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80 lines
2.7 KiB
Matlab
80 lines
2.7 KiB
Matlab
%ProjectEuler/Octave/Problem4.m
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%Matthew Ellison
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% Created:
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%Modified: 03-28-19
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%Find the largest palindrome made from the product of two 3-digit numbers
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%{
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Copyright (C) 2019 Matthew Ellison
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This program is free software: you can redistribute it and/or modify
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it under the terms of the GNU Lesser General Public License as published by
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the Free Software Foundation, either version 3 of the License, or
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(at your option) any later version.
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This program is distributed in the hope that it will be useful,
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but WITHOUT ANY WARRANTY; without even the implied warranty of
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MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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GNU Lesser General Public License for more details.
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You should have received a copy of the GNU Lesser General Public License
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along with this program. If not, see <https://www.gnu.org/licenses/>.
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%}
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%Make your variables
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answer = 0; %For the product of the two numbers
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numbers = [100:999]; %Create an array with a list of all 3 digit numbers
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palindromes = []; %Holds all the numbers that are palindromes
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%Create 2 counters for an inner loop and an outer loop
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%This allows you to multiply 2 numbers from the same array
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outerCounter = 1;
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innerCounter = 1;
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%Start the timer
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startTime = clock();
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while(outerCounter < size(numbers)(2))
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innerCounter = outerCounter; %Once you have multiplied 2 numbers there is no need to multiply them again, so skip what has already been done
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while(innerCounter < size(numbers)(2))
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%Multiply the two numbers
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answer = numbers(outerCounter) * numbers(innerCounter);
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%See if the number is a palindromes
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%%WARNING - Ocatave does not have a Reverse function. I had to create one that reversed strings
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if(num2str(answer) == Reverse(num2str(answer)))
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%Add it to the palindromes list
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palindromes(end + 1) = answer;
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end
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++innerCounter; %Increment
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end
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++outerCounter; %Increment
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end
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%Stop the timer
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endTime = clock(); %This is for timing purposes
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%Print the results
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printf("The largest palindrome made from the product of two 3-digit numbers is %d\n", max(palindromes))
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printf("It took %f seconds to run this algorithm\n", etime(endTime, startTime))
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%Cleanup your variables
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clear outerCounter;
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clear innerCounter;
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clear answer;
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clear numbers;
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clear palindromes;
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clear startTime;
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clear endTime;
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%{
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Results:
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The largest palindrome made from the product of two 3-digit numbers is 906609
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It took 663.732803 seconds to run this algorithm
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%}
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%This way is slow. I would like to find a faster way
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%{
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The palindrome can be written as: abccba Which then simpifies to: 100000a + 10000b + 1000c + 100c + 10b + a And then: 100001a + 10010b + 1100c Factoring out 11, you get: 11(9091a + 910b + 100c) So the palindrome must be divisible by 11. Seeing as 11 is prime, at least one of the numbers must be divisible by 11
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%}
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