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104 lines
3.3 KiB
Matlab
104 lines
3.3 KiB
Matlab
function [] = Problem37()
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%ProjectEuler/ProjectEulerOctave/Problem37.m
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%Matthew Ellison
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% Created: 07-01-21
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%Modified: 07-01-21
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%Find the sum of the only eleven primes that are both truncatable from left to right and right to left (2, 3, 5, and 7 are not counted).
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%{
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Copyright (C) 2021 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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%Setup the variables
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truncPrimes = []; %All numbers that are truncatable primes
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sumOfTrunc = 0; %The sum of all elements in truncPrimes
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%Start the timer
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startTime = clock();
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%Get all the primes up to a max number
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primeList = primes(750000);
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%primeList = primes(30);
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for loc = 5 : size(primeList)(2)
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currentPrime = primeList(loc);
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isTruncPrime = true;
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%Convert the prime to a string
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primeString = num2str(currentPrime);
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%If the string contains an even digit move to the next prime
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strLoc = 1;
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while((strLoc <= size(primeString)(2)) && (isTruncPrime))
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ch = primeString(strLoc);
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%Allow 2 to be the first digit
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if((strLoc == 1) && (ch == '2'))
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strLoc = strLoc;
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else
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if((ch == '0') || (ch == '2') || (ch == '4') || (ch == '6') || (ch == '8'))
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isTruncPrime = false;
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end
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end
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++strLoc;
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end
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%Start removing digits from the left and see if the number stays prime
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if(isTruncPrime)
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for truncLoc = 2 : size(primeString)(2)
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%Create a substring of the prime, removing the needed digits frome the left
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primeSubstring = substr(primeString, truncLoc);
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%Convert the string to an int and see if the number is still prime
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newPrime = str2num(primeSubstring);
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if(~isprime(newPrime))
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isTruncPrime = false;
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break;
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end
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end
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end
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%Start removing digits from the right and see if the number stays prime
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if(isTruncPrime)
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for truncLoc = 1 : size(primeString)(2) - 1
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%Create a substring of the prime, removing the needed digits from the right
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primeSubstring = substr(primeString, 1, size(primeString)(2) - truncLoc);
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%Convert the string to an int and see if the number is still a prime
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newPrime = str2num(primeSubstring);
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if(~isprime(newPrime))
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isTruncPrime = false;
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break;
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end
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end
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end
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%If the number remained prime through all operations add it to the table
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if(isTruncPrime)
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truncPrimes(end + 1) = currentPrime;
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end
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%End the loop if we have collected enough primes
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if(size(truncPrimes)(2) == 11)
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break;
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end
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end
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%Get the sum of all elements in the truncPrimes vector
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sumOfTrunc = sum(truncPrimes);
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%Stop the timer
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endTime = clock();
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%print the results
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printf("The sum of all left and right truncatable primes is %d\n", sumOfTrunc);
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printf("It took %f seconds to run this algorithm\n", etime(endTime, startTime))
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end
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%{
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The sum of all left and right truncatable primes is 748317
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It took 38.635521 seconds to run this algorithm
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%}
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