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88 lines
2.4 KiB
Matlab
88 lines
2.4 KiB
Matlab
function [] = Problem27()
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%ProjectEuler/Octave/Problem27.m
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%Matthew Ellison
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% Created: 09-15-19
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%Modified: 09-15-19
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%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.
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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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%Setup variables
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topA = 0;
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topB = 0;
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topN = 0;
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primeNums = primes(12000);
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%Start timer
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startTime = clock();
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%Start with the lowest possible A and check all possibilities after that
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for a = -999 : 999
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%Start with the lowest possible B and check all possibilities after that
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for b = -1000 : 1000
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%Start with n=0 and check the formula to see how many primes you can get get with concecutive n's
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n = 0;
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quadratic = (n * n) + (a * n) + b;
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while(isFound(primeNums, quadratic))
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++n;
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quadratic = (n * n) + (a * n) + b;
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end
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--n;
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%Set all the largest number if this creaed more primes than any other
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if(n > topN)
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topN = n;
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topB = b;
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topA = a;
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end
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end
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end
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%End the timer
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endTime = clock();
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%Print the results
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printf("The greatest number of primes found is %d", topN)
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printf("\nIt was found with A = %d, B = %d", topA, topB)
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printf("\nThe product of A and B is %d\n", topA * topB)
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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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function [found] = isFound(array, key)
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found = false; %Start with a false. It only turns true if you find key in array
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for location = 1 : size(array)(2)
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if(key < array(location))
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return;
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elseif(key == array(location))
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found = true;
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return;
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end
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end
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end
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%{
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Results:
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The greatest number of primes found is 70
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It was found with A = -61, B = 971
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The product of A and B is -59231
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It took 1298.651146 seconds to run this algorithm
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%}
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