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101 lines
3.0 KiB
Matlab
101 lines
3.0 KiB
Matlab
function [] = Problem28()
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%ProjectEuler/Octave/Problem28.m
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%Matthew Ellison
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% Created: 09-29-19
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%Modified: 10-06-19
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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 the variables
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finalLocation = false; %A flag to indicate if the final location to be filled has been reached
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currentNum = 1; %Set the number that is going to be put at each location
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%Make a 1001x1001 grid full of 0's
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square = zeros(1001, 1001);
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%Start the timer
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startTime = clock();
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%Start with the middle location and set it correctly and advance the tracker to the next number
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xLocation = 501;
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yLocation = 501;
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square(yLocation, xLocation) = currentNum++;
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%Move right the first time
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++xLocation;
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%Move in a circular pattern until you reach the final location
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while(~finalLocation)
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%Move down until you reach a blank location on the left
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while(square(yLocation, xLocation - 1) ~= 0)
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square(yLocation, xLocation) = currentNum++;
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++yLocation;
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end
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%Move left until you reach a blank location above
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while(square(yLocation - 1, xLocation) ~= 0)
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square(yLocation, xLocation) = currentNum++;
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--xLocation;
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end
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%Move up until you reach a blank location to the right
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while(square(yLocation, xLocation + 1) ~= 0)
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square(yLocation, xLocation) = currentNum++;
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--yLocation;
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end
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%Move right until you reach a blank location below
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while(square(yLocation + 1, xLocation) ~= 0)
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square(yLocation, xLocation) = currentNum++;
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++xLocation;
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%Check if you are at the final location and break the loop if you are
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if(xLocation > size(square)(2))
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finalLocation = true;
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break;
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end
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end
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end
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%Get the sum of the diagonals
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sumOfDiag = 0;
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leftSide = 1;
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rightSide = size(square)(2);
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row = 1;
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while(row <= size(square)(2))
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%This ensure the middle location is only counted one
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if(leftSide == rightSide)
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sumOfDiag += square(row, leftSide);
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else
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sumOfDiag += square(row, leftSide);
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sumOfDiag += square(row, rightSide);
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end
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++row;
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++leftSide;
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--rightSide;
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end
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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 the diagonals in the given grid is %d\n", sumOfDiag);
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printf("It took %f to run this algorithm\n", etime(endTime, startTime));
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end
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%{
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Results:
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The sum of the diagonals in the given grid is 669171001
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It took 8.751038 to run this algorithm
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%}
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