Added a file with some helpful algorithms

Algorithms.lua

@@ -0,0 +1,92 @@
+--luaClasses/Algorithms.lua
+--Matthew Ellison
+-- Created: 2-4-19
+--Modified: 2-4-19
+--This is a file of algorithms that I have found it useful to keep around at all times
+
+
+--This function returns a list with all the primes numbers <= goalNumber
+function getPrimes(goalNumber)
+	local primes = {};	--Holds the prime numbers
+	local foundFactor = false;
+
+	--If the number is 0 or negative return an empty table
+	if(goalNumber <= 1) then
+		return primes;
+	--Otherwise the number is at lease 2, therefore 2 should be added to the list
+	else
+		primes[#primes + 1] = 2;
+	end
+
+	--We can now start at 3 and skip all even numbers, because they cannot be prime
+	for possiblePrime=3,goalNumber,2 do
+		--Check all current primes, up to sqrt(possiblePrime), to see if there is a divisor
+		primesCnt = 1;
+		--We can safely assume that there will be at least 1 element in the primes list because of 2 being added before the loop
+		topPossibleFactor = math.ceil(math.sqrt(possiblePrime))
+		while(primes[primesCnt] <= topPossibleFactor) do
+			if((possiblePrime % primes[primesCnt]) == 0) then
+				foundFactor = true;
+				break;
+			else
+				primesCnt = primesCnt + 1;
+			end
+			--Check if the index has gone out of range
+			if(primesCnt >= #primes) then
+				break;
+			end
+		end
+
+		--If you didn't find a factor then the current number must be prime
+			if(not foundFactor) then
+				primes[#primes + 1] = possiblePrime;
+			else
+				foundFactor = false;
+			end
+	end
+
+	--Sort the array just to be neat and safe
+	table.sort(primes);
+
+	--Return the array
+	return primes;
+end
+
+--This function gets a specific number of primes
+function getNumPrimes(numberOfPrimes)
+
+end
+
+--This is a function that returns all the factors of goalNumber
+function getFactors(goalNumber)
+	local primes = getPrimes(math.ceil(math.sqrt(goalNumber)));	--Get all the primes up the largest possible divisor
+	local factors = {};	--Holds all the factors
+
+	--You need to step through each prime and see if it is a factor of the number
+	cnt = 1;
+	while((cnt <= #primes) and (goalNumber > 1)) do
+		--If the prime is a factor you need to add it to the factor list
+		if((goalNumber % primes[cnt]) == 0) then
+			factors[#factors + 1] = primes[cnt];
+			goalNumber = goalNumber / primes[cnt];
+		--Otherwise advance the location in the primes array you are looking at
+		--By not advancing if the primes is a factor you allow for multiple of the same prime number as a factor
+		else
+			cnt = cnt + 1
+		end
+	end
+
+	--If you didn't get any factors the number itself must be a prime number
+	if(#factors == 0) then
+		factors[#factors + 1] = goalNumber;
+		goalNumber = 1
+	end
+
+	--If your some reason teh goalNumber is not 1 print an error message
+	if(goalNumber > 1) then
+		print("There was an error in getFactors(). A leftover of " .. goalNumber);
+	end
+
+	--Return the list of factors
+	return factors;
+end