From 3e191e9d742ac2e17b4d790ad9fdf0ba7684d1d3 Mon Sep 17 00:00:00 2001
From: Mattrixwv <m_ellison@ymail.com>
Date: Sun, 6 Jun 2021 12:19:13 -0400
Subject: [PATCH] Added solution for problem 35

---
 Problem35.lua | 82 +++++++++++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 82 insertions(+)
 create mode 100644 Problem35.lua

diff --git a/Problem35.lua b/Problem35.lua
new file mode 100644
index 0000000..20fcc21
--- /dev/null
+++ b/Problem35.lua
@@ -0,0 +1,82 @@
+--ProjectEuler/ProjectEulerLua/Problem35.lua
+--Matthew Ellison
+-- Created: 06-05-21
+--Modified: 06-05-21
+--How many circular primes are there below one million?
+--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 MAX_NUM = 999999;	--The largest number that we are checking for primes
+local primes = {};	--The primes below MAX_NUM
+local circularPrimes = {};	--The circular primes below MAX_NUM
+
+--Functions
+--Returns a list of all rotations of a string passed to it
+local function getRotations(str)
+	local rotations = {};
+	table.insert(rotations, str);
+	for cnt = 1, string.len(str) - 1 do
+		str = string.sub(str, 2) .. string.sub(str, 1, 1);
+		table.insert(rotations, str);
+	end
+	return rotations;
+end
+
+--Start the timer
+timer:start();
+
+--Get all primes under 1,000,000
+primes = getPrimes(MAX_NUM);
+--Go through all primes, get all their rotations, and check if those numbers are also primes
+for cnt = 1, #primes do
+	local prime = primes[cnt];
+	local allRotationsPrime = true;
+	--Get all of the rotations of the prime and see if they are also prime
+	local rotations = getRotations(tostring(prime));
+	for rotCnt = 1, #rotations do
+		local rotation = rotations[rotCnt];
+		local p = tonumber(rotation, 10);
+		if(not isFound(primes, p)) then
+			allRotationsPrime = false;
+			break;
+		end
+	end
+	--If all rotations are prime add it to the list of circular primes
+	if(allRotationsPrime) then
+		table.insert(circularPrimes, prime);
+	end
+end
+
+--Stop the timer
+timer:stop();
+
+--Print the results
+io.write("The number of all circular prime numbers under " .. MAX_NUM .. " is " .. #circularPrimes .. "\n");
+io.write("It took " .. timer:getString() .. " to run this algorithm\n");
+
+--[[ Results:
+The number of all circular prime numbers under 999999 is 55
+It took 102.268 seconds to run this algorithm
+]]