--ProjectEUler/lua/Problem12.lua
--Matthew Ellison
-- Created: 02-07-19
--Modified: 03-28-19
--What is the value of the first triangle number to have over five hundred divisors?
--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"
require "Algorithms"


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

GOAL_DIVISORS = 500;

local triangularNumber = 1;
local nextNumber = 2;
local foundNumber = false;
local divisors = {};

while((not foundNumber) and (triangularNumber > 0)) do
	--See how many divisors this triangular number has
	divisors = getDivisors(triangularNumber);
	--If it has more than GOAL_DIVISORS  raise a flag to stop the loop
	if(#divisors > GOAL_DIVISORS) then
		foundNumber = true;
	else
		triangularNumber = triangularNumber + nextNumber;	--Add the next number to continue the triangular sequence
		nextNumber = nextNumber + 1;	--Advance to the next number for the triangular sequence
	end
end

timer:stop();

--Print the results
if(foundNumber) then
	print("The first triangular number with more than " .. GOAL_DIVISORS .. " divisors is " .. triangularNumber);
else
	print("There was an error. Could not find a triangular number with " .. GOAL_DIVISORS .. " divisors before overflow");
end
print("It took " .. timer:getSeconds() .. " seconds to run this algorithm");


--[[Results
The first triangular number with more than 500divisors is 76576500
It took 1.498547 seconds to run this algorithm
]]