commit 321e91c0985b251264a18b6c140489184b9fee17 Author: Mattrixwv Date: Sat Jun 6 17:15:36 2020 -0400 Initial commit with existing files 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. 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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.lua b/Problem1.lua new file mode 100644 index 0000000..aa8b6f0 --- /dev/null +++ b/Problem1.lua @@ -0,0 +1,51 @@ +--ProjectEuler/lua/Problem1.lua +--Matthew Ellison +-- Created: 02-01-19 +--Modified: 03-28-19 +--What is the sum of all the multiples of 3 or 5 that are less than 1000 +--All of my requires, unless otherwise listed, can be found at https://bitbucket.org/Mattrixwv/luaClasses +--[[ + 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 . +]] + + +require "Stopwatch" + + +timer = Stopwatch:create(); +timer:start(); + +TOP_NUMBER = 999; --This is the largest number that you are going to check +sumOfMultiples = 0; +for num = 1, TOP_NUMBER do + if((num % 3) == 0) then + sumOfMultiples = sumOfMultiples + num; + elseif((num % 5) == 0) then + sumOfMultiples = sumOfMultiples + num; + end +end + +timer:stop() + +--Print the results +print("The sum of all numbers < 1000 is " .. sumOfMultiples); +print("It took " .. timer:getMicroseconds() .. " microseconds to run this algorithm"); + + +--[[Results: +The sum of all numbers < 1000 is 233168 +It took 148 microseconds to run this algorithm +]] diff --git a/Problem10.lua b/Problem10.lua new file mode 100644 index 0000000..15aebcb --- /dev/null +++ b/Problem10.lua @@ -0,0 +1,52 @@ +--ProjectEuler/lua/Problem10.lua +--Matthew Ellison +-- Created: 02-06-19 +--Modified: 03-28-19 +--Find the sum of all the primes below two million +--All of my requires, unless otherwise listed, can be found at https://bitbucket.org/Mattrixwv/luaClasses +--[[ + 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 . +]] + + +require "Stopwatch" +require "Algorithms" + + +timer = Stopwatch:create(); +timer:start(); + +LARGEST_PRIME = 2000000; --Sum all prime numbers smaller than this + +--Get all of the prime numbers < LARGEST_PRIME +local primes = getPrimes(LARGEST_PRIME); + +--Get the sum of the table +local sumOfPrimes = 0; +for location=1,#primes do + sumOfPrimes = sumOfPrimes + primes[location]; +end + +timer:stop(); + +--Print the results +print("The sum of all prime numbers less than " .. LARGEST_PRIME .. " is " .. sumOfPrimes); +print("It took " .. timer:getSeconds() .. " seconds to run this algorithm"); + +--[[Results: +The sum of all prime numbers less than 2000000 is 142913828922 +It took 5.940409 seconds to run this algorithm +]] diff --git a/Problem11.lua b/Problem11.lua new file mode 100644 index 0000000..f05c920 --- /dev/null +++ b/Problem11.lua @@ -0,0 +1,183 @@ +--ProjectEuler/lua/Problem11.lua +--Matthew Ellison +-- Created: 02-06-19 +--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 +]] +--All of my requires, unless otherwise listed, can be found at https://bitbucket.org/Mattrixwv/luaClasses +--[[ + 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 . +]] + + +require "Stopwatch" + + +timer = Stopwatch:create(); +timer:start(); + +--Setup the grid of numbers +local GRID = {}; +GRID[1] = {8, 2, 22, 97, 38, 15, 00, 40, 00, 75, 4, 5, 7, 78, 52, 12, 50, 77, 91, 8}; +GRID[2] = {49, 49, 99, 40, 17, 81, 18, 57, 60, 87, 17, 40, 98, 43, 69, 48, 4, 56, 62, 00}; +GRID[3] = {81, 49, 31, 73, 55, 79, 14, 29, 93, 71, 40, 67, 53, 88, 30, 3, 49, 13, 36, 65}; +GRID[4] = {52, 70, 95, 23, 4, 60, 11, 42, 69, 24, 68, 56, 1, 32, 56, 71, 37, 2, 36, 91}; +GRID[5] = {22, 31, 16, 71, 51, 67, 63, 89, 41, 92, 36, 54, 22, 40, 40, 28, 66, 33, 13, 80}; +GRID[6] = {24, 47, 32, 60, 99, 3, 45, 2, 44, 75, 33, 53, 78, 36, 84, 20, 35, 17, 12, 50}; +GRID[7] = {32, 98, 81, 28, 64, 23, 67, 10, 26, 38, 40, 67, 59, 54, 70, 66, 18, 38, 64, 70}; +GRID[8] = {67, 26, 20, 68, 2, 62, 12, 20, 95, 63, 94, 39, 63, 8, 40, 91, 66, 49, 94, 21}; +GRID[9] = {24, 55, 58, 5, 66, 73, 99, 26, 97, 17, 78, 78, 96, 83, 14, 88, 34, 89, 63, 72}; +GRID[10] = {21, 36, 23, 9, 75, 00, 76, 44, 20, 45, 35, 14, 00, 61, 33, 97, 34, 31, 33, 95}; +GRID[11] = {78, 17, 53, 28, 22, 75, 31, 67, 15, 94, 3, 80, 4, 62, 16, 14, 9, 53, 56, 92}; +GRID[12] = {16, 39, 5, 42, 96, 35, 31, 47, 55, 58, 88, 24, 00, 17, 54, 24, 36, 29, 85, 57}; +GRID[13] = {86, 56, 00, 48, 35, 71, 89, 7, 5, 44, 44, 37, 44, 60, 21, 58, 51, 54, 17, 58}; +GRID[14] = {19, 80, 81, 68, 5, 94, 47, 69, 28, 73, 92, 13, 86, 52, 17, 77, 4, 89, 55, 40}; +GRID[15] = {4, 52, 8, 83, 97, 35, 99, 16, 7, 97, 57, 32, 16, 26, 26, 79, 33, 27, 98, 66}; +GRID[16] = {88, 36, 68, 87, 57, 62, 20, 72, 3, 46, 33, 67, 46, 55, 12, 32, 63, 93, 53, 69}; +GRID[17] = {4, 42, 16, 73, 38, 25, 39, 11, 24, 94, 72, 18, 8, 46, 29, 32, 40, 62, 76, 36}; +GRID[18] = {20, 69, 36, 41, 72, 30, 23, 88, 34, 62, 99, 69, 82, 67, 59, 85, 74, 4, 36, 16}; +GRID[19] = {20, 73, 35, 29, 78, 31, 90, 1, 74, 31, 49, 71, 48, 86, 81, 16, 23, 57, 5, 54}; +GRID[20] = {1, 70, 54, 71, 83, 51, 54, 69, 16, 92, 33, 48, 61, 43, 52, 1, 89, 19, 67, 48}; + +--This function returns the product of all elements in a table +function getTableProduct(numbers) + local product = 1; --Start with 1 because you are working with multiplication + --Loop through ever element in a table and multiply them all together + for location=1,#numbers do + product = product * numbers[location]; + end + --Return the product of all elements + return product; +end + +local greatestNumbers = {0, 0, 0, 0}; --Holds the numbers that give the greatest product +local currentNumbers = {0, 0, 0, 0}; --Holds the numbers that you are currently working with +--Loop through ever location in the grid +for row=1,#GRID do + for col=1,#GRID[row] do + --Setup variables for know what direction you can move + local moveLeft = false; + local moveRight = false; + local moveDown = false; + + --Check which directions you will be able to move + if((col - 3) >= 1) then + moveLeft = true; + end + if((col + 3) <= #GRID[row]) then + moveRight = true; + end + if((row + 3) <= #GRID) then + moveDown = true; + end + + --With these movements check for the greatest product of 4 adjacent numbers + --Move Right + if(moveRight) then + currentNumbers[1] = GRID[row][col]; + currentNumbers[2] = GRID[row][col + 1]; + currentNumbers[3] = GRID[row][col + 2]; + currentNumbers[4] = GRID[row][col + 3]; + --Check if the current set is greater than the maximum + if(getTableProduct(currentNumbers) > getTableProduct(greatestNumbers)) then + greatestNumbers[1] = currentNumbers[1]; + greatestNumbers[2] = currentNumbers[2]; + greatestNumbers[3] = currentNumbers[3]; + greatestNumbers[4] = currentNumbers[4]; + end + end + + --Move Down + if(moveDown) then + currentNumbers[1] = GRID[row][col]; + currentNumbers[2] = GRID[row + 1][col]; + currentNumbers[3] = GRID[row + 2][col]; + currentNumbers[4] = GRID[row + 3][col]; + --Check if the current set is greater than the maximum + if(getTableProduct(currentNumbers) > getTableProduct(greatestNumbers)) then + greatestNumbers[1] = currentNumbers[1]; + greatestNumbers[2] = currentNumbers[2]; + greatestNumbers[3] = currentNumbers[3]; + greatestNumbers[4] = currentNumbers[4]; + end + end + + --Move Down & Left + if(moveDown and moveLeft) then + currentNumbers[1] = GRID[row][col]; + currentNumbers[2] = GRID[row + 1][col - 1]; + currentNumbers[3] = GRID[row + 2][col - 2]; + currentNumbers[4] = GRID[row + 3][col - 3]; + + --Check if the current set is greater than the maximum + if(getTableProduct(currentNumbers) > getTableProduct(greatestNumbers)) then + greatestNumbers[1] = currentNumbers[1]; + greatestNumbers[2] = currentNumbers[2]; + greatestNumbers[3] = currentNumbers[3]; + greatestNumbers[4] = currentNumbers[4]; + end + end + + --Move Down & Right + if(moveDown and moveRight) then + currentNumbers[1] = GRID[row][col]; + currentNumbers[2] = GRID[row + 1][col + 1]; + currentNumbers[3] = GRID[row + 2][col + 2]; + currentNumbers[4] = GRID[row + 3][col + 3]; + --Check if the current set is greater than the maximum + if(getTableProduct(currentNumbers) > getTableProduct(greatestNumbers)) then + greatestNumbers[1] = currentNumbers[1]; + greatestNumbers[2] = currentNumbers[2]; + greatestNumbers[3] = currentNumbers[3]; + greatestNumbers[4] = currentNumbers[4]; + end + end + end +end + +timer:stop(); + +--Print the results +print("The greatest product of 4 numbers in a line is " .. getTableProduct(greatestNumbers)); +print("The numbers are " .. greatestNumbers[1] .. ' ' .. greatestNumbers[2] .. ' ' .. greatestNumbers[3] .. ' ' .. greatestNumbers[4]); +print("It took " .. timer:getMilliseconds() .. " milliseconds to run this algorithm"); + +--[[Results: +The greatest product of 4 numbers in a line is 70600674 +The numbers are 89 94 97 87 +It took 0.701 milliseconds to run this algorithm +]] diff --git a/Problem12.lua b/Problem12.lua new file mode 100644 index 0000000..0ce6644 --- /dev/null +++ b/Problem12.lua @@ -0,0 +1,65 @@ +--ProjectEUler/lua/Problem12.lua +--Matthew Ellison +-- Created: 02-07-19 +--Modified: 03-28-19 +--What is the value of the first triangle number to have over five hundred divisors? +--All of my requires, unless otherwise listed, can be found at https://bitbucket.org/Mattrixwv/luaClasses +--[[ + 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 . +]] + + +require "Stopwatch" +require "Algorithms" + + +timer = Stopwatch:create(); +timer:start(); + +GOAL_DIVISORS = 500; + +local triangularNumber = 1; +local nextNumber = 2; +local foundNumber = false; +local divisors = {}; + +while((not foundNumber) and (triangularNumber > 0)) do + --See how many divisors this triangular number has + divisors = getDivisors(triangularNumber); + --If it has more than GOAL_DIVISORS raise a flag to stop the loop + if(#divisors > GOAL_DIVISORS) then + foundNumber = true; + else + triangularNumber = triangularNumber + nextNumber; --Add the next number to continue the triangular sequence + nextNumber = nextNumber + 1; --Advance to the next number for the triangular sequence + end +end + +timer:stop(); + +--Print the results +if(foundNumber) then + print("The first triangular number with more than " .. GOAL_DIVISORS .. " divisors is " .. triangularNumber); +else + print("There was an error. Could not find a triangular number with " .. GOAL_DIVISORS .. " divisors before overflow"); +end +print("It took " .. timer:getSeconds() .. " seconds to run this algorithm"); + + +--[[Results +The first triangular number with more than 500divisors is 76576500 +It took 1.498547 seconds to run this algorithm +]] diff --git a/Problem13.lua b/Problem13.lua new file mode 100644 index 0000000..927479c --- /dev/null +++ b/Problem13.lua @@ -0,0 +1,251 @@ +--ProjectEuler/lua/Problem13.lua +--Matthew Ellison +-- Created: 02-07-19 +--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 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+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 +]] +--All of my requires, unless otherwise listed, can be found at https://bitbucket.org/Mattrixwv/luaClasses +--I used the bigint library from https://github.com/empyreuma/bigint.lua +--[[ + 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 . +]] + + +require "Stopwatch" +local bigint = require "bigint" + + +timer = Stopwatch:create(); +timer:start(); + +NUMBERS = {}; +NUMBERS[#NUMBERS+1] = bigint.new("37107287533902102798797998220837590246510135740250") +NUMBERS[#NUMBERS+1] = bigint.new("46376937677490009712648124896970078050417018260538") +NUMBERS[#NUMBERS+1] = bigint.new("74324986199524741059474233309513058123726617309629") +NUMBERS[#NUMBERS+1] = bigint.new("91942213363574161572522430563301811072406154908250") +NUMBERS[#NUMBERS+1] = bigint.new("23067588207539346171171980310421047513778063246676") +NUMBERS[#NUMBERS+1] = bigint.new("89261670696623633820136378418383684178734361726757") +NUMBERS[#NUMBERS+1] = bigint.new("28112879812849979408065481931592621691275889832738") +NUMBERS[#NUMBERS+1] = bigint.new("44274228917432520321923589422876796487670272189318") +NUMBERS[#NUMBERS+1] = bigint.new("47451445736001306439091167216856844588711603153276") +NUMBERS[#NUMBERS+1] = bigint.new("70386486105843025439939619828917593665686757934951") +NUMBERS[#NUMBERS+1] = bigint.new("62176457141856560629502157223196586755079324193331") +NUMBERS[#NUMBERS+1] = bigint.new("64906352462741904929101432445813822663347944758178") +NUMBERS[#NUMBERS+1] = bigint.new("92575867718337217661963751590579239728245598838407") +NUMBERS[#NUMBERS+1] = bigint.new("58203565325359399008402633568948830189458628227828") +NUMBERS[#NUMBERS+1] = bigint.new("80181199384826282014278194139940567587151170094390") +NUMBERS[#NUMBERS+1] = bigint.new("35398664372827112653829987240784473053190104293586") +NUMBERS[#NUMBERS+1] = bigint.new("86515506006295864861532075273371959191420517255829") +NUMBERS[#NUMBERS+1] = bigint.new("71693888707715466499115593487603532921714970056938") +NUMBERS[#NUMBERS+1] = bigint.new("54370070576826684624621495650076471787294438377604") +NUMBERS[#NUMBERS+1] = bigint.new("53282654108756828443191190634694037855217779295145") +NUMBERS[#NUMBERS+1] = bigint.new("36123272525000296071075082563815656710885258350721") +NUMBERS[#NUMBERS+1] = bigint.new("45876576172410976447339110607218265236877223636045") +NUMBERS[#NUMBERS+1] = bigint.new("17423706905851860660448207621209813287860733969412") +NUMBERS[#NUMBERS+1] = bigint.new("81142660418086830619328460811191061556940512689692") +NUMBERS[#NUMBERS+1] = bigint.new("51934325451728388641918047049293215058642563049483") +NUMBERS[#NUMBERS+1] = bigint.new("62467221648435076201727918039944693004732956340691") +NUMBERS[#NUMBERS+1] = bigint.new("15732444386908125794514089057706229429197107928209") +NUMBERS[#NUMBERS+1] = bigint.new("55037687525678773091862540744969844508330393682126") +NUMBERS[#NUMBERS+1] = bigint.new("18336384825330154686196124348767681297534375946515") +NUMBERS[#NUMBERS+1] = bigint.new("80386287592878490201521685554828717201219257766954") +NUMBERS[#NUMBERS+1] = bigint.new("78182833757993103614740356856449095527097864797581") +NUMBERS[#NUMBERS+1] = bigint.new("16726320100436897842553539920931837441497806860984") +NUMBERS[#NUMBERS+1] = bigint.new("48403098129077791799088218795327364475675590848030") +NUMBERS[#NUMBERS+1] = bigint.new("87086987551392711854517078544161852424320693150332") +NUMBERS[#NUMBERS+1] = bigint.new("59959406895756536782107074926966537676326235447210") +NUMBERS[#NUMBERS+1] = bigint.new("69793950679652694742597709739166693763042633987085") +NUMBERS[#NUMBERS+1] = bigint.new("41052684708299085211399427365734116182760315001271") +NUMBERS[#NUMBERS+1] = bigint.new("65378607361501080857009149939512557028198746004375") +NUMBERS[#NUMBERS+1] = bigint.new("35829035317434717326932123578154982629742552737307") +NUMBERS[#NUMBERS+1] = bigint.new("94953759765105305946966067683156574377167401875275") +NUMBERS[#NUMBERS+1] = bigint.new("88902802571733229619176668713819931811048770190271") +NUMBERS[#NUMBERS+1] = bigint.new("25267680276078003013678680992525463401061632866526") +NUMBERS[#NUMBERS+1] = bigint.new("36270218540497705585629946580636237993140746255962") +NUMBERS[#NUMBERS+1] = bigint.new("24074486908231174977792365466257246923322810917141") +NUMBERS[#NUMBERS+1] = bigint.new("91430288197103288597806669760892938638285025333403") +NUMBERS[#NUMBERS+1] = bigint.new("34413065578016127815921815005561868836468420090470") +NUMBERS[#NUMBERS+1] = bigint.new("23053081172816430487623791969842487255036638784583") +NUMBERS[#NUMBERS+1] = bigint.new("11487696932154902810424020138335124462181441773470") +NUMBERS[#NUMBERS+1] = bigint.new("63783299490636259666498587618221225225512486764533") +NUMBERS[#NUMBERS+1] = bigint.new("67720186971698544312419572409913959008952310058822") +NUMBERS[#NUMBERS+1] = bigint.new("95548255300263520781532296796249481641953868218774") +NUMBERS[#NUMBERS+1] = bigint.new("76085327132285723110424803456124867697064507995236") +NUMBERS[#NUMBERS+1] = bigint.new("37774242535411291684276865538926205024910326572967") +NUMBERS[#NUMBERS+1] = bigint.new("23701913275725675285653248258265463092207058596522") +NUMBERS[#NUMBERS+1] = bigint.new("29798860272258331913126375147341994889534765745501") +NUMBERS[#NUMBERS+1] = bigint.new("18495701454879288984856827726077713721403798879715") +NUMBERS[#NUMBERS+1] = bigint.new("38298203783031473527721580348144513491373226651381") +NUMBERS[#NUMBERS+1] = bigint.new("34829543829199918180278916522431027392251122869539") +NUMBERS[#NUMBERS+1] = bigint.new("40957953066405232632538044100059654939159879593635") +NUMBERS[#NUMBERS+1] = bigint.new("29746152185502371307642255121183693803580388584903") +NUMBERS[#NUMBERS+1] = bigint.new("41698116222072977186158236678424689157993532961922") +NUMBERS[#NUMBERS+1] = bigint.new("62467957194401269043877107275048102390895523597457") +NUMBERS[#NUMBERS+1] = bigint.new("23189706772547915061505504953922979530901129967519") +NUMBERS[#NUMBERS+1] = bigint.new("86188088225875314529584099251203829009407770775672") +NUMBERS[#NUMBERS+1] = bigint.new("11306739708304724483816533873502340845647058077308") +NUMBERS[#NUMBERS+1] = bigint.new("82959174767140363198008187129011875491310547126581") +NUMBERS[#NUMBERS+1] = bigint.new("97623331044818386269515456334926366572897563400500") +NUMBERS[#NUMBERS+1] = bigint.new("42846280183517070527831839425882145521227251250327") +NUMBERS[#NUMBERS+1] = bigint.new("55121603546981200581762165212827652751691296897789") +NUMBERS[#NUMBERS+1] = bigint.new("32238195734329339946437501907836945765883352399886") +NUMBERS[#NUMBERS+1] = bigint.new("75506164965184775180738168837861091527357929701337") +NUMBERS[#NUMBERS+1] = bigint.new("62177842752192623401942399639168044983993173312731") +NUMBERS[#NUMBERS+1] = bigint.new("32924185707147349566916674687634660915035914677504") +NUMBERS[#NUMBERS+1] = bigint.new("99518671430235219628894890102423325116913619626622") +NUMBERS[#NUMBERS+1] = bigint.new("73267460800591547471830798392868535206946944540724") +NUMBERS[#NUMBERS+1] = bigint.new("76841822524674417161514036427982273348055556214818") +NUMBERS[#NUMBERS+1] = bigint.new("97142617910342598647204516893989422179826088076852") +NUMBERS[#NUMBERS+1] = bigint.new("87783646182799346313767754307809363333018982642090") +NUMBERS[#NUMBERS+1] = bigint.new("10848802521674670883215120185883543223812876952786") +NUMBERS[#NUMBERS+1] = bigint.new("71329612474782464538636993009049310363619763878039") +NUMBERS[#NUMBERS+1] = bigint.new("62184073572399794223406235393808339651327408011116") +NUMBERS[#NUMBERS+1] = bigint.new("66627891981488087797941876876144230030984490851411") +NUMBERS[#NUMBERS+1] = bigint.new("60661826293682836764744779239180335110989069790714") +NUMBERS[#NUMBERS+1] = bigint.new("85786944089552990653640447425576083659976645795096") +NUMBERS[#NUMBERS+1] = bigint.new("66024396409905389607120198219976047599490197230297") +NUMBERS[#NUMBERS+1] = bigint.new("64913982680032973156037120041377903785566085089252") +NUMBERS[#NUMBERS+1] = bigint.new("16730939319872750275468906903707539413042652315011") +NUMBERS[#NUMBERS+1] = bigint.new("94809377245048795150954100921645863754710598436791") +NUMBERS[#NUMBERS+1] = bigint.new("78639167021187492431995700641917969777599028300699") +NUMBERS[#NUMBERS+1] = bigint.new("15368713711936614952811305876380278410754449733078") +NUMBERS[#NUMBERS+1] = bigint.new("40789923115535562561142322423255033685442488917353") +NUMBERS[#NUMBERS+1] = bigint.new("44889911501440648020369068063960672322193204149535") +NUMBERS[#NUMBERS+1] = bigint.new("41503128880339536053299340368006977710650566631954") +NUMBERS[#NUMBERS+1] = bigint.new("81234880673210146739058568557934581403627822703280") +NUMBERS[#NUMBERS+1] = bigint.new("82616570773948327592232845941706525094512325230608") +NUMBERS[#NUMBERS+1] = bigint.new("22918802058777319719839450180888072429661980811197") +NUMBERS[#NUMBERS+1] = bigint.new("77158542502016545090413245809786882778948721859617") +NUMBERS[#NUMBERS+1] = bigint.new("72107838435069186155435662884062257473692284509516") +NUMBERS[#NUMBERS+1] = bigint.new("20849603980134001723930671666823555245252804609722") +NUMBERS[#NUMBERS+1] = bigint.new("53503534226472524250874054075591789781264330331690") + +--Get the sum of all the numbers in the table +local sum = bigint.new(0); +for location=1,#NUMBERS do + sum = bigint.add(sum, NUMBERS[location]); +end + +timer:stop(); + +--Print the results +print("The sum off all " .. #NUMBERS .. " numbers is " .. bigint.unserialize(sum, 's')); +print("The first 10 digits are " .. string.sub(bigint.unserialize(sum, 's'), 1, 10)); + +--[[Results: + +]] diff --git a/Problem14.lua b/Problem14.lua new file mode 100644 index 0000000..34e05ff --- /dev/null +++ b/Problem14.lua @@ -0,0 +1,83 @@ +--ProjectEuler/lua/Problem14.lua +--Matthew Ellison +-- Created: 02-07-19 +--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? +]] +--All of my requires, unless otherwise listed, can be found at https://bitbucket.org/Mattrixwv/luaClasses +--[[ + 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 . +]] + + +require "Stopwatch" + + +timer = Stopwatch:create(); +timer:start(); + +TOP_NUM = 1000000 --The largest number that you will check against the chain + +--This function returns a table of numbers created by the chain +function getChain(startNum) + --Put the starting number in the list + local chain = {}; + chain[#chain+1] = startNum; + + --Starting with the current number perform the correct opperations on the numbers until that number reaches 1 + while(startNum > 1) do + --Determine if the number is odd or even and perform the correct operations and add the new number to the list + if((startNum % 2) == 0) then + startNum = startNum / 2; + else + startNum = (3 * startNum) + 1; + end + --Add the new number to the chain + chain[#chain+1] = startNum; + end + + --Return the list + return chain; +end + +--Setup your variables +local largestChain = {}; + +--Start at 1 and run up to TOP_NUM checking how long the chain is when started with each number +for startingNumber=1,TOP_NUM do + local currentChain = getChain(startingNumber); + --If the new chain is longer than the current longest chain replace it + if(#currentChain > #largestChain) then + for location=1,#currentChain do + largestChain[location] = currentChain[location]; + end + end +end + +timer:stop(); + +--Print the results +print("The longest chain with a starting number < " .. TOP_NUM .. " starts with " .. largestChain[1] .. " with a length of " .. #largestChain); +print("It took " .. timer:getSeconds() .. " seconds to run this algorithm") + +--[[Results: +The longest chain with a starting number < 1000000 starts with 837799 with a length of 525 +It took 13.704 seconds to run this algorithm +]] diff --git a/Problem15.lua b/Problem15.lua new file mode 100644 index 0000000..fd3e341 --- /dev/null +++ b/Problem15.lua @@ -0,0 +1,74 @@ +--ProjectEuler/lua/Problem15.lua +--Matthew Ellison +-- Created: 02-07-19 +--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? +--All of my requires, unless otherwise listed, can be found at https://bitbucket.org/Mattrixwv/luaClasses +--[[ + 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 . +]] + + +require "Stopwatch" + + +timer = Stopwatch:create(); +timer:start(); + +GRID_WIDTH = 20; +GRID_HEIGHT = 20; +lowestXReached = 20; +function movement(currentX, currentY) + --Return 1 if you are at the finish location + if((currentX == GRID_WIDTH) and (currentY == GRID_HEIGHT)) then + return 1; + end + + local numberMoves = 0; + --Otherwise move one right if you can and recurse + if(currentX < GRID_WIDTH) then + numberMoves = numberMoves + movement(currentX + 1, currentY); + end + + --Then move one down and recurse + if(currentY < GRID_HEIGHT) then + numberMoves = numberMoves + movement(currentX, currentY + 1); + end + ---Helps keep track of where it is for timing purposes + if(currentX < lowestXReached) then + lowestXReached = currentX; + print("X hit"); + print("NumberMoves = " .. numberMoves); + print("position = " .. currentX .. "; " .. currentY); + end + + return numberMoves; --Return the number of moves that have been found so far +end + +--Start the recursion at the correct location and catch what is returned +numberMoves = movement(0, 0); + +timer:stop(); + +--Print the results +print("The number of paths from 1 corner of a " .. GRID_WIDTH .. " x " .. GRID_HEIGHT .. " grid to the opposite corner is " .. numberMoves); +print("It took " .. timer:getMinutes() .. " seconds to run this algorithm"); + +--[[Results: +Did not run this program to completion. It ran for 12.5 hours and was over half way done, but I got tired of waiting. +It is coded the same way as the C++ version so should come up to the same answer. +There has got to be a better way to do this problem. +]] diff --git a/Problem16.lua b/Problem16.lua new file mode 100644 index 0000000..1729ab0 --- /dev/null +++ b/Problem16.lua @@ -0,0 +1,57 @@ +--ProjectEuler/lua/Problem16.lua +--Matthew Ellison +-- Created: 02-07-19 +--Modified: 03-28-19 +--What is the sum of the digits of the number 2^1000? +--All of my requires, unless otherwise listed, can be found at https://bitbucket.org/Mattrixwv/luaClasses +--I used the bigint library from https://github.com/empyreuma/bigint.lua +--[[ + 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 . +]] + + +require "Stopwatch" +local bigint = require("bigint") + + +local timer = Stopwatch:create(); +timer:start(); + +--Get the number +local num = bigint.exponentiate(bigint.new(2), bigint.new(1000)); + +--Change the number to the string +local stringOfNum = bigint.unserialize(num, 's'); + +--Step through the string one element at a time +local sumOfNum = 0; +for location=1,string.len(stringOfNum) do + --Treat the character like a num and add it to the sum + sumOfNum = sumOfNum + string.sub(stringOfNum, location, location); +end + +timer:stop(); + +--Print the results +print("2^1000 = " .. stringOfNum); +print("The sum of the digits is: " .. math.floor(sumOfNum)); +print("It took " .. timer:getMilliseconds() .. " milliseconds to run this algorithm"); + +--[[Results: +2^1000 = 10715086071862673209484250490600018105614048117055336074437503883703510511249361224931983788156958581275946729175531468251871452856923140435984577574698574803934567774824230985421074605062371141877954182153046474983581941267398767559165543946077062914571196477686542167660429831652624386837205668069376 +The sum of the digits is: 1366 +It took 352.0 milliseconds to run this algorithm +]] diff --git a/Problem17.lua b/Problem17.lua new file mode 100644 index 0000000..b940914 --- /dev/null +++ b/Problem17.lua @@ -0,0 +1,186 @@ +--ProjectEuler/lua/Problem17.lua +--Matthew Ellison +-- Created: 02-07-19 +--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? +--All of my requires, unless otherwise listed, can be found at https://bitbucket.org/Mattrixwv/luaClasses +--[[ + 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 . +]] + + +require "Stopwatch" + + +timer = Stopwatch:create(); +timer:start(); + +--This function takes a number and returns it as a string in english +--This function only works for numbers -1,000,000 < num < 1,000,000 +function getStringFromNum(number) + local numberString = ""; + --Starting with the largest digit create a string based on the number passed in + --Check for negative + if(number < 0) then + numberString = numberString .. "negative "; + --Check if the number is zero + elseif(number == 0) then + numberString = numberString .. "zero"; + end + + --Start with the thousands place + if((number / 1000) >= 1) then + numberString = numberString .. getStringFromNum(math.floor(number / 1000)); + numberString = numberString .. " thousand"; + number = number - (math.floor(number / 1000) * 1000); + end + + --Check for hundreds place + if((number / 100) >= 1) then + numberString = numberString .. getStringFromNum(math.floor(number / 100)); + numberString = numberString .. " hundred"; + number = number - (math.floor(number / 100) * 100); + end + + --Insert an and if there is need + if((numberString ~= "") and (number > 0)) then + numberString = numberString .. " and "; + end + + --Check for tens place + if((number / 10) >= 2) then + --For the tens you need to do something special + local tensPlace = math.floor(number / 10); + if(tensPlace == 9) then + numberString = numberString .. "ninety"; + elseif(tensPlace == 8) then + numberString = numberString .. "eighty"; + elseif(tensPlace == 7) then + numberString = numberString .. "seventy"; + elseif(tensPlace == 6) then + numberString = numberString .. "sixty"; + elseif(tensPlace == 5) then + numberString = numberString .. "fifty"; + elseif(tensPlace == 4) then + numberString = numberString .. "forty"; + elseif(tensPlace == 3) then + numberString = numberString .. "thrity"; + elseif(tensPlace == 2) then + numberString = numberString .. "twenty"; + end + number = number - (tensPlace * 10); + --If there is something left in the number you will need a space to separate it + if(number > 0) then + numberString = numberString .. ' '; + end + --Check for teens + elseif((number / 10) >= 1) then + local onesPlace = (number % 10); + if(onesPlace == 9) then + numberString = numberString .. "nineteen"; + elseif(onesPlace == 8) then + numberString = numberString .. "eighteen"; + elseif(onesPlace == 7) then + numberString = numberString .. "seventeen"; + elseif(onesPlace == 6) then + numberString = numberString .. "sixteen"; + elseif(onesPlace == 5) then + numberString = numberString .. "fifteen"; + elseif(onesPlace == 4) then + numberString = numberString .. "fourteen"; + elseif(onesPlace == 3) then + numberString = numberString .. "thirteen"; + elseif(onesPlace == 2) then + numberString = numberString .. "twelve"; + elseif(onesPlace == 1) then + numberString = numberString .. "eleven"; + elseif(onesPlace == 0) then + numberString = numberString .. "ten"; + end + --If this if was hit number was used up + number = 0; + end + + --Check for ones place + if(number >= 1) then + if(number == 9) then + numberString = numberString .. "nine"; + elseif(number == 8) then + numberString = numberString .. "eight"; + elseif(number == 7) then + numberString = numberString .. "seven"; + elseif(number == 6) then + numberString = numberString .. "six"; + elseif(number == 5) then + numberString = numberString .. "five"; + elseif(number == 4) then + numberString = numberString .. "four"; + elseif(number == 3) then + numberString = numberString .. "three"; + elseif(number == 2) then + numberString = numberString .. "two"; + elseif(number == 1) then + numberString = numberString .. "one"; + end + --If this if was hit number was used up + number = 0; + end + + --Return the string + return numberString; +end + +--This function returns the number of letters in a string, ignoring punctuation, whitespace, and numbers +function getNumberChars(number) + local sumOfLetters = 0; + --Start at location 1 and count the number of letters, ignoring punctuation and whitespace + for location=1,string.len(number) do + local tempString = string.sub(number, location, location); + if(string.match(tempString, "%w")) then + sumOfLetters = sumOfLetters + 1; + end + end + + --Return the number of letters + return sumOfLetters; +end + + +timer = Stopwatch:create(); +timer:start(); + +START_NUM = 1; +STOP_NUM = 1000; + +local sumOfLetters = 0; +--Start with 1 and increment +for num=START_NUM,STOP_NUM do + --Pass the number to a function that will create a string for the number + local currentNumString = getStringFromNum(num); + --Pass the string to a function that will count the number of letters in a string, ignoring whitespace, punctuation, and numbers and add the amount tot he running tally + sumOfLetters = sumOfLetters + getNumberChars(currentNumString); +end + +timer:stop(); + +--Print the results +print("The sum of all the letters in all the numbers " .. START_NUM .. '-' .. STOP_NUM .. " is " .. sumOfLetters); +print("It took " .. timer:getMilliseconds() .. " milliseconds to run this algorithm"); + +--[[Results: +The sum of all the letters in all the numbers 1-1000 is 21124 +It took 4.0 milliseconds to run this algorithm +]] diff --git a/Problem18.lua b/Problem18.lua new file mode 100644 index 0000000..c5a90a6 --- /dev/null +++ b/Problem18.lua @@ -0,0 +1,227 @@ +--ProjectEuler/lua/Problem18.lua +--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 +]] +--This is done using a breadth first search +--All of my requires, unless otherwise listed, can be found at https://bitbucket.org/Mattrixwv/luaClasses +--[[ + 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 . +]] + + +require "Stopwatch" + +--[[ This is what locations should look like +location = { + xLocation = 0, + yLocation = 0, + total = 0, + fromRight = false +}; +]] + +function invert(list) + for rowCnt=1,NUM_ROWS do + for colCnt=1,#list[rowCnt] do + list[rowCnt][colCnt] = 100 - list[rowCnt][colCnt]; + end + end +end + +function foundInList(list, loc) + for location=1,#list do + if((list[location].xLocation == loc.xLocation) and (list[location].yLocation == loc.yLocation)) then + return true; + end + end + return false; +end + +function remove_if(list, loc) + location = 1; + while(location <= #list) do + if((list[location].xLocation == loc.xLocation) and (list[location].yLocation == loc.yLocation)) then + table.remove(list, location); + else + location = location + 1; + end + end +end + +--Create a timer and time the algorithm +timer = Stopwatch:create(); +timer:start(); + +NUM_ROWS = 15; + + +list = {}; +list[1] = {75}; +list[2] = {95, 64}; +list[3] = {17, 47, 82}; +list[4] = {18, 35, 87, 10}; +list[5] = {20, 04, 82, 47, 65}; +list[6] = {19, 01, 23, 75, 03, 34}; +list[7] = {88, 02, 77, 73, 07, 63, 67}; +list[8] = {99, 65, 04, 28, 06, 16, 70, 92}; +list[9] = {41, 41, 26, 56, 83, 40, 80, 70, 33}; +list[10] = {41, 48, 72, 33, 47, 32, 37, 16, 94, 29}; +list[11] = {53, 71, 44, 65, 25, 43, 91, 52, 97, 51, 14}; +list[12] = {70, 11, 33, 28, 77, 73, 17, 78, 39, 68, 17, 57}; +list[13] = {91, 71, 52, 38, 17, 14, 91, 43, 58, 50, 27, 29, 48}; +list[14] = {63, 66, 04, 68, 89, 53, 67, 30, 73, 16, 69, 87, 40, 31}; +list[15] = {04, 62, 98, 27, 23, 9, 70, 98, 73, 93, 38, 53, 60, 04, 23}; + +--Invert the list so all elements are 100 - element +invert(list); + +foundPoints = {}; --This is a table of locations +foundPoints[1] = {xLocation = 1, yLocation = 1, total = list[1][1], fromRight = false}; +possiblePoints = {}; --This is a table of locations +--Add the second row as possible points +possiblePoints[1] = {xLocation = 1, yLocation = 2, total = (list[1][1] + list[2][1]), fromRight = true}; +possiblePoints[2] = {xLocation = 2, yLocation = 2, total = (list[1][1] + list[2][2]), fromRight = false}; +foundBottom = false; --Used when you find a point at the bottom + +--Loop until you find the bottom +while(not foundBottom) do + --Check which possible point gives us the lowest number. If more than one has the same number simply keep the first one + minLoc = possiblePoints[1]; + for loc=1,#possiblePoints do + if(possiblePoints[loc].total < minLoc.total) then + minLoc = possiblePoints[loc]; + end + end + + --Remove it from the list of possible points + remove_if(possiblePoints, minLoc); + + --[[ Aids in tracing the trail instead of using line after this + --Add that point to the list of found points + if(not foundInList(foundPoints, minLoc)) then + table.insert(foundPoints, minLoc); + end + ]] + table.insert(foundPoints, 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; --Add one because you will always be moving to the next row + if(yLoc > NUM_ROWS) then + foundBottom = true; + else + --print("minLoc.total = " .. minLoc.total); + --print("list[" .. yLoc .. "][" .. xLoc .. "] = "); + table.insert(possiblePoints, {xLocation = xLoc, yLocation = yLoc, total = (minLoc.total + list[yLoc][xLoc]), fromRight = true}); + xLoc = xLoc + 1; --Advance the x location to simulate going right + table.insert(possiblePoints, {xLocation = xLoc, yLocation = yLoc, total = (minLoc.total + list[yLoc][xLoc]), fromRight = false}); + end +end + +actualTotal = ((100 * (NUM_ROWS)) - foundPoints[#foundPoints].total); + +--Stop the timer +timer:stop(); + +--Reinvert the list so it will print propperly +invert(list); + +--Print the results +print("The value of the longest path is " .. actualTotal); +print("It took " .. timer:getMilliseconds() .. " milliseconds to run this algorithm"); + +--[[ +--Print the pyramid of numbers out +for rowCnt=1,NUM_ROWS do + for colCnt=1,#list[rowCnt] do + if(list[rowCnt][colCnt] < 10) then + io.write(' ' .. list[rowCnt][colCnt] .. ' '); + else + io.write(list[rowCnt][colCnt] .. ' '); + end + end + print(""); +end +print("\n\n") + +--Find the trail followed +trail = {}; --Holds the locations that were traveled along +table.insert(trail, 1, foundPoints[#foundPoints]); --Start with the last point and continue adding to the front of the list +top = false; +while(not top) do + --Find the shortest way from the last location to the current one + found = false; + location = #foundPoints; + while(not found) do + --print("Location: " .. location); + --print("trail[1].xLocation = " .. trail[1].xLocation .. "\ntrail[1].yLocation = " .. trail[1].yLocation); + --print("foundPoints[location].xLocation = " .. foundPoints[location].xLocation .. "\nfoundPoints[location].yLocation = " .. foundPoints[location].yLocation); + if(trail[1].fromRight) then + if((foundPoints[location].xLocation == trail[1].xLocation) and (foundPoints[location].yLocation == (trail[1].yLocation - 1))) then + found = true; + else + location = location - 1; + end + else + if((foundPoints[location].xLocation == (trail[1].xLocation) - 1) and (foundPoints[location].yLocation == (trail[1].yLocation - 1))) then + found = true; + else + location = location - 1; + end + end + end + + --Insert the location into the trail + table.insert(trail, 1, foundPoints[location]); + + --If the current location is 1 then we are at the top + if(trail[1].yLocation == 1) then + top = true; + end +end + + +--Print the trail +for location=1,#trail do + io.write(list[trail[location].yLocation][trail[location].xLocation] .. "->"); +end +print(""); +]] + + +--[[ Results: +The value of the longest path is 1074 +It took 1.162 milliseconds to run this algorithm +]] diff --git a/Problem19.lua b/Problem19.lua new file mode 100644 index 0000000..a4c1bf7 --- /dev/null +++ b/Problem19.lua @@ -0,0 +1,186 @@ +--ProjectEuler/lua/Problem19.lua +--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. +]] +--All of my requires, unless otherwise listed, can be found at https://bitbucket.org/Mattrixwv/luaClasses +--[[ + 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 . +]] + + +require "Stopwatch" + + +DAYS = { + SUNDAY = 0, + MONDAY = 1, + TUESDAY = 2, + WEDNESDAY = 3, + THURSDAY = 4, + FRIDAY = 5, + SATURDAY = 6, + NUMBER_OF_DAYS = 7, + ERROR = 8; +} + +START_YEAR = 1901; +END_YEAR = 2000; + +--Return the day of the week that the date you pass into it is on +function getDay(month, day, year) + --Make sure the numbers are within propper bounds + if((month < 1) or (month > 12) or (day < 1) or (day > 31) or (year < 1)) then + return DAYS.ERROR; + end + + numDays = 0; + currentYear = 1; + currentMonth = 1; + currentDay = DAYS.SATURDAY; + day = day - 1; + + --Add the correct number of days for every year + while(currentYear < year) do + if(isLeapYear(currentYear)) then + numDays = numDays + 366; + else + numDays = numDays + 365; + end + currentYear = currentYear + 1; + end + --Add the correct number of days for every month + while(currentMonth < month) do + --February + if(currentMonth == 2) then + if(isLeapYear(currentYear)) then + numDays = numDays + 29; + else + numDays = numDays + 28; + end + --31 day months + elseif((currentMonth == 1) or (currentMonth == 3) or (currentMonth == 5) or (currentMonth == 7) or (currentMonth == 8) or (currentMonth == 10) or (currentMonth == 12)) then + numDays = numDays + 31; + --30 day months + else + numDays = numDays + 30; + end + currentMonth = currentMonth + 1; + end + --Account for the weird year of 1752 + if(year > 1752) then + numDays = numDays - 11; + elseif(year == 1752) then + if(month > 9) then + numDays = numDays - 11; + elseif(month == 9) then + if(day >= 14) then + numDays = numDays - 11; + --Days 3-13 were skipped that year + elseif((day > 2) and (day < 14)) then + return DAYS.ERROR; + end + end + end + --Add the correct number of days for every day + numDays = numDays + day; + + currentDay = currentDay + numDays; + currentDay = currentDay % DAYS.NUMBER_OF_DAYS; + if(currentDay == DAYS.SUNDAY) then + day = DAYS.SUNDAY; + elseif(currentDay == DAYS.MONDAY) then + day = DAYS.MONDAY; + elseif(currentDay == DAYS.TUESDAY) then + day = DAYS.TUESDAY; + elseif(currentDay == DAYS.WEDNESDAY) then + day = DAYS.WEDNESDAY; + elseif(currentDay == DAYS.THURSDAY) then + day = DAYS.THURSDAY; + elseif(currentDay == DAYS.FRIDAY) then + day = DAYS.FRIDAY; + elseif(currentDay == DAYS.SATURDAY) then + day = DAYS.SATURDAY; + else + day = DAYS.ERROR; + end + --Return the day generated + return day; +end + +function isLeapYear(year) + if(year < 1) then + answer = false; + elseif((year % 100) == 0) then + --This rule only applies at and after 1800 + if(year <= 1700) then + answer = true; + elseif((year % 400) == 0) then + answer = true; + else + answer = false; + end + elseif((year % 4) == 0) then + answer = true; + else + answer = false; + end + return answer; +end + +--Setup the variables +timer = Stopwatch:create(); +totalSundays = 0; + +--Start the timer +timer:start(); + +--Run for all years up to 2000 +for year=START_YEAR,END_YEAR do + --Run for all months in the year + for month=1,12 do + day = getDay(month, 1, year); + if(day == DAYS.ERROR) then + io.output("There was an error with the day\n"); + os.exit(); + elseif(day == DAYS.SUNDAY) then + totalSundays = totalSundays + 1; + end + end +end + +--Stop the timer +timer:stop() + +--Print the results +io.write("There are " .. totalSundays .. " Sundays that landed on the first of the months from " .. START_YEAR .. " to " .. END_YEAR .. '\n'); +io.write("It took " .. timer:getMilliseconds() .. " milliseconds to run this algorithm\n"); + +--[[ Results: +There are 171 Sundays that landed on the first of the months from 1901 to 2000 +It took 390.0 milliseconds to run this algorithm +]] \ No newline at end of file diff --git a/Problem2.lua b/Problem2.lua new file mode 100644 index 0000000..93081bb --- /dev/null +++ b/Problem2.lua @@ -0,0 +1,59 @@ +--ProjectEuler/lua/Problem1.lua +--Matthew Ellison +-- Created: 02-01-19 +--Modified: 03-28-19 +--The sum of the even Fibonacci numbers less than 4,000,000 +--All of my requires, unless otherwise listed, can be found at https://bitbucket.org/Mattrixwv/luaClasses +--[[ + 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 . +]] + + +require "Stopwatch" + + +timer = Stopwatch:create(); +timer:start(); + +--Setup the variables +TOP_NUM = 4000000; --The highest looked for Fibonacci numbers +fibSum = 0; --Holds the sum of the Fibonacci numbers +fibNums = {1, 1, 2}; --An array to keep track of the Fibonacci numbers + +--Loop to generate the Fibonacci numbers +cnt = 2; --A counter to hold the location in the array of the currently working Fibonacci number +fibNums[(cnt % 3) + 1] = fibNums[((cnt - 1) % 3) + 1] + fibNums[((cnt - 2) % 3) + 1]; +while(fibNums[(cnt % 3) + 1] < TOP_NUM) do + --If the number is even add it to the sum, otherwise ignore it + if((fibNums[(cnt % 3) + 1] % 2) == 0) then + fibSum = fibSum + fibNums[(cnt % 3) + 1]; + end + --Generate the next Fibonacci number in the sequence + cnt = cnt + 1 + fibNums[(cnt % 3) + 1] = fibNums[((cnt - 1) % 3) + 1] + fibNums[((cnt - 2) % 3) + 1]; +end + +timer:stop(); + +--Print the results +print("The sum of all even Fibonacci numbers less than " .. TOP_NUM .. " is " .. fibSum); +print("It took " .. timer:getMicroseconds() .. " microseconds to run this algorithm"); + + +--[[Results: +The sum of all even Fibonacci numbers less than 4000000 is 4613732 +It took 56 microseconds to run this algorithm +]] diff --git a/Problem20.lua b/Problem20.lua new file mode 100644 index 0000000..197e4dc --- /dev/null +++ b/Problem20.lua @@ -0,0 +1,62 @@ +--ProjectEuler/lua/Problem20.lua +--Matthew Ellison +-- Created: 03-14-19 +--Modified: 03-28-19 +--What is the sum of the digits of 100! +--All of my requires, unless otherwise listed, can be found at https://bitbucket.org/Mattrixwv/luaClasses +--I used the bigint library from https://github.com/empyreuma/bigint.lua +--[[ + 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 . +]] + + +require "Stopwatch" +local bigint = require("bigint") + +TOP_NUM = 100; + + +--Start the timer +timer = Stopwatch:create(); +timer:start(); + +local num = bigint.new(1); --The number to be generated +local sum = 0; --The sum of the digits in num + +for cnt = 1, TOP_NUM do + num = bigint.multiply(num, bigint.new(cnt)); +end + +--Get a string of the number because it is easier to pull appart the individual characters to get the sum +numString = bigint.unserialize(num, 's'); +--Run through every character in the string, convert it back to an integer and add it to the running sum +for cnt = 1, string.len(numString) do + sum = sum + tonumber(string.sub(numString, cnt, cnt)); +end + +--Stop the timer +timer:stop() + +--Print the results +io.write("100! = " .. numString .. '\n'); +io.write("The sum of the digits is: " .. sum .. '\n'); +io.write("It took " .. timer:getMilliseconds() .. " milliseconds to run this algorithm\n"); + +--[[ Results: +100! = 93326215443944152681699238856266700490715968264381621468592963895217599993229915608941463976156518286253697920827223758251185210916864000000000000000000000000 +The sum of the digits is: 648 +It took 81.113 milliseconds to run this algorithm +]] diff --git a/Problem21.lua b/Problem21.lua new file mode 100644 index 0000000..98bef74 --- /dev/null +++ b/Problem21.lua @@ -0,0 +1,94 @@ +--ProjectEuler/lua/Problem21.lua +--Matthew Ellison +-- Created: 03-19-19 +--Modified: 03-28-19 +--Evaluate the sum of all the amicable numbers under 10000 +--All of my requires, unless otherwise listed, can be found at https://bitbucket.org/Mattrixwv/luaClasses +--[[ + 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 . +]] + + +require "Stopwatch" +require "Algorithms" + +LIMIT = 10000; --The top number that will be evaluated + + +--Setup the timer +timer = Stopwatch:create(); + +--Setup the variables +divisorSum = {}; --Holds the sum of the factors of the subscript number + +--Start the timer +timer:start(); + +--Generate the factors of all the numbers < 10000, get their sum, and add it to the list +for cnt = 1, LIMIT do + divisors = getDivisors(cnt); --Get all the divisors of a number + if(#divisors > 1) then + table.remove(divisors); --Remove the last entry because it will be the number itself + end + divisorSum[#divisorSum + 1] = getSum(divisors); --Add the sum of the divisors to the vector +end +--Check every sum of divisors in the list for a matching sum +amicable = {}; +for cnt = 1, #divisorSum do + sum = 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(sum >= #divisorSum) then + --We know that divisorSum[cnt] == sum, do if divisorSum[sum] == cnt we have found an amicable number + elseif(divisorSum[sum] == cnt) then + --A number can't be amicable with itself, so skip those numbers + if(sum == cnt) then + --Add the number to the amicable vector + else + amicable[#amicable + 1] = cnt; + end + end +end + +--Stop the timer +timer:stop(); + +--Sort the vector for neatness +table.sort(amicable); + +--Print the results +io.write("All amicable numbers less than " .. LIMIT .. " are \n"); +--Print the list of amicable numbers +for location = 1, #amicable do + io.write(amicable[location] .. '\n'); +end +io.write("The sum of all of these amicable numbers is " .. getSum(amicable) .. '\n'); +io.write("It took " .. timer:getMilliseconds() .. " milliseconds to run this algorithm\n"); + +--[[ 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 46.0 milliseconds to run this algorithm +]] diff --git a/Problem22.lua b/Problem22.lua new file mode 100644 index 0000000..dc247b8 --- /dev/null +++ b/Problem22.lua @@ -0,0 +1,436 @@ +--ProjectEuler/lua/Problem22.lua +--Matthew Ellison +-- Created: 03-20-19 +--Modified: 03-28-19 +--What is the total of all the name scores in the file? +--All of my requires, unless otherwise listed, can be found at https://bitbucket.org/Mattrixwv/luaClasses +--[[ + 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 . +]] + + +require("Stopwatch") +require("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", 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+"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"}; + + +--Setup the variables +timer = Stopwatch:create(); +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 + +--Start the timer +timer:start(); + +--Sort all the names +table.sort(NAMES); + +--Step through every name adding up the values of the characters +for nameCnt = 1, #NAMES do + --Step through every character in the current name adding up the value + sums[nameCnt] = 0; + for charCnt = 1, string.len(NAMES[nameCnt]) do + --A = 65 so subtracting 64 means A - 1. This will only work correctly if all letters are capitalized + sums[nameCnt] = sums[nameCnt] + utf8.codepoint(string.sub(NAMES[nameCnt], charCnt, charCnt)) - 64; + end +end + +--Get the product for all numbers +for cnt = 1, #sums do + prod[cnt] = sums[cnt] * cnt; +end + +--Stop the timer +timer:stop(); + +--Print the results +io.write("The answer to the question is " .. getSum(prod) .. '\n'); +io.write("It tooks " .. timer:getMilliseconds() .. " milliseconds to run this algorithm\n"); + + +--[[ Results: +The answer to the question is 871198282 +It tooks 0.0 milliseconds to run this algorithm +]] diff --git a/Problem23.lua b/Problem23.lua new file mode 100644 index 0000000..5030b78 --- /dev/null +++ b/Problem23.lua @@ -0,0 +1,91 @@ +--ProjectEuler/lua/Problem23.lua +--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 requires, unless otherwise listed, can be found at https://bitbucket.org/Mattrixwv/luaClasses +--[[ + 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 . +]] + + +require "Stopwatch" +require "Algorithms" + + +MAX_NUM = 28123; --The highest number that will be evaluated + + +function isSum(abund, num) + local sumOfNums = 0; + --Pick a number for the first part of the sum + for firstNum = 1, #abund do + for secondNum = firstNum, #abund do + sumOfNums = abund[firstNum] + abund[secondNum]; + if(sumOfNums == num) then + return true; + elseif(sumOfNums > num) then + break; + end + end + end + return false; +end + + +--Setup the variables +local timer = Stopwatch:create(); +local divisorSums = {}; + +--Start the timer +timer:start(); + +--Get the sum of the divisors of all numbers < MAX_NUM +for cnt = 1, MAX_NUM do + local div = getDivisors(cnt); + if(#div > 1) then + table.remove(div, #div); + end + divisorSums[cnt] = getSum(div); +end + +--Get the abundant numbers +local abund = {}; +for cnt = 1, #divisorSums do + if(divisorSums[cnt] > cnt) then + abund[#abund + 1] = cnt; + end +end + +--Check if each number can be the sum of 2 abundant numbers and add to the sum if no +local sumOfNums = 0; +for cnt = 1, MAX_NUM do + if(not isSum(abund, cnt)) then + sumOfNums = sumOfNums + cnt; + end +end + +--Stop the timer +timer:stop(); + +--Print the results +io.write("The answer is " .. sumOfNums .. '\n'); +io.write("It took " .. timer:getSeconds() .. " seconds to run this algorithm\n"); + +--[[Results: +The answer is 4179871 +It took 393.139 seconds to run this algorithm +]] diff --git a/Problem24.lua b/Problem24.lua new file mode 100644 index 0000000..7a68020 --- /dev/null +++ b/Problem24.lua @@ -0,0 +1,51 @@ +--ProjectEuler/lua/Problem24.lua +--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? +--All of my requires, unless otherwise listed, can be found at https://bitbucket.org/Mattrixwv/luaClasses +--[[ + 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 . +]] + + +require "Stopwatch" +require "Algorithms" + +NEEDED_PERM = 1000000; --The number of the permutation that you need + + +--Setup the variables +timer = Stopwatch:create(); +nums = "0123456789"; + +--Start the timer +timer:start(); + +--Get all permutations of the string +permutations = getPermutations(nums); + +--Stop the timer +timer:stop(); + +--Print the results +io.write("The 1 millionth permutation is " .. permutations[NEEDED_PERM] .. '\n'); +io.write("It took " .. timer:getSeconds() .. " seconds to run this algorithm\n"); + +--[[ Results: +The 1 millionth permutation is 2783915460 +It took 50.175 seconds to run this algorithm +]] diff --git a/Problem25.lua b/Problem25.lua new file mode 100644 index 0000000..db52598 --- /dev/null +++ b/Problem25.lua @@ -0,0 +1,63 @@ +--ProjectEuler/lua/Problem25.lua +--Matthew Ellison +-- Created: 03-26-19 +--Modified: 03-28-19 +--What is the index of the first term in the Fibonacci sequence to contain 1000 digits? +--All of my requires, unless otherwise listed, can be found at https://bitbucket.org/Mattrixwv/luaClasses +--I used the bigint library from https://github.com/empyreuma/bigint.lua +--[[ + 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 . +]] + + +require "Stopwatch"; +require "Algorithms"; +local bigint = require "bigint"; + + +NUM_DIGITS = 1000; --The number of digits to calculate up to + + +--Setup the variables +local timer = Stopwatch:create(); +local number = bigint.new(0); --The current Fibonacci number +local index = 2; --The index of the jest calculated Fibonacci number + +--Start the timer +timer:start(); + +--Move through all Fibonacci numbers until you reach the one with at least NUM_DIGITS digits +while(#bigint.unserialize(number, 's') < NUM_DIGITS) do + index = index + 1; --Increase the index number. Doing this at the beginning keeps the index correct at the end of the loop + print("index: " .. index); + --print("Size: " .. #bigint.unserialize(number, 's')); + --print("number: " .. bigint.unserialize(number, 's')); + number = getLargeFib(index); --Calculate the number +end + +--Stop the timer +timer:stop(); + +--Print the results +io.write("The first Fibonacci number with " .. NUM_DIGITS .. " digits is " .. bigint.unserialize(number, 's') .. '\n'); +io.write("The index is " .. index .. '\n'); +io.write("It took " .. timer:getMinutes() .. " minutes to run this algorithm\n"); + +--[[ Results: +The first Fibonacci number with 1000 digits is 1070066266382758936764980584457396885083683896632151665013235203375314520604694040621889147582489792657804694888177591957484336466672569959512996030461262748092482186144069433051234774442750273781753087579391666192149259186759553966422837148943113074699503439547001985432609723067290192870526447243726117715821825548491120525013201478612965931381792235559657452039506137551467837543229119602129934048260706175397706847068202895486902666185435124521900369480641357447470911707619766945691070098024393439617474103736912503231365532164773697023167755051595173518460579954919410967778373229665796581646513903488154256310184224190259846088000110186255550245493937113651657039447629584714548523425950428582425306083544435428212611008992863795048006894330309773217834864543113205765659868456288616808718693835297350643986297640660000723562917905207051164077614812491885830945940566688339109350944456576357666151619317753792891661581327159616877487983821820492520348473874384736771934512787029218636250627816 +The index is 4782 +It took 182.529 minutes to run this algorithm +]] diff --git a/Problem26.lua b/Problem26.lua new file mode 100644 index 0000000..04bafe3 --- /dev/null +++ b/Problem26.lua @@ -0,0 +1,86 @@ +--ProjectEuler/lua/Problem26.lua +--Matthew Ellison +-- Created: 08-02-19 +--Modified: 08-02-19 +--Find the value of d < 1000 for which 1/d contains the longest recurring cycle in its decimal fraction part. +--All of my requires, unless otherwise listed, can be found at https://bitbucket.org/Mattrixwv/luaClasses +--[[ + 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 . +]] + + +require "Stopwatch" + +local TOP_NUMBER = 999 --The largest denominator to tbe checked + + +--Setup the variables +local timer = Stopwatch:create(); +local longestCycle = 0; +local longestNumber = 1; + +--Start the timer +timer:start(); + +--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 = 2, TOP_NUMBER do + local remainderList = {}; --Holds the list of remainders + local endFound = false; --Holds whether we have found an end to the number (either a cycle or a 0 for remainder) + local cycleFound = false; --Holds whether a cycle was detected + local numerator = 1; --The numerator that will be divided + while(not endFound) do + --Get the remainder after the division + local remainder = numerator % denominator + --Check if the remainder is 0 + --If it is, set the flag + if(remainder == 0) then + endFound = true; + --Check if the remainder is in the list + --If it is in the list, set the appropriate flags + elseif(remainderList[remainder]) then + endFound = true; + cycleFound = true; + --Else add it to the list + else + remainderList[remainder] = true; + end + --Multiply the remainder by 10 to continue finding the next remainder + numerator = remainder * 10; + end + --If a cycle was found check the size of the list against the largest cycle + if(cycleFound) then + --If it is larger than the largest, set it as the new largest + if(#remainderList > longestCycle) then + longestCycle = #remainderList; + longestNumber = denominator; + end + end +end + +--End the timer +timer:stop(); + +--Print the results +io.write("The longest cycle is " .. longestCycle .. " digits long\n"); +io.write("It is started with the number " .. longestNumber .. '\n'); +io.write("It took " .. timer:getString() .. " to run this algorithm\n"); + +--[[ Results: +The longest cycle is 982 digits long +It is started with the number 983 +It took 28.222 milliseconds to run this algorithm +]] diff --git a/Problem27.lua b/Problem27.lua new file mode 100644 index 0000000..879c76e --- /dev/null +++ b/Problem27.lua @@ -0,0 +1,77 @@ +--ProjectEuler/lua/Problem27.lua +--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. +--All of my requires, unless otherwise listed, can be found at https://bitbucket.org/Mattrixwv/luaClasses +--[[ + 