#ProjectEuler/Python/Problem23.py
#Matthew Ellison
# Created: 03-22-19
#Modified: 03-28-19
#Find the sum of all the positive integers which cannot be written as the sum of two abundant numbers
#All of my imports can be gotten from my pyClasses repository at https://bitbucket.org/Mattrixwv/pyClasses
"""
	Copyright (C) 2019  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/>.
"""


from Stopwatch import Stopwatch
import Algorithms

__maxNum = 28123


#A function that returns true if num can be created by adding two elements from abund and false if it cannot
def isSum(abund: list, num: int) -> bool:
	sumOfNums = 0
	#Pick a number for the first part of the sum
	for firstNum in range(0, len(abund)):
		#Pick a number for the second part of the sum
		for secondNum in range(0, len(abund)):
			sumOfNums = abund[firstNum] + abund[secondNum]
			if(sumOfNums == num):
				return True
			elif(sumOfNums > num):
				break
	#If you have run through the entire list and did not find a sum then it is false
	return False


def Problem23():
	#Setup the variables
	divisorSums = []
	#Make sure every element has a 0 in it's location
	for cnt in range(0, __maxNum):
		divisorSums.append(0)

	#Get the sum of the divisors of all numbers < __maxNum
	for cnt in range(1, __maxNum):
		div = Algorithms.getDivisors(cnