Initial commit with existing files

Problem28.lua

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+--ProjectEuler/lua/Problem28.lua
+--Matthew Ellison
+-- Created: 09-15-19
+--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.
+--All of my requires, unless otherwise listed, can be found at https://bitbucket.org/Mattrixwv/luaClasses
+--[[
+	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/>.
+]]
+
+
+require "Stopwatch"
+
+
+--Setup the variables
+local timer = Stopwatch:create();
+local grid = {};
+local finalLocation = false;	--A flag to indicate if the final location to be filled has been reached
+local currentNum = 1;	--Set the number that is going to be put at each location
+--Make a 1001x1001 grid full of 0's
+for row = 0, 1001 do
+	grid[row] = {};
+	for col = 0, 1001 do
+		grid[row][col] = 0;
+	end
+end
+
+--Start the timer
+timer:start();
+
+--Start with the middle location and set it correctly and advance the tracker to the next number
+local xLocation = 500;
+local yLocation = 500;
+grid[yLocation][xLocation] = currentNum;
+currentNum = currentNum + 1;
+--Move right the first time
+xLocation = xLocation + 1;
+--Move in a circular pattern until you reach the final location
+while(not finalLocation) do
+	--Move down until you reach a blank location on the left
+	while(grid[yLocation][xLocation - 1] ~= 0) do
+		grid[yLocation][xLocation] = currentNum;
+		currentNum = currentNum + 1;
+		yLocation = yLocation + 1;
+	end
+	--Move left until you reach a blank location above
+	while(grid[yLocation - 1][xLocation] ~= 0) do
+		grid[yLocation][xLocation] = currentNum;
+		currentNum = currentNum + 1;
+		xLocation = xLocation - 1;
+	end
+
+	--Move up until you reach a blank location to the right
+	while(grid[yLocation][xLocation + 1] ~= 0) do
+		grid[yLocation][xLocation] = currentNum;
+		currentNum = currentNum + 1;
+		yLocation = yLocation - 1;
+	end
+
+	--Move right until you reach a blank location below
+	while(grid[yLocation + 1][xLocation] ~= 0) do
+		grid[yLocation][xLocation] = currentNum;
+		currentNum = currentNum + 1;
+		xLocation = xLocation + 1;
+		--Check if you are at the final location and break the loop if you are
+		if(xLocation == #grid) then
+			finalLocation = true;
+			break;
+		end
+	end
+end
+
+--Get the sum of the diagonals
+local leftSide = 0;
+local rightSide = #grid - 1;
+local row = 0;
+local sumOfDiag = 0;
+while(row < #grid) do
+	--This ensures the middle location is only counted once
+	if(leftSide == rightSide) then
+		sumOfDiag = sumOfDiag + grid[row][leftSide];
+	else
+		sumOfDiag = sumOfDiag + grid[row][leftSide];
+		sumOfDiag = sumOfDiag + grid[row][rightSide];
+	end
+	row = row + 1;
+	leftSide = leftSide + 1;
+	rightSide = rightSide - 1;
+end
+
+--Stop the timer
+timer:stop();
+
+--Print the results
+io.write("The sum of the diagonals in the given grid is " .. sumOfDiag .. '\n');
+io.write("It took " .. timer:getString() .. " to run this algorithm\n");
+
+--[[ Results:
+The sum of the diagonals in the given grid is 669171001
+It took 81.680 milliseconds to run this algorithm
+]]