--ProjectEuler/lua/Problem15.lua
--Matthew Ellison
-- Created: 02-07-19
--Modified: 06-19-20
--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) 2020  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"


local timer = Stopwatch:create();
timer:start();

GRID_WIDTH = 20;
GRID_HEIGHT = 20;
local lowestXReached = 20;
local 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
local 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.
]]