From df797ac327886267e044c596d9199c486b9c2bc0 Mon Sep 17 00:00:00 2001
From: Mattrixwv <m_ellison@ymail.com>
Date: Wed, 10 Feb 2021 11:50:55 -0500
Subject: [PATCH] Added solution to problem 33

---
 Problem33.lua | 104 ++++++++++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 104 insertions(+)
 create mode 100644 Problem33.lua

diff --git a/Problem33.lua b/Problem33.lua
new file mode 100644
index 0000000..910a628
--- /dev/null
+++ b/Problem33.lua
@@ -0,0 +1,104 @@
+--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
+]]