, 8, 51, 33, 22, 45, 19, 13, 58, 33, 90, 15, 22, 50, 36, 13, 55, 6, 35, 47, 82, 52, 33, 61, 36, 27, 28, 46, 98, 14, 73, 20, 73, 32, 16, 26, 80, 53, 47, 66, 76, 38, 94, 45, 2, 1, 22, 52, 47, 96, 64, 58, 52, 39], + [88, 46, 23, 39, 74, 63, 81, 64, 20, 90, 33, 33, 76, 55, 58, 26, 10, 46, 42, 26, 74, 74, 12, 83, 32, 43, 9, 2, 73, 55, 86, 54, 85, 34, 28, 23, 29, 79, 91, 62, 47, 41, 82, 87, 99, 22, 48, 90, 20, 5, 96, 75, 95, 4, 43, 28, 81, 39, 81, 1, 28, 42, 78, 25, 39, 77, 90, 57, 58, 98, 17, 36, 73, 22, 63, 74, 51], + [29, 39, 74, 94, 95, 78, 64, 24, 38, 86, 63, 87, 93, 6, 70, 92, 22, 16, 80, 64, 29, 52, 20, 27, 23, 50, 14, 13, 87, 15, 72, 96, 81, 22, 8, 49, 72, 30, 70, 24, 79, 31, 16, 64, 59, 21, 89, 34, 96, 91, 48, 76, 43, 53, 88, 1, 57, 80, 23, 81, 90, 79, 58, 1, 80, 87, 17, 99, 86, 90, 72, 63, 32, 69, 14, 28, 88, 69], + [37, 17, 71, 95, 56, 93, 71, 35, 43, 45, 4, 98, 92, 94, 84, 96, 11, 30, 31, 27, 31, 60, 92, 3, 48, 5, 98, 91, 86, 94, 35, 90, 90, 8, 48, 19, 33, 28, 68, 37, 59, 26, 65, 96, 50, 68, 22, 7, 9, 49, 34, 31, 77, 49, 43, 6, 75, 17, 81, 87, 61, 79, 52, 26, 27, 72, 29, 50, 7, 98, 86, 1, 17, 10, 46, 64, 24, 18, 56], + [51, 30, 25, 94, 88, 85, 79, 91, 40, 33, 63, 84, 49, 67, 98, 92, 15, 26, 75, 19, 82, 5, 18, 78, 65, 93, 61, 48, 91, 43, 59, 41, 70, 51, 22, 15, 92, 81, 67, 91, 46, 98, 11, 11, 65, 31, 66, 10, 98, 65, 83, 21, 5, 56, 5, 98, 73, 67, 46, 74, 69, 34, 8, 30, 5, 52, 7, 98, 32, 95, 30, 94, 65, 50, 24, 63, 28, 81, 99, 57], + [19, 23, 61, 36, 9, 89, 71, 98, 65, 17, 30, 29, 89, 26, 79, 74, 94, 11, 44, 48, 97, 54, 81, 55, 39, 66, 69, 45, 28, 47, 13, 86, 15, 76, 74, 70, 84, 32, 36, 33, 79, 20, 78, 14, 41, 47, 89, 28, 81, 5, 99, 66, 81, 86, 38, 26, 6, 25, 13, 60, 54, 55, 23, 53, 27, 5, 89, 25, 23, 11, 13, 54, 59, 54, 56, 34, 16, 24, 53, 44, 6], + [13, 40, 57, 72, 21, 15, 60, 8, 4, 19, 11, 98, 34, 45, 9, 97, 86, 71, 3, 15, 56, 19, 15, 44, 97, 31, 90, 4, 87, 87, 76, 8, 12, 30, 24, 62, 84, 28, 12, 85, 82, 53, 99, 52, 13, 94, 6, 65, 97, 86, 9, 50, 94, 68, 69, 74, 30, 67, 87, 94, 63, 7, 78, 27, 80, 36, 69, 41, 6, 92, 32, 78, 37, 82, 30, 5, 18, 87, 99, 72, 19, 99], + [44, 20, 55, 77, 69, 91, 27, 31, 28, 81, 80, 27, 2, 7, 97, 23, 95, 98, 12, 25, 75, 29, 47, 71, 7, 47, 78, 39, 41, 59, 27, 76, 13, 15, 66, 61, 68, 35, 69, 86, 16, 53, 67, 63, 99, 85, 41, 56, 8, 28, 33, 40, 94, 76, 90, 85, 31, 70, 24, 65, 84, 65, 99, 82, 19, 25, 54, 37, 21, 46, 33, 2, 52, 99, 51, 33, 26, 4, 87, 2, 8, 18, 96], + [54, 42, 61, 45, 91, 6, 64, 79, 80, 82, 32, 16, 83, 63, 42, 49, 19, 78, 65, 97, 40, 42, 14, 61, 49, 34, 4, 18, 25, 98, 59, 30, 82, 72, 26, 88, 54, 36, 21, 75, 3, 88, 99, 53, 46, 51, 55, 78, 22, 94, 34, 40, 68, 87, 84, 25, 30, 76, 25, 8, 92, 84, 42, 61, 40, 38, 9, 99, 40, 23, 29, 39, 46, 55, 10, 90, 35, 84, 56, 70, 63, 23, 91, 39], + [52, 92, 3, 71, 89, 7, 9, 37, 68, 66, 58, 20, 44, 92, 51, 56, 13, 71, 79, 99, 26, 37, 2, 6, 