--ProjectEuler/lua/Problem33.lua
-- Created: 02-07-21
--Modified: 02-07-21
--[[
The fraction 49/98 is a curious fraction, as an inexperienced mathematician in attempting to simplify it may incorrectly believe that 49/98 = 4/8, which is correct, is obtained by cancelling the 9s
We shall consider fractions like, 30/50 = 3/5, to be trivial examples
There are exactly four non-trivial examples of this type of fraction, less than one in value, and containing two digits in the numerator and denominator
If the product of these four fractions is given in its lowest common terms, find the value of the denominator
]]
--All of my requires, unless otherwise listed, can be found at https://bitbucket.org/Mattrixwv/luaClasses
--[[
	Copyright (C) 2021  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"


--Setup the variables
local timer = Stopwatch:create();
local minNumerator = 10;
local maxNumerator = 98;
local minDenominator = 11;
local maxDenominator = 99;
local numerators = {};
local denominators = {};
local prodDenominator = 1;

--Start the timer
timer:start();

--Search every possible numerator/denominator pair
for denominator = minDenominator, maxDenominator do
	for numerator = minNumerator, (denominator - 1) do
		local num = tostring(numerator)
		local denom = tostring(denominator)
		local tempNum = 0;
		local tempDenom = 1;

		--Check that this isn't a trivial example
		if((string.sub(num, 2, 2) == '0') and (string.sub(denom, 2, 2) == '0')) then
			goto continue;
		--Remove the offending digits if they exist
		elseif(string.sub(num, 1, 1) == string.sub(denom, 1, 1)) then
			tempNum = tonumber(string.sub(num, 2, 2));
			tempDenom = tonumber(string.sub(denom, 2, 2));
		elseif(string.sub(num, 1, 1) == string.sub(denom, 2, 2)) then
			tempNum = tonumber(string.sub(num, 2, 2));
			tempDenom = tonumber(string.sub(denom, 1, 1));
		elseif(string.sub(num, 2, 2) == string.sub(denom, 1, 1)) then
			tempNum = tonumber(string.sub(num, 1, 1));
			tempDenom = tonumber(string.sub(denom, 2, 2));
		elseif(string.sub(num, 2, 2) == string.sub(denom, 2, 2)) then
			tempNum = tonumber(string.sub(num, 1, 1));
			tempDenom = tonumber(string.sub(denom, 1, 1));
		end
		if(tempDenom == 0) then
			goto continue;
		end

		--Test if the new fraction is the same as the old one
		if((tempNum / tempDenom) == (numerator / denominator)) then
			table.insert(numerators, numerator);
			table.insert(denominators, denominator);
		end

		::continue::
	end
end

--Get the product of the numbers
local numProd = getProd(numerators);
local denomProd = getProd(denominators);
--Get the gcd to reduce to lowest terms
local gcd = gcd(numProd, denomProd);
--Save the denominator
prodDenominator = denomProd / gcd;

--Stop the timer
timer:stop();

--Print the results
io.write("The denominator of the product is " .. prodDenominator .. '\n');
io.write("It took " .. timer:getString() .. " to run this algorithm\n");


--[[ Results:
The denominator of the product is 100.0
It took 4.000 milliseconds to run this algorithm
]]