#Python/myClasses/Algorithms.py
#Matthew Ellison
# Created: 1-27-19
#Modified: 1-29-19
#This is a file that contains a few algorithms that I have used several times

import math

#This function returns a list with all the prime numbers <= goalNumber
def getPrimes(goalNumber: int):
	primes = []
	foundFactor = False

	#If the number is 0 or negative return an empty list
	if(goalNumber <= 1):
		return primes
	
	#If the number is even 2 is a factor and all other factors will be odd
	if((goalNumber %2) == 0):
		primes.append(2)
	#We can now start at 3 and skip all even numbers, because they cannot be prime
	for possiblePrime in range(3, goalNumber + 1, 2): #Need goalNumber + 1 to account for goalNumber being prime
		#See if the current possible prime is divisible by any prime less than it. If not it is a prime itself
		for primeNum in primes:
			if((possiblePrime % primeNum) == 0):
				foundFactor = True
				break
	
		#If you didn't find a factor then the current number must be prime
		if(not foundFactor):
			primes.append(possiblePrime)
		else:
			foundFactor = False

	primes.sort()
	return primes

#This function gets a certain number of primes
def getNumPrimes(numberOfPrimes: int):
	primes = []
	foundFactor = False

	#If the number is 0 or negative return an empty list
	if(numberOfPrimes < 1):
		return primes
	#Otherwise there is at lease 1, meaning 2 will be the first entry
	else:
		primes.append(2)

	#Loop through every odd number starting at 3 until you reach the correct number of entries looking for a prime number
	possiblePrime = 3	#Holds the next possible prime number
	while((len(primes) < numberOfPrimes) and (possiblePrime > 0)):
		#Loop through all primes we have already found, checking for a factor
		for primeNum in primes:
			#If you find a factor the number is not a prime so raise the flag and break the loop
			if((possiblePrime % primeNum) == 0):
				foundFactor = True
				break

		#If you don't find a factor then this number is prime so add it to the list
		if(not foundFactor):
			primes.append(possiblePrime)
		#If it wasn't prime simply reset the flag
		else:
			foundFactor = False
		#Increment to the next possible prime number
		possiblePrime += 2

	#Everything should already be in order, but sort it just in case
	primes.sort()

	#Return the list with all the prime numbers
	return primes
	

#This is a function that returns all the factors of goalNumber
def getFactors(goalNumber: int):
	#You need to get all the primes up to this number
	primes = getPrimes(math.ceil(math.sqrt(goalNumber)))	#If there is a prime it must be <= sqrt(num)
	factors = []

	#You need to step through each prime and see if it is a factor in the number
	cnt = 0
	while((cnt < len(primes)) and (goalNumber > 1)):
		#If the prime is a factor you need to add it to the factor list
		if((goalNumber % primes[cnt]) == 0):
			factors.append(primes[cnt])
			goalNumber /= primes[cnt]
		#Otherwise advance the location in primes you are looking at
		#By not advancing if the prime is a factor you allow for multiple of the same prime number as a factor
		else:
			cnt += 1

	#If you didn't get any factors the number itself must be a prime
	if(len(factors) == 0):
		factors.append(goalNumber)
		goalNumber /= goalNumber

	#If for some reason the goalNumber is not 0 print an error message
	if(goalNumber > 1):
		print("There was an error in getFactors(). A leftover of " + str(goalNumber))
	
	#Return the list of factors
	return factors