16, 67, 36, 52, 58, 16, 79, 73, 56, 60, 59, 27, 44, 77, 94, 82, 20, 50, 98, 33, 9, 87, 94, 37, 40, 83, 64, 83, 58, 85, 17, 76, 53, 2, 83, 52, 22, 27, 39, 20, 48, 92, 45, 21, 9, 42, 24, 23, 12, 37, 52, 28, 50, 78, 79, 20, 86, 62, 73, 20, 59], + [54, 96, 80, 15, 91, 90, 99, 70, 10, 9, 58, 90, 93, 50, 81, 99, 54, 38, 36, 10, 30, 11, 35, 84, 16, 45, 82, 18, 11, 97, 36, 43, 96, 79, 97, 65, 40, 48, 23, 19, 17, 31, 64, 52, 65, 65, 37, 32, 65, 76, 99, 79, 34, 65, 79, 27, 55, 33, 3, 1, 33, 27, 61, 28, 66, 8, 4, 70, 49, 46, 48, 83, 1, 45, 19, 96, 13, 81, 14, 21, 31, 79, 93, 85, 50, 5], + [92, 92, 48, 84, 59, 98, 31, 53, 23, 27, 15, 22, 79, 95, 24, 76, 5, 79, 16, 93, 97, 89, 38, 89, 42, 83, 2, 88, 94, 95, 82, 21, 1, 97, 48, 39, 31, 78, 9, 65, 50, 56, 97, 61, 1, 7, 65, 27, 21, 23, 14, 15, 80, 97, 44, 78, 49, 35, 33, 45, 81, 74, 34, 5, 31, 57, 9, 38, 94, 7, 69, 54, 69, 32, 65, 68, 46, 68, 78, 90, 24, 28, 49, 51, 45, 86, 35], + [41, 63, 89, 76, 87, 31, 86, 9, 46, 14, 87, 82, 22, 29, 47, 16, 13, 10, 70, 72, 82, 95, 48, 64, 58, 43, 13, 75, 42, 69, 21, 12, 67, 13, 64, 85, 58, 23, 98, 9, 37, 76, 5, 22, 31, 12, 66, 50, 29, 99, 86, 72, 45, 25, 10, 28, 19, 6, 90, 43, 29, 31, 67, 79, 46, 25, 74, 14, 97, 35, 76, 37, 65, 46, 23, 82, 6, 22, 30, 76, 93, 66, 94, 17, 96, 13, 20, 72], + [63, 40, 78, 8, 52, 9, 90, 41, 70, 28, 36, 14, 46, 44, 85, 96, 24, 52, 58, 15, 87, 37, 5, 98, 99, 39, 13, 61, 76, 38, 44, 99, 83, 74, 90, 22, 53, 80, 56, 98, 30, 51, 63, 39, 44, 30, 91, 91, 4, 22, 27, 73, 17, 35, 53, 18, 35, 45, 54, 56, 27, 78, 48, 13, 69, 36, 44, 38, 71, 25, 30, 56, 15, 22, 73, 43, 32, 69, 59, 25, 93, 83, 45, 11, 34, 94, 44, 39, 92], + [12, 36, 56, 88, 13, 96, 16, 12, 55, 54, 11, 47, 19, 78, 17, 17, 68, 81, 77, 51, 42, 55, 99, 85, 66, 27, 81, 79, 93, 42, 65, 61, 69, 74, 14, 1, 18, 56, 12, 1, 58, 37, 91, 22, 42, 66, 83, 25, 19, 4, 96, 41, 25, 45, 18, 69, 96, 88, 36, 93, 10, 12, 98, 32, 44, 83, 83, 4, 72, 91, 4, 27, 73, 7, 34, 37, 71, 60, 59, 31, 1, 54, 54, 44, 96, 93, 83, 36, 4, 45], + [30, 18, 22, 20, 42, 96, 65, 79, 17, 41, 55, 69, 94, 81, 29, 80, 91, 31, 85, 25, 47, 26, 43, 49, 2, 99, 34, 67, 99, 76, 16, 14, 15, 93, 8, 32, 99, 44, 61, 77, 67, 50, 43, 55, 87, 55, 53, 72, 17, 46, 62, 25, 50, 99, 73, 5, 93, 48, 17, 31, 70, 80, 59, 9, 44, 59, 45, 13, 74, 66, 58, 94, 87, 73, 16, 14, 85, 38, 74, 99, 64, 23, 79, 28, 71, 42, 20, 37, 82, 31, 23], + [51, 96, 39, 65, 46, 71, 56, 13, 29, 68, 53, 86, 45, 33, 51, 49, 12, 91, 21, 21, 76, 85, 2, 17, 98, 15, 46, 12, 60, 21, 88, 30, 92, 83, 44, 59, 42, 50, 27, 88, 46, 86, 94, 73, 45, 54, 23, 24, 14, 10, 94, 21, 20, 34, 23, 51, 4, 83, 99, 75, 90, 63, 60, 16, 22, 33, 83, 70, 11, 32, 10, 50, 29, 30, 83, 46, 11, 5, 31, 17, 86, 42, 49, 1, 44, 63, 28, 60, 7, 78, 95, 40], + [44, 61, 89, 59, 4, 49, 51, 27, 69, 71, 46, 76, 44, 4, 9, 34, 56, 39, 15, 6, 94, 91, 75, 90, 65, 27, 56, 23, 74, 6, 23, 33, 36, 69, 14, 39, 