--ProjectEuler/lua/Problem28.lua
--Matthew Ellison
-- Created: 09-15-19
--Modified: 06-19-20
--What is the sum of the numbers on the diagonals in a 1001 by 1001 spiral formed by starting with the number 1 and moving to the right in a clockwise direction a 5 by 5 spiral
--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"


--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
]]