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Problem28.m

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