5, 34, 35, 57, 33, 22, 76, 46, 56, 10, 61, 65, 98, 9, 16, 69, 4, 62, 65, 18, 99, 76, 49, 18, 72, 66, 73, 83, 82, 40, 76, 31, 89, 91, 27, 88, 17, 35, 41, 35, 32, 51, 32, 67, 52, 68, 74, 85, 80, 57, 7, 11, 62, 66, 47, 22, 67], + [65, 37, 19, 97, 26, 17, 16, 24, 24, 17, 50, 37, 64, 82, 24, 36, 32, 11, 68, 34, 69, 31, 32, 89, 79, 93, 96, 68, 49, 90, 14, 23, 4, 4, 67, 99, 81, 74, 70, 74, 36, 96, 68, 9, 64, 39, 88, 35, 54, 89, 96, 58, 66, 27, 88, 97, 32, 14, 6, 35, 78, 20, 71, 6, 85, 66, 57, 2, 58, 91, 72, 5, 29, 56, 73, 48, 86, 52, 9, 93, 22, 57, 79, 42, 12, 1, 31, 68, 17, 59, 63, 76, 7, 77], + [73, 81, 14, 13, 17, 20, 11, 9, 1, 83, 8, 85, 91, 70, 84, 63, 62, 77, 37, 7, 47, 1, 59, 95, 39, 69, 39, 21, 99, 9, 87, 2, 97, 16, 92, 36, 74, 71, 90, 66, 33, 73, 73, 75, 52, 91, 11, 12, 26, 53, 5, 26, 26, 48, 61, 50, 90, 65, 1, 87, 42, 47, 74, 35, 22, 73, 24, 26, 56, 70, 52, 5, 48, 41, 31, 18, 83, 27, 21, 39, 80, 85, 26, 8, 44, 2, 71, 7, 63, 22, 5, 52, 19, 8, 20], + [17, 25, 21, 11, 72, 93, 33, 49, 64, 23, 53, 82, 3, 13, 91, 65, 85, 2, 40, 5, 42, 31, 77, 42, 5, 36, 6, 54, 4, 58, 7, 76, 87, 83, 25, 57, 66, 12, 74, 33, 85, 37, 74, 32, 20, 69, 3, 97, 91, 68, 82, 44, 19, 14, 89, 28, 85, 85, 80, 53, 34, 87, 58, 98, 88, 78, 48, 65, 98, 40, 11, 57, 10, 67, 70, 81, 60, 79, 74, 72, 97, 59, 79, 47, 30, 20, 54, 80, 89, 91, 14, 5, 33, 36, 79, 39], + [60, 85, 59, 39, 60, 7, 57, 76, 77, 92, 6, 35, 15, 72, 23, 41, 45, 52, 95, 18, 64, 79, 86, 53, 56, 31, 69, 11, 91, 31, 84, 50, 44, 82, 22, 81, 41, 40, 30, 42, 30, 91, 48, 94, 74, 76, 64, 58, 74, 25, 96, 57, 14, 19, 3, 99, 28, 83, 15, 75, 99, 1, 89, 85, 79, 50, 3, 95, 32, 67, 44, 8, 7, 41, 62, 64, 29, 20, 14, 76, 26, 55, 48, 71, 69, 66, 19, 72, 44, 25, 14, 1, 48, 74, 12, 98, 7], + [64, 66, 84, 24, 18, 16, 27, 48, 20, 14, 47, 69, 30, 86, 48, 40, 23, 16, 61, 21, 51, 50, 26, 47, 35, 33, 91, 28, 78, 64, 43, 68, 4, 79, 51, 8, 19, 60, 52, 95, 6, 68, 46, 86, 35, 97, 27, 58, 4, 65, 30, 58, 99, 12, 12, 75, 91, 39, 50, 31, 42, 64, 70, 4, 46, 7, 98, 73, 98, 93, 37, 89, 77, 91, 64, 71, 64, 65, 66, 21, 78, 62, 81, 74, 42, 20, 83, 70, 73, 95, 78, 45, 92, 27, 34, 53, 71, 15], + [30, 11, 85, 31, 34, 71, 13, 48, 5, 14, 44, 3, 19, 67, 23, 73, 19, 57, 6, 90, 94, 72, 57, 69, 81, 62, 59, 68, 88, 57, 55, 69, 49, 13, 7, 87, 97, 80, 89, 5, 71, 5, 5, 26, 38, 40, 16, 62, 45, 99, 18, 38, 98, 24, 21, 26, 62, 74, 69, 4, 85, 57, 77, 35, 58, 67, 91, 79, 79, 57, 86, 28, 66, 34, 72, 51, 76, 78, 36, 95, 63, 90, 8, 78, 47, 63, 45, 31, 22, 70, 52, 48, 79, 94, 15, 77, 61, 67, 68], + [23, 33, 44, 81, 80, 92, 93, 75, 94, 88, 23, 61, 39, 76, 22, 3, 28, 94, 32, 6, 49, 65, 41, 34, 18, 23, 8, 47, 62, 60, 3, 63, 33, 13, 80, 52, 31, 54, 73, 43, 70, 26, 16, 69, 57, 87, 83, 31, 3, 93, 70, 81, 47, 95, 77, 44, 29, 68, 39, 51, 56, 59, 63, 7, 25, 70, 7, 77, 43, 53, 64, 3, 94, 42, 95, 39, 18, 1, 66, 21, 16, 97, 20, 50, 90, 16, 70, 10, 95, 69, 