Initial commit with existing files

Problem15.lua

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+--ProjectEuler/lua/Problem15.lua
+--Matthew Ellison
+-- Created: 02-07-19
+--Modified: 03-28-19
+--How many routes from the top left corner to the bottom right corner are there through a 20×20 grid if you can only move right and down?
+--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"
+
+
+timer = Stopwatch:create();
+timer:start();
+
+GRID_WIDTH = 20;
+GRID_HEIGHT = 20;
+lowestXReached = 20;
+function movement(currentX, currentY)
+	--Return 1 if you are at the finish location
+	if((currentX == GRID_WIDTH) and (currentY == GRID_HEIGHT)) then
+		return 1;
+	end
+
+	local numberMoves = 0;
+	--Otherwise move one right if you can and recurse
+	if(currentX < GRID_WIDTH) then
+		numberMoves = numberMoves + movement(currentX + 1, currentY);
+	end
+
+	--Then move one down and recurse
+	if(currentY < GRID_HEIGHT) then
+		numberMoves = numberMoves + movement(currentX, currentY + 1);
+	end
+	---Helps keep track of where it is for timing purposes
+	if(currentX < lowestXReached) then
+		lowestXReached = currentX;
+		print("X hit");
+		print("NumberMoves = " .. numberMoves);
+		print("position = " .. currentX .. "; " .. currentY);
+	end
+
+	return numberMoves;	--Return the number of moves that have been found so far
+end
+
+--Start the recursion at the correct location and catch what is returned
+numberMoves = movement(0, 0);
+
+timer:stop();
+
+--Print the results
+print("The number of paths from 1 corner of a " .. GRID_WIDTH .. " x " .. GRID_HEIGHT .. " grid to the opposite corner is " .. numberMoves);
+print("It took " .. timer:getMinutes() .. " seconds to run this algorithm");
+
+--[[Results:
+Did not run this program to completion. It ran for 12.5 hours and was over half way done, but I got tired of waiting.
+It is coded the same way as the C++ version so should come up to the same answer.
+There has got to be a better way to do this problem.
+]]