--ProjectEuler/lua/Problem9.lua
--Matthew Ellison
-- Created: 02-06-19
--Modified: 06-19-20
--There exists exactly one Pythagorean triplet for which a + b + c = 1000. Find the product abc.
--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();

local foundTriplet = false;	--A simple flag to determine if we have found what we are looking for
local sideA = 1;	--Start with the lowest possible a and search for the b that completes the triplet
local sideB = 0;	--Holds the second side of the triangle
local sideC = 0;	--Holds the hyp
while((sideA <= (1000 / 3)) and (not foundTriplet)) do
	--Setup sides b and c
	sideB = sideA + 1;
	sideC = math.sqrt(sideA^2 + sideB^2);	--Get the hyp
	if((sideC % 1) == 0) then --If the hyp is an integer then make it one
		sideC = math.floor(sideC);
	end
	--Loop through all possible b's and calculate c's until you find a number >= 1000
	while((sideA + sideB + sideC) < 1000) do
		sideB = sideB + 1;
		sideC = math.sqrt(sideA^2 + sideB^2);	--Get the hyp
		if((sideC % 1) == 0) then	--If the hyp is an integer then make it one
			sideC = math.floor(sideC);
		end
	end
	--Check if the correct sides were found, otherwise continue to the next possible side
	if((sideA + sideB + sideC) == 1000) then
		foundTriplet = true;
	else
		sideA = sideA + 1;
	end
end

timer:stop();
--Print the results
if(foundTriplet) then
	print("The Pythagorean triplet where a + b + c = 1000 is " .. sideA .. ' ' .. sideB .. ' ' .. sideC);
	print("The product of those numbers is " .. sideA * sideB * sideC);
else
	print("Could not find the Pythagorean triplet where a + b + c = 1000");
end

print("It took " .. timer:getMilliseconds() .. " milliseconds to run this algorithm");

--[[Results
The Pythagorean triplet where a + b + c = 1000 is 200 375 425
The product of those numbers is 31875000
It took 17.104 milliseconds to run this algorithm
]]