29, 6, 25, 61, 41, 26, 15, 59, 63, 35]] + + #Invert the list so that each element = 100 - element + invert(listNum) + + #Holds points we know are of the shortest route + foundPoints = [] + #Add the tip of the pyramid because everything has to go through that + foundPoints.append(location(0, 0, listNum[0][0], True)) + #Holds points that might be the shortest route + possiblePoints = [] + #Add the second row as possible points because everything must pass through the second row + possiblePoints.append(location(0, 1, (listNum[0][0] + listNum[1][0]), True)) + possiblePoints.append(location(1, 1, (listNum[0][0] + listNum[1][1]), False)) + foundBottom = False + + #Loop until you find the bottom + while(not foundBottom): + #Check which possible point gives us the lowest number. If more than one has the same number simply keep the first one + minLoc = possiblePoints[0] + for loc in possiblePoints: + if(loc.total < minLoc.total): + minLoc = loc + + #Remove it from the list of possible points + removeIf(possiblePoints, minLoc) + + foundPoints.append(minLoc) + + #Add to the list of possible points from the point we just found and + #If you are at the bottom raise the flag to end the program + xLoc = minLoc.xLocation + yLoc = minLoc.yLocation + 1 + if(yLoc >= NUM_ROWS): + foundBottom = True + else: + possiblePoints.append(location(xLoc, yLoc, minLoc.total + listNum[yLoc][xLoc], True)) + xLoc += 1 + possiblePoints.append(location(xLoc, yLoc, minLoc.total + listNum[yLoc][xLoc], False)) + + #Get the real total of the journey + actualTotal = ((100 * NUM_ROWS) - foundPoints[len(foundPoints) - 1].total) + + #Invert the list so it can be read again + invert(listNum) + + #Print the results + print("The value of the longest path is " + str(actualTotal)) + + +if __name__ == "__main__": + timer = Stopwatch() + timer.start() + Problem67() + timer.stop() + print("It took " + timer.getString() + " to run this algorithm") + +""" Results: +The value of the longest path is 7273 +It took 16.483 seconds to run this algorithm +""" diff --git a/Problem7.py b/Problem7.py new file mode 100644 index 0000000..6d9e5a7 --- /dev/null +++ b/Problem7.py @@ -0,0 +1,50 @@ +#Project Eulter/Python/Problem7.py +#Matthew Ellison +# Created: 01-29-19 +#Modified: 03-28-19 +#What is the 10001th prime number? +#Unless otherwise listed, all of my non-standard imports can be gotten from my pyClasses repository at https://bitbucket.org/Mattrixwv/pyClasses +""" + Copyright (C) 2019 Matthew Ellison + + This program is free software: you can redistribute it and/or modify + it under the terms of the GNU Lesser General Public License as published by + the Free Software Foundation, either version 3 of the License, or + (at your option) any later version. + + This program is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the + GNU Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public