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 . +]] + + +require "Stopwatch" +require "Algorithms" + + +--Setup the variables +local timer = Stopwatch:create(); +local topA = 0; --The A for the most n's generated +local topB = 0; --The B for the most n's generated +local topN = 0; --The most n's generated +local primes = getPrimes(12000) --A list of all primes that could possibly be generated with this formula + + +--Start the timer +timer:start(); + +--Start with the lowest possible A and check all possibilities after that +for a = -999, 999 do + --Start with the lowest possible B and check all possibilities after that + for b = -1000, 1000 do + --Start with n=0 and check the formula to see how many primes you can get get with concecutive n's + local n = 0; + local quadratic = (n * n) + (a * n) + b; + while(isFound(primes, quadratic)) do + n = n + 1; + quadratic = (n * n) + (a * n) + b; + end + n = 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) then + topN = n; + topB = b; + topA = a; + end + end +end + + +--Stop the timer +timer:stop(); + +--Print the results +io.write("The greatest number of primes found is " .. topN .. '\n'); +io.write("It was found with A = " .. topA .. ", B = " .. topB .. '\n'); +io.write("The product of A and B is " .. topA * topB .. '\n'); +io.write("It took " .. timer:getString() .. " to run this algorithm\n"); + +--[[ 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 119.350 seconds to run this algorithm +]] diff --git a/Problem28.lua b/Problem28.lua new file mode 100644 index 0000000..4b7fd4f --- /dev/null +++ b/Problem28.lua @@ -0,0 +1,114 @@ +--ProjectEuler/lua/Problem28.lua +--Matthew Ellison +-- Created: 09-15-19 +--Modified: 10-06-19 +--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. +--All of my requires, unless otherwise listed, can be found at https://bitbucket.org/Mattrixwv/luaClasses +--[[ + 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 . +]] + + +require "Stopwatch" + + +--Setup the variables +local timer = Stopwatch:create(); +local grid = {}; +local finalLocation = false; --A flag to indicate if the final location to be filled has been reached +local currentNum = 1; --Set the number that is going to be put at each location +--Make a 1001x1001 grid full of 0's +for row = 0, 1001 do + grid[row] = {}; + for col = 0, 1001 do + grid[row][col] = 0; + end +end + +--Start the timer +timer:start(); + +--Start with the middle location and set it correctly and advance the tracker to the next number +local xLocation = 500; +local yLocation = 500; +grid[yLocation][xLocation] = currentNum; +currentNum = currentNum + 1; +--Move right the first time +xLocation = xLocation + 1; +--Move in a circular pattern until you reach the final location +while(not finalLocation) do + --Move down until you reach a blank location on the left + while(grid[yLocation][xLocation - 1] ~= 0) do + grid[yLocation][xLocation] = currentNum; + currentNum = currentNum + 1; + yLocation = yLocation + 1; + end + --Move left until you reach a blank location above + while(grid[yLocation - 1][xLocation] ~= 0) do + grid[yLocation][xLocation] = currentNum; + currentNum = currentNum + 1; + xLocation = xLocation - 1; + end + + --Move up until you reach a blank location to the right + while(grid[yLocation][xLocation + 1] ~= 0) do + grid[yLocation][xLocation] = currentNum; + currentNum = currentNum + 1; + yLocation = yLocation - 1; + end + + --Move right until you reach a blank location below + while(grid[yLocation + 1][xLocation] ~= 0) do + grid[yLocation][xLocation] = currentNum; + currentNum = currentNum + 1; + xLocation = xLocation + 1; + --Check if you are at the final location and break the loop if you are + if(xLocation == #grid) then + finalLocation = true; + break; + end + end +end + +--Get the sum of the diagonals +local leftSide = 0; +local rightSide = #grid - 1; +local row = 0; +local sumOfDiag = 0; +while(row < #grid) do + --This ensures the middle location is only counted once + if(leftSide == rightSide) then + sumOfDiag = sumOfDiag + grid[row][leftSide]; + else + sumOfDiag = sumOfDiag + grid[row][leftSide]; + sumOfDiag = sumOfDiag + grid[row][rightSide]; + end + row = row + 1; + leftSide = leftSide + 1; + rightSide = rightSide - 1; +end + +--Stop the timer +timer:stop(); + +--Print the results +io.write("The sum of the diagonals in the given grid is " .. sumOfDiag .. '\n'); +io.write("It took " .. timer:getString() .. " to run this algorithm\n"); + +--[[ Results: +The sum of the diagonals in the given grid is 669171001 +It took 81.680 milliseconds to run this algorithm +]] diff --git a/Problem29.lua b/Problem29.lua new file mode 100644 index 0000000..d43ef41 --- /dev/null +++ b/Problem29.lua @@ -0,0 +1,64 @@ +--ProjectEuler/lua/Problem29.lua +-- 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? +--All of my requires, unless otherwise listed, can be found at https://bitbucket.org/Mattrixwv/luaClasses +--I used the bigint library from https://github.com/empyreuma/bigint.lua +--[[ + 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 . +]] + + +require "Stopwatch" +require "Algorithms" +local bigint = require("bigint") + +--Setup the variables +local timer = Stopwatch:create(); +local BOTTOM_A = 2; --The lowest possible value for A +local TOP_A = 100; --The highest possible value for A +local BOTTOM_B = 2; --The lowest possible value for B +local TOP_B = 100; --The highest possible value for B +local unique = {}; --A table to hold all of the unique answers for the equation +local currentNum = bigint.new(); --Holds the answer to the equation for a particular loop + +--Start the timer +timer:start(); + +--Start with the lowest A and move towards the largest +for currentA = BOTTOM_A, TOP_A do + --Start with the lowest B and move towards the largest + for currentB = BOTTOM_B, TOP_B do + --Get the new number + currentNum = bigint.unserialize(bigint.exponentiate(bigint.new(currentA), bigint.new(currentB)), "s"); + --If the number isn't in the list add it + if(not isFound(unique, currentNum)) then + table.insert(unique, currentNum); + end + end +end + +--Stop the timer +timer:stop(); + +--Print the results +io.write("The number of unique values generated by a^b for " .. BOTTOM_A .. " <= a <= " .. TOP_A .. " and " .. BOTTOM_B .. " <= b <= " .. TOP_B .. " is " .. #unique .. '\n'); +io.write("It took " .. timer:getString() .. " to run this algorithm\n"); + +--[[ Results: +The number of unique values generated by a^b for 2 <= a <= 100 and 2 <= b <= 100 is 9183 +It took 2.714 minutes to run this algorithm +]] diff --git a/Problem3.lua b/Problem3.lua new file mode 100644 index 0000000..978eaa3 --- /dev/null +++ b/Problem3.lua @@ -0,0 +1,46 @@ +--ProjectEuler/lua/Problem3.lua +--Matthew Ellison +-- Created: 02-04-19 +--Modified: 03-28-19 +--The largest prime factor of 600851475143 +--All of my requires, unless otherwise listed, can be found at https://bitbucket.org/Mattrixwv/luaClasses +--[[ + 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 . +]] + + +require "Stopwatch" +require "Algorithms" + + +timer = Stopwatch:create(); +timer:start(); + + +TARGET_NUMBER = 600851475143; +--Get the factors of the number +factors = getFactors(TARGET_NUMBER); +timer:stop(); + +--The largest number will be the answer +--Print the results +print("The largest prime factor of " .. TARGET_NUMBER .. " is " .. factors[#factors]); +print("It took " .. timer:getSeconds() .. " seconds to run this algorithm"); + +--[[Results: +The largest prime factor of 600851475143 is 6857 +It took 1.612 seconds to run this algorithm +]] diff --git a/Problem30.lua b/Problem30.lua new file mode 100644 index 0000000..a933b27 --- /dev/null +++ b/Problem30.lua @@ -0,0 +1,89 @@ +--ProjectEuler/lua/Problem29.lua +-- 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. +--All of my requires, unless otherwise listed, can be found at https://bitbucket.org/Mattrixwv/luaClasses +--[[ + 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 . +]] + + +require "Stopwatch" + + +--Returns a table with the individual digits of the number passed to it +function getDigits(num) + local listOfDigits = {}; --This table holds the individual digits of num + --The easiest way to get the individual digits of a number is by converting it to a string + local digits = tostring(num); + --Start with the first digit, convert it to an integer, store it in the table, and move to the next digit + for cnt = 1, #digits do + table.insert(listOfDigits, tonumber(string.sub(digits, cnt, cnt))); + end + --Return the table of digits + return listOfDigits; +end + +--Gets the sum of a table of numbers +function getSumOfTable(ary) + local sum = 0; --Start the sum at 0 so you can add to it + --Add every number in the table to the sum + for cnt = 1, #ary do + sum = sum + ary[cnt]; + end + --Return the sum + return sum; +end + + +--Setup the variables +local timer = Stopwatch:create(); +local TOP_NUM = 1000000; --This is the largest number that will be checked +local BOTTOM_NUM = 2; --Starts with 2 because 0 and 1 don't count +local POWER_RAISED = 5; --This is the power that the digits are raised to +local sumOfFifthNumbers = {}; --This is a table of the numbers that are the sum of the fifth power of their digits + +--Start the timer +timer:start(); + +--Start with the lowest number and increment until you reach the largest number +for currentNum = BOTTOM_NUM, TOP_NUM do + --Get the digits of the number + local digits = getDigits(currentNum); + --Get the sum of the powers + local sumOfPowers = 0; + for cnt = 1, #digits do + sumOfPowers = sumOfPowers + math.pow(digits[cnt], POWER_RAISED); + end + --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) then + table.insert(sumOfFifthNumbers, currentNum); + end +end + +--Stop the timer +timer:stop(); + +--Print the results +io.write("The sum of all the numbers that can be written as the sum of the fifth powers of their digits is " .. getSumOfTable(sumOfFifthNumbers) .. '\n'); +io.write("It took " .. timer:getString() .. " to run this algorithm\n"); + + +--[[ 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 2.706 seconds to run this algorithm +]] diff --git a/Problem4.lua b/Problem4.lua new file mode 100644 index 0000000..b14e0df --- /dev/null +++ b/Problem4.lua @@ -0,0 +1,56 @@ +--ProjectEuler/lua/Problem4.lua +--Matthew Ellison +-- Created: 02-05-19 +--Modified: 03-28-19 +--Find the largest palindrome made from the product of two 3-digit numbers +--All of my requires, unless otherwise listed, can be found at https://bitbucket.org/Mattrixwv/luaClasses +--[[ + 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 . +]] + + +require "Stopwatch" + + +timer = Stopwatch:create(); +timer:start(); + +palindromes = {}; --Holds all palindromes the program finds +--Loop through every number 100-999 twice, nested, so you can multiply every number by every other number in the array +for num1=100,999 do + for num2=num1,999 do + 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(tostring(currentNum) == string.reverse(tostring(currentNum))) then + palindromes[#palindromes+1] = currentNum; + end + end +end + +--Sort the list for neatness +table.sort(palindromes); + +timer:stop(); + +--Print the results +print("The largest palindrome made from the product of two 3-digit numbers is " .. palindromes[#palindromes]); +print("It took " .. timer:getMilliseconds() .. " milliseconds to run this algorithm"); + +--[[Results: +The largest palindrome made from the product of two 3-digit numbers is 906609 +It took 268.412 milliseconds to run this algorithm +]] diff --git a/Problem5.lua b/Problem5.lua new file mode 100644 index 0000000..d419a37 --- /dev/null +++ b/Problem5.lua @@ -0,0 +1,66 @@ +--ProjectEuler/lua/Problem5.lua +--Matthew Ellison +-- Created: 02-05-19 +--Modified: 03-28-19 +--What is the smallest positive number that is evenly divisible by all of the numbers from 1 to 20? +--All of my requires, unless otherwise listed, can be found at https://bitbucket.org/Mattrixwv/luaClasses +--[[ + 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 . +]] + + +require "Stopwatch" + + +timer = Stopwatch:create(); +timer:start(); + +--Setup the variables you need +numFound = false; +currentNum = 22; --Start looking at 22 becuase it must be divisible by 2 and greater than 20 +--Start a loop looking for the correct number +while((not numFound) and (currentNum > 0)) do + --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 number from 1 to 20 + for divisor=1,20 do + --If it is not set a flag to move to the next possible number + if((currentNum % divisor) ~= 0) then + numFound = false; + break; + end + end + + --Increment the number by 2 to check the next one if you didn't find the number + if(not numFound) then + currentNum = currentNum + 2 + end +end + +timer:stop(); + +--Print the results +if(currentNum < 0) then + 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 " .. currentNum); + print("It took " .. timer:getSeconds() .. " seconds to run this algorithm") +end + +--[[Results: +The smallest positive number that is evenly divisible by all numbers 1-20 is 232792560 +It took 24.788324 seconds to run this algorithm +]] diff --git a/Problem6.lua b/Problem6.lua new file mode 100644 index 0000000..a4697c1 --- /dev/null +++ b/Problem6.lua @@ -0,0 +1,51 @@ +--ProjectEuler/lua/Problem6.lua +--Matthew Ellison +-- Created: 02-06-19 +--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 +--All of my requires, unless otherwise listed, can be found at https://bitbucket.org/Mattrixwv/luaClasses +--[[ + 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 . +]] + + +require "Stopwatch" + + +timer = Stopwatch:create(); +timer:start(); + +--Create the variables you need +sumOfSquares = 0; +squareOfSum = 0; +--Loop through all numbers 1-100 to do the appropriate math with them +for num=1,100 do + sumOfSquares = sumOfSquares + num^2; --Get the sum of the squares of the first 100 natural number + squareOfSum = squareOfSum + num; --Get the sum of the first 100 natural numbers +end +--Square the normal sum +squareOfSum = squareOfSum^2; + +timer:stop(); + +--Print the result +print("The difference between the sum of the squares and the square of the sum of the numbers 1-100 is " .. math.floor(math.abs(sumOfSquares - squareOfSum))); +print("It took " .. timer:getMicroseconds() .. " microseconds 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 53 microseconds to run this algorithm +]] diff --git a/Problem67.lua b/Problem67.lua new file mode 100644 index 0000000..66a2edd --- /dev/null +++ b/Problem67.lua @@ -0,0 +1,331 @@ +--ProjectEuler/lua/Problem67.lua +--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 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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 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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 +]] +--This is done using a breadth first search +--All of my requires, unless otherwise listed, can be found at https://bitbucket.org/Mattrixwv/luaClasses +--[[ + 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 . +]] + + +require "Stopwatch" + +--[[ This is what locations should look like +location = { + xLocation = 0, + yLocation = 0, + total = 0, + fromRight = false +}; +]] + +function invert(list) + for rowCnt=1,NUM_ROWS do + for colCnt=1,#list[rowCnt] do + list[rowCnt][colCnt] = 100 - list[rowCnt][colCnt]; + end + end +end + +function foundInList(list, loc) + for location=1,#list do + if((list[location].xLocation == loc.xLocation) and (list[location].yLocation == loc.yLocation)) then + return true; + end + end + return false; +end + +function remove_if(list, loc) + location = 1; + while(location <= #list) do + if((list[location].xLocation == loc.xLocation) and (list[location].yLocation == loc.yLocation)) then + table.remove(list, location); + else + location = location + 1; + end + end +end + +--Create a timer and time the algorithm +timer = Stopwatch:create(); +timer:start(); + +NUM_ROWS = 100; + + +list = {}; +list[1] = {59}; +list[2] = {73, 41}; +list[3] = {52, 40, 9}; +list[4] = {26, 53, 06, 34}; +list[5] = {10, 51, 87, 86, 81}; +list[6] = {61, 95, 66, 57, 25, 68}; +list[7] = {90, 81, 80, 38, 92, 67, 73}; +list[8] = {30, 28, 51, 76, 81, 18, 75, 44}; +list[9] = {84, 14, 95, 87, 62, 81, 17, 78, 58}; +list[10] = {21, 46, 71, 58, 02, 79, 62, 39, 31, 9}; +list[11] = {56, 34, 35, 53, 78, 31, 81, 18, 90, 93, 15}; +list[12] = {78, 53, 04, 21, 84, 93, 32, 13, 97, 11, 37, 51}; +list[13] = {45, 03, 81, 79, 05, 18, 78, 86, 13, 30, 63, 99, 95}; +list[14] = {39, 87, 96, 28, 03, 38, 42, 17, 82, 87, 58, 07, 22, 57}; +list[15] = {06, 17, 51, 17, 07, 93, 9, 07, 75, 97, 95, 78, 87, 8, 53}; +list[16] = {67, 66, 59, 60, 88, 99, 94, 65, 55, 77, 55, 34, 27, 53, 78, 28}; +list[17] = {76, 40, 41, 04, 87, 16, 9, 42, 75, 69, 23, 97, 30, 60, 10, 79, 87}; +list[18] = {12, 10, 44, 26, 21, 36, 32, 84, 98, 60, 13, 12, 36, 16, 63, 31, 91, 35}; +list[19] = {70, 39, 06, 05, 55, 27, 38, 48, 28, 22, 34, 35, 62, 62, 15, 14, 94, 89, 86}; +list[20] = {66, 56, 68, 84, 96, 21, 34, 34, 34, 81, 62, 40, 65, 54, 62, 05, 98, 03, 02, 60}; +list[21] = {38, 89, 46, 37, 99, 54, 34, 53, 36, 14, 70, 26, 02, 90, 45, 13, 31, 61, 83, 73, 47}; +list[22] = {36, 10, 63, 96, 60, 49, 41, 05, 37, 42, 14, 58, 84, 93, 96, 17, 9, 43, 05, 43, 06, 59}; +list[23] = {66, 57, 87, 57, 61, 28, 37, 51, 84, 73, 79, 15, 39, 95, 88, 87, 43, 39, 11, 86, 77, 74, 18}; +list[24] = {54, 42, 05, 79, 30, 49, 99, 73, 46, 37, 50, 02, 45, 9, 54, 52, 27, 95, 27, 65, 19, 45, 26, 45}; +list[25] = {71, 39, 17, 78, 76, 29, 52, 90, 18, 99, 78, 19, 35, 62, 71, 19, 23, 65, 93, 85, 49, 33, 75, 9, 02}; +list[26] = {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}; +list[27] = {92, 9, 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}; +list[28] = {24, 59, 06, 8, 98, 74, 66, 26, 61, 60, 13, 03, 9, 9, 24, 30, 71, 8, 88, 70, 72, 70, 29, 90, 11, 82, 41, 34}; +list[29] = {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, 9, 74, 90}; +list[30] = {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}; +list[31] = {37, 60, 69, 70, 72, 71, 9, 59, 13, 60, 38, 13, 57, 36, 9, 30, 43, 89, 30, 39, 15, 02, 44, 73, 05, 73, 26, 63, 56, 86, 12}; +list[32] = {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}; +list[33] = {04, 9, 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}; +list[34] = {75, 63, 02, 49, 14, 12, 89, 14, 60, 78, 92, 16, 44, 82, 38, 30, 72, 11, 46, 52, 90, 27, 8, 65, 78, 03, 85, 41, 57, 79, 39, 52, 33, 48}; +list[35] = {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}; +list[36] = {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}; +list[37] = {52, 9, 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}; +list[38] = {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}; +list[39] = {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}; +list[40] = {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}; +list[41] = {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, 06, 02, 83, 50, 60, 66}; +list[42] = {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, 9, 48, 66, 69, 83, 91, 60, 40, 36, 61}; +list[43] = {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, 8, 20, 36, 47, 81, 44, 50, 64, 68, 85, 40, 81, 85, 52, 9}; +list[44] = {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}; +list[45] = {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}; +list[46] = {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}; +list[47] = {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, 8, 56, 80, 67, 18, 46, 66, 63, 01, 20, 8, 80, 47, 07, 91, 16, 03, 79, 87}; +list[48] = {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}; +list[49] = {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}; +list[50] = {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, 9, 48, 17, 24, 52, 36, 23, 15, 72, 16, 84, 56, 02, 99, 43, 76, 81, 71, 29, 39, 49, 17}; +list[51] = {64, 39, 59, 84, 86, 16, 17, 66, 03, 9, 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}; +list[52] = {43, 83, 18, 37, 32, 31, 52, 29, 95, 47, 8, 76, 35, 11, 04, 53, 35, 43, 34, 10, 52, 57, 12, 36, 20, 39, 40, 55, 78, 44, 07, 31, 38, 26, 8, 15, 56, 88, 86, 01, 52, 62, 10, 24, 32, 05, 60, 65, 53, 28, 57, 99}; +list[53] = {03, 50, 03, 52, 07, 73, 49, 92, 66, 80, 01, 46, 8, 67, 25, 36, 73, 93, 07, 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, 03, 81, 30}; +list[54] = {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, 9, 16, 96, 68, 52, 74, 79, 68, 32, 21, 13, 78, 96, 60, 9, 69, 20, 36}; +list[55] = {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}; +list[56] = {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}; +list[57] = {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, 9, 69, 26, 81, 07}; +list[58] = {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, 9, 39, 47, 91, 43, 54, 69, 47, 42, 95, 62, 46, 32, 85}; +list[59] = {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}; +list[60] = {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}; +list[61] = {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}; +list[62] = {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}; +list[63] = {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, 8, 87, 36, 03, 60, 31, 36, 36, 81, 26, 97, 36, 48, 54, 56, 56, 27, 16, 91, 8, 23, 11, 87, 99, 33, 47, 02, 14, 44, 73, 70, 99, 43, 35, 33}; +list[64] = {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, 8, 31, 76, 63, 26, 90, 85, 96, 67, 65, 91, 19, 14, 17, 86, 04, 71, 32, 95}; +list[65] = {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}; +list[66] = {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}; +list[67] = {22, 97, 41, 13, 34, 31, 54, 61, 56, 94, 03, 24, 59, 27, 98, 77, 04, 9, 37, 40, 12, 26, 87, 9, 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}; +list[68] = {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}; +list[69] = { 8, 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, 9, 81, 95, 22, 28, 76, 69, 46, 48, 64, 87, 67, 76, 27, 89, 31, 11, 74, 16, 62, 03, 60, 94, 42, 47, 9, 34, 94, 93, 72}; +list[70] = {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, 8, 22, 97, 32, 85, 27}; +list[71] = {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, 8, 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}; +list[72] = {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, 9, 03, 40, 38, 12, 03, 32}; +list[73] = { 9, 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, 9, 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, 8, 52, 23, 70}; +list[74] = {47, 81, 28, 9, 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, 8, 9, 48, 44, 80, 90, 22, 93, 45, 82, 17, 13, 96, 25, 26, 8, 73, 34, 99, 06, 49, 24, 06, 83, 51, 40, 14, 15, 10, 25, 01}; +list[75] = {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, 9, 97, 70, 01, 60, 46, 37, 91, 39, 75, 75, 18, 58, 52, 72, 78, 51, 81, 86, 52, 8, 97, 01, 46, 43, 66, 98, 62, 81, 18, 70, 93, 73, 8, 32, 46, 34}; +list[76] = {96, 80, 82, 07, 59, 71, 92, 53, 19, 20, 88, 66, 03, 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, 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}; +list[77] = {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, 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}; +list[78] = {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, 8, 