From 69c08cc70d11f678d9ca89818901ad29439f44cd Mon Sep 17 00:00:00 2001
From: Mattrixwv <m_ellison@ymail.com>
Date: Fri, 2 Jul 2021 00:47:19 -0400
Subject: [PATCH] Added solution to problem 37

---
 Problem36.lua |   2 +-
 Problem37.lua | 111 ++++++++++++++++++++++++++++++++++++++++++++++++++
 2 files changed, 112 insertions(+), 1 deletion(-)
 create mode 100644 Problem37.lua

diff --git a/Problem36.lua b/Problem36.lua
index db26730..5a18718 100644
--- a/Problem36.lua
+++ b/Problem36.lua
@@ -1,4 +1,4 @@
---ProjectEuler/ProjectEuler/Problem36.luaClasses
+--ProjectEuler/ProjectEulerLua/Problem36.lua
 --Matthew Ellison
 -- Created: 06-29-21
 --Modified: 06-29-21
diff --git a/Problem37.lua b/Problem37.lua
new file mode 100644
index 0000000..7744a34
--- /dev/null
+++ b/Problem37.lua
@@ -0,0 +1,111 @@
+--ProjectEuler/ProjectEulerLua/Problem37.lua
+--Matthew Ellison
+-- Created: 07-01-21
+--Modified: 07-01-21
+--Find the sum of the only eleven primes that are both truncatable from left to right and right to left (2, 3, 5, and 7 are not counted).
+--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"
+require "SieveOfEratosthenes"
+
+
+--Setup the variables
+local timer = Stopwatch:create();
+local LAST_PRIME_BEFORE_CHECK = 7;	--The last prime before 11 since single digit primes aren't checked
+local truncPrimes = {};	--All numbers that are truncatable primes
+local sum = 0;	--The sum of all elements in truncPrimes
+
+--Start the timer
+timer:start();
+
+--Create the sieve and get the first prime number
+local sieve = SieveOfEratosthenes:create();
+local currentPrime = sieve:next();
+--Loop through the sieve until you get to LAS_PRIME_BEFORE_CHECK
+while(currentPrime < LAST_PRIME_BEFORE_CHECK) do
+	currentPrime = sieve:next();
+end
+--Loop until truncPrimes contains 11 elements
+while(#truncPrimes < 11)do
+	local isTruncPrime = true;
+	--Get the next rpime
+	currentPrime = sieve:next();
+	--Convert the prime to a string
+	local primeString = tostring(currentPrime);
+	--If the string contains an even digit move to the next prime
+	local strLoc = 1;
+	while((strLoc <= #primeString) and (isTruncPrime)) do
+		local char = string.sub(primeString, strLoc, strLoc);
+		--Allow 2 to be the first digit
+		if((strLoc == 1) and (char == "2")) then
+		else
+			if((char == "0") or (char == "2") or (char == "4") or (char == "6") or (char == "8")) then
+				isTruncPrime = false;
+			end
+		end
+		strLoc = strLoc + 1;
+	end
+	--Start removing digits from the left and see if the number stays prime
+	if(isTruncPrime) then
+		for truncLoc = 2, #primeString do
+			--Create a substring of the prime, removing the needed digits from the left
+			local primeSubstring = string.sub(primeString, truncLoc);
+			--Convert the string to an int and see if the number is still prime
+			local newPrime = tonumber(primeSubstring);
+			if(not isPrime(newPrime)) then
+				isTruncPrime = false;
+				break;
+			end
+		end
+	end
+	--Start removing digits from the right and see if the number stays prime
+	if(isTruncPrime) then
+		for truncLoc = 1, #primeString - 1 do
+			--Create a substring of the prime, removing the needed digits from the right
+			local primeSubstring = string.sub(primeString, 1, #primeString - truncLoc);
+			--Convert the string to an int and see if the number is still a prime
+			local newPrime = tonumber(primeSubstring);
+			if(not isPrime(newPrime)) then
+				isTruncPrime = false;
+				break;
+			end
+		end
+	end
+	--If the number remained prime through all operations add it to the table
+	if(isTruncPrime) then
+		table.insert(truncPrimes, currentPrime);
+	end
+end
+--Get the sum of all elements in the truncPrimes vector
+sum = getSum(truncPrimes);
+
+--Stop the timer
+timer:stop();
+
+--Print the results
+io.write("The sum of all left and right truncatable primes is " .. sum .. "\n");
+io.write("It took " .. timer:getString() .. " to run this algorithm\n");
+
+
+--[[ Results:
+The sum of all left and right truncatable primes is 748317
+It took 491.000 milliseconds to run this algorithm
+]]