License + along with this program. If not, see . +""" + + +from Stopwatch import Stopwatch +from Algorithms import getNumPrimes + +__numPrimes = 10001 #The number of the prime number desired + + +def Problem7(): + #Get the correct number of primes + primes = getNumPrimes(__numPrimes) + + #Print the results + print("The " + str(__numPrimes) + "th prime number is " + str(primes[__numPrimes - 1])) + +#If you are running this file, automatically start the correct function +if __name__ == '__main__': + timer = Stopwatch() #Determines the algorithm's run time + timer.start() #Start the timer + Problem7() #Call the function that answers the question + timer.stop() #Stop the timer + #Print the results of the timer + print("It took " + timer.getString() + " to run this algorithm") + +"""Results: +The 10001th prime number is 104743 +It took 139.545 milliseconds to run this algorithm +""" diff --git a/Problem8.py b/Problem8.py new file mode 100644 index 0000000..279e188 --- /dev/null +++ b/Problem8.py @@ -0,0 +1,85 @@ +#Project Euler/Python/Problem8.py +#Matthew Ellison +# Created: 01-29-19 +#Modified: 03-28-19 +#Find the thirteen adjacent digits in the 1000-digit number that have the greatest product. What is the value of this product? +""" +73167176531330624919225119674426574742355349194934 +96983520312774506326239578318016984801869478851843 +85861560789112949495459501737958331952853208805511 +12540698747158523863050715693290963295227443043557 +66896648950445244523161731856403098711121722383113 +62229893423380308135336276614282806444486645238749 +30358907296290491560440772390713810515859307960866 +70172427121883998797908792274921901699720888093776 +65727333001053367881220235421809751254540594752243 +52584907711670556013604839586446706324415722155397 +53697817977846174064955149290862569321978468622482 +83972241375657056057490261407972968652414535100474 +82166370484403199890008895243450658541227588666881 +16427171479924442928230863465674813919123162824586 +17866458359124566529476545682848912883142607690042 +24219022671055626321111109370544217506941658960408 +07198403850962455444362981230987879927244284909188 +84580156166097919133875499200524063689912560717606 +05886116467109405077541002256983155200055935729725 +71636269561882670428252483600823257530420752963450 +""" +#Unless otherwise listed, all of my non-standard imports can be gotten from my pyClasses repository at https://bitbucket.org/Mattrixwv/pyClasses +""" + Copyright (C) 2019 Matthew Ellison + + This program is free software: you can redistribute it and/or modify + it under the terms of the GNU Lesser General Public License as published by + the Free Software Foundation, either version 3 of the License, or + (at your option) any later version. + + This program is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the + GNU Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public License + along with this program. If not, see . +""" + + +from Stopwatch import Stopwatch + +#The number +__number = "7316717653133062491922511967442657474235534919493496983520312774506326239578318016984801869478851843858615607891129494954595017379583319528532088055111254069874715852386305071569329096329522744304355766896648950445244523161731856403098711121722383113622298934233803081353362766142828064444866452387493035890729629049156044077239071381051585930796086670172427121883998797908792274921901699720888093776657273330010533678812202354218097512545405947522435258490771167055601360483958644670632441572215539753697817977846174064955149290862569321978468622482839722413756570560574902614079729686524145351004748216637048440319989000889524345065854122758866688116427171479924442928230863465674813919123162824586178664583591245665294765456828489128831426076900422421902267105562632111110937054421750694165896040807198403850962455444362981230987879927244284909188845801561660979191338754992005240636899125607176060588611646710940507754100225698315520005593572972571636269561882670428252483600823257530420752963450" + + +def Problem8(): + #Setup the variables + largestProduct = 0 #Holds the largest product of 13 adjacent digits + largestString = "" #Holds the 13 adjacent numbers that produce the largest product + + #Start at the 13th entry and multiply all single digit numbers before and including that number together + numberLocation = 12 #The location in the number that you are working from + while(numberLocation < len(__number)): + currentProduct = int(__number[numberLocation]) * int(__number[numberLocation - 1]) * int(__number[numberLocation - 2]) * int(__number[numberLocation - 3]) * int(__number[numberLocation - 4]) * int(__number[numberLocation - 5]) * int(__number[numberLocation - 6]) * int(__number[numberLocation - 7]) * int(__number[numberLocation - 8]) * int(__number[numberLocation - 9]) * int(__number[numberLocation - 10]) * int(__number[numberLocation - 11]) * int(__number[numberLocation - 12]) + #Save the largest product + if(currentProduct > largestProduct): + largestProduct = currentProduct + largestString = __number[numberLocation - 12:numberLocation + 1] #Have to add one because it stops before the second subscript + #Move to the next location + numberLocation += 1 + + #Print the results + print("The largest product of 13 adjacent digits in the number is " + str(largestProduct)) + print("The numbers are: " + largestString) + +#If you are running this file, automatically start the correct function +if __name__ == '__main__': + timer = Stopwatch() #Determines the algorithm's run time + timer.start() #Start the timer + Problem8() #Call the function that answers the question + timer.stop() #Stop the timer + print("It took " + timer.getString() + " to run this