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}; +list[79] = {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, 8, 48, 19, 33, 28, 68, 37, 59, 26, 65, 96, 50, 68, 22, 07, 9, 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}; +list[80] = {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, 8, 30, 05, 52, 07, 98, 32, 95, 30, 94, 65, 50, 24, 63, 28, 81, 99, 57}; +list[81] = {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, 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}; +list[82] = {13, 40, 57, 72, 21, 15, 60, 8, 04, 19, 11, 98, 34, 45, 9, 97, 86, 71, 03, 15, 56, 19, 15, 44, 97, 31, 90, 04, 87, 87, 76, 8, 12, 30, 24, 62, 84, 28, 12, 85, 82, 53, 99, 52, 13, 94, 06, 65, 97, 86, 9, 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}; +list[83] = {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, 8, 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, 8, 18, 96}; +list[84] = {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, 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}; +list[85] = {52, 92, 03, 71, 89, 07, 9, 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, 9, 87, 94, 37, 40, 83, 64, 83, 58, 85, 17, 76, 53, 02, 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}; +list[86] = {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, 03, 01, 33, 27, 61, 28, 66, 8, 04, 70, 49, 46, 48, 83, 01, 45, 19, 96, 13, 81, 14, 21, 31, 79, 93, 85, 50, 05}; +list[87] = {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, 9, 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, 9, 38, 94, 07, 69, 54, 69, 32, 65, 68, 46, 68, 78, 90, 24, 28, 49, 51, 45, 86, 35}; +list[88] = {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, 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}; +list[89] = {63, 40, 78, 8, 52, 9, 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}; +list[90] = {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}; +list[91] = {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, 8, 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, 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}; +list[92] = {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}; +list[93] = {44, 61, 89, 59, 04, 49, 51, 27, 69, 71, 46, 76, 44, 04, 9, 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, 9, 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}; +list[94] = {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, 9, 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, 9, 93, 22, 57, 79, 42, 12, 01, 31, 68, 17, 59, 63, 76, 07, 77}; +list[95] = {73, 81, 14, 13, 17, 20, 11, 9, 01, 83, 8, 85, 91, 70, 84, 63, 62, 77, 37, 07, 47, 01, 59, 95, 39, 69, 39, 21, 99, 9, 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, 8, 44, 02, 71, 07, 63, 22, 05, 52, 19, 8, 20}; +list[96] = {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}; +list[97] = {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, 8, 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}; +list[98] = {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, 8, 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}; +list[99] = {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, 8, 78, 47, 63, 45, 31, 22, 70, 52, 48, 79, 94, 15, 77, 61, 67, 68}; +list[100] ={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, 8, 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}; + +--Invert the list so all elements are 100 - element +invert(list); + +foundPoints = {}; --This is a table of locations +foundPoints[1] = {xLocation = 1, yLocation = 1, total = list[1][1], fromRight = false}; +possiblePoints = {}; --This is a table of locations +--Add the second row as possible points +possiblePoints[1] = {xLocation = 1, yLocation = 2, total = (list[1][1] + list[2][1]), fromRight = true}; +possiblePoints[2] = {xLocation = 2, yLocation = 2, total = (list[1][1] + list[2][2]), fromRight = false}; +foundBottom = false; --Used when you find a point at the bottom + +--Loop until you find the bottom +while(not foundBottom) do + --Check which possible point gives us the lowest number. If more than one has the same number simply keep the first one + minLoc = possiblePoints[1]; + for loc=1,#possiblePoints do + if(possiblePoints[loc].total < minLoc.total) then + minLoc = possiblePoints[loc]; + end + end + + --Remove it from the list of possible points + remove_if(possiblePoints, minLoc); + + table.insert(foundPoints, 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; --Add one because you will always be moving to the next row + if(yLoc > NUM_ROWS) then + foundBottom = true; + else + table.insert(possiblePoints, {xLocation = xLoc, yLocation = yLoc, total = (minLoc.total + list[yLoc][xLoc]), fromRight = true}); + xLoc = xLoc + 1; --Advance the x location to simulate going right + table.insert(possiblePoints, {xLocation = xLoc, yLocation = yLoc, total = (minLoc.total + list[yLoc][xLoc]), fromRight = false}); + end +end + +actualTotal = ((100 * (NUM_ROWS)) - foundPoints[#foundPoints].total); + +--Stop the timer +timer:stop(); + +--Reinvert the list so it will print propperly +invert(list); + +--Print the results +print("The value of the longest path is " .. actualTotal); +print("It took " .. timer:getSeconds() .. " seconds to run this algorithm"); + + +--[[ Results: +The value of the longest path is 7273 +It took 8.145 seconds to run this algorithm +]] diff --git a/Problem7.lua b/Problem7.lua new file mode 100644 index 0000000..5ff8c83 --- /dev/null +++ b/Problem7.lua @@ -0,0 +1,45 @@ +--ProjectEuler/lua/Problem7.lua +--Matthew Ellison +-- Created: 02-05-19 +--Modified: 03-28-19 +--What is the 10001th prime number? +--All of my requires, unless otherwise listed, can be found at https://bitbucket.org/Mattrixwv/luaClasses +--[[ + 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 . +]] + + +require "Stopwatch" +require "Algorithms" + + +timer = Stopwatch:create(); +timer:start(); + +NUM_PRIMES = 10001; --The number of the prime number desired +--Get the correct number of primes +primes = getNumPrimes(NUM_PRIMES); + +timer:stop(); + +--Print the results +print("The " .. NUM_PRIMES .. "th prime number is " .. primes[NUM_PRIMES]); +print("It took " .. timer:getMilliseconds() .. " milliseconds to run this algorithm"); + +--[[Results: +The 10001th prime number is 104743 +It took 127.505 milliseconds to run this algorithm +]] diff --git a/Problem8.lua b/Problem8.lua new file mode 100644 index 0000000..13aadd2 --- /dev/null +++ b/Problem8.lua @@ -0,0 +1,81 @@ +--ProjectEuler/lua/Problem8.lua +--Matthew Ellison +-- Created: 02-06-19 +--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 +]] +--All of my requires, unless otherwise listed, can be found at https://bitbucket.org/Mattrixwv/luaClasses +--[[ + 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 . +]] + + +require "Stopwatch" + + +timer = Stopwatch:create(); +timer:start(); + +--Put the number into a variable. A string will do for now +NUMBER = "7316717653133062491922511967442657474235534919493496983520312774506326239578318016984801869478851843858615607891129494954595017379583319528532088055111254069874715852386305071569329096329522744304355766896648950445244523161731856403098711121722383113622298934233803081353362766142828064444866452387493035890729629049156044077239071381051585930796086670172427121883998797908792274921901699720888093776657273330010533678812202354218097512545405947522435258490771167055601360483958644670632441572215539753697817977846174064955149290862569321978468622482839722413756570560574902614079729686524145351004748216637048440319989000889524345065854122758866688116427171479924442928230863465674813919123162824586178664583591245665294765456828489128831426076900422421902267105562632111110937054421750694165896040807198403850962455444362981230987879927244284909188845801561660979191338754992005240636899125607176060588611646710940507754100225698315520005593572972571636269561882670428252483600823257530420752963450"; +local maxNum = ""; --Holds the largest number product we have found so far +local maxProduct = 0; --Holds the product of what is currently stored in maxNum + +--Loop through all elements in the number string +for location=13,string.len(NUMBER) do + --Added 13 elements to it's own table + local currentProduct = string.sub(NUMBER, location, location) * string.sub(NUMBER, location - 1, location - 1) * string.sub(NUMBER, location - 2, location - 2) * string.sub(NUMBER, location - 3, location - 3) * string.sub(NUMBER, location - 4, location - 4) * string.sub(NUMBER, location - 5, location - 5) * string.sub(NUMBER, location - 6, location - 6) * string.sub(NUMBER, location - 7, location - 7) * string.sub(NUMBER, location - 8, location - 8) * string.sub(NUMBER, location - 9, location - 9) * string.sub(NUMBER, location - 10, location - 10) * string.sub(NUMBER, location - 11, location - 11) * string.sub(NUMBER, location - 12, location - 12); + --If the number is larger than the current max make it the max + if(currentProduct > maxProduct) then + maxProduct = currentProduct; + maxNum = string.sub(NUMBER, location - 12, location); + end +end + +timer:stop(); + +--Print the results +print("The largest product of 13 adjacent digits in the number is " .. math.floor(maxProduct)) +print("The numbers are " .. maxNum); +print("It took " .. timer:getMilliseconds() .. " milliseconds to run this algorithm"); + + +--[[Results: +The largest product of 13 adjacent digits in the number is 23514624000 +The numbers are 5576689664895 +It took 2.662 milliseconds to run this algorithm +]] diff --git a/Problem9.lua b/Problem9.lua new file mode 100644 index 0000000..4153b13 --- /dev/null +++ b/Problem9.lua @@ -0,0 +1,72 @@ +--ProjectEuler/lua/Problem9.lua +--Matthew Ellison +-- Created: 02-06-19 +--Modified: 03-28-19 +--There exists exactly one Pythagorean triplet for which a + b + c = 1000. Find the product abc. +--All of my requires, unless otherwise listed, can be found at https://bitbucket.org/Mattrixwv/luaClasses +--[[ + 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 . +]] + + +require "Stopwatch" + +timer = Stopwatch:create(); +timer:start(); + +local foundTriplet = false; --A simple flag to determine if we have found what we are looking for +local sideA = 1; --Start with the lowest possible a and search for the b that completes the triplet +local sideB = 0; --Holds the second side of the triangle +local sideC = 0; --Holds the hyp +while((sideA <= (1000 / 3)) and (not foundTriplet)) do + --Setup sides b and c + sideB = sideA + 1; + sideC = math.sqrt(sideA^2 + sideB^2); --Get the hyp + if((sideC % 1) == 0) then --If the hyp is an integer then make it one + sideC = math.floor(sideC); + end + --Loop through all possible b's and calculate c's until you find a number >= 1000 + while((sideA + sideB + sideC) < 1000) do + sideB = sideB + 1; + sideC = math.sqrt(sideA^2 + sideB^2); --Get the hyp + if((sideC % 1) == 0) then --If the hyp is an integer then make it one + sideC = math.floor(sideC); + end + end + --Check if the correct sides were found, otherwise continue to the next possible side + if((sideA + sideB + sideC) == 1000) then + foundTriplet = true; + else + sideA = sideA + 1; + end +end + +timer:stop(); +--Print the results +if(foundTriplet) then + print("The Pythagorean triplet where a + b + c = 1000 is " .. sideA .. ' ' .. sideB .. ' ' .. sideC); + print("The product of those numbers is " .. sideA * sideB * sideC); +else + print("Could not find the Pythagorean triplet where a + b + c = 1000"); +end + +print("It took " .. timer:getMilliseconds() .. " milliseconds 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 17.104 milliseconds to run this algorithm +]]