algorithm") + +"""Results: +The largest product of 13 adjacent digits in the number is 23514624000 +The numbers are: 5576689664895 +It took 2.593 milliseconds to run this algorithm +""" diff --git a/Problem9.py b/Problem9.py new file mode 100644 index 0000000..e790b06 --- /dev/null +++ b/Problem9.py @@ -0,0 +1,73 @@ +#Project Euler/Python/Problem9.py +#Matthew Ellison +# Created: 01-29-19 +#Modified: 03-28-19 +#There exists exactly one Pythagorean triplet for which a + b + c = 1000. Find the product abc. +#Unless otherwise listed, all of my non-standard imports can be gotten from my pyClasses repository at https://bitbucket.org/Mattrixwv/pyClasses +""" + Copyright (C) 2019 Matthew Ellison + + This program is free software: you can redistribute it and/or modify + it under the terms of the GNU Lesser General Public License as published by + the Free Software Foundation, either version 3 of the License, or + (at your option) any later version. + + This program is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the + GNU Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public License + along with this program. If not, see . +""" + + +from Stopwatch import Stopwatch +import math + + +def Problem9(): + #Setup the variables + foundTriplet = False + sideA = 1 + + #Start with the lowest possible a , 1, and search for the b and c to complete the triplet + while((sideA <= (1000 / 3)) and (not foundTriplet)): + #Setup b and c + sideB = sideA + 1 #b must be > a to be a triplet + sideC = math.hypot(sideA, sideB) #C is the hyp + #Loop through possible b's and calculate c's until you find the numbers or the sum gets too large + while((sideA + sideB + sideC) < 1000): + sideB += 1 + sideC = math.hypot(sideA, sideB) + #If c is an integer make it one + if((sideC % 1) == 0): + sideC = int(round(sideC)) + #Check if the correct sides were found + if((sideA + sideB + sideC) == 1000): + foundTriplet = True + #Otherwise increment a to the next possible number + else: + sideA += 1 + + #Print the results + if(foundTriplet): + print("The Pythagorean triplet where a + b + c = 1000 is " + str(sideA) + " " + str(sideB) + " " + str(int(sideC))) + print("The product of those numbers is " + str(int(sideA * sideB * sideC))) + else: + print("Could not find the triplet where a + b + c = 1000") + +#If you are running this file, automatically start the correct function +if __name__ == "__main__": + timer = Stopwatch() #Determines the algorithm's run time + timer.start() #Start the timer + Problem9() #Call the function that answers the question + timer.stop() #Start the timer + #Print the results of the timer + print("It took " + timer.getString() + " to run this algorithm") + +"""Results: +The Pythagorean triplet where a + b + c = 1000 is 200 375 425 +The product of those numbers is 31875000 +It took 22.106 milliseconds to run this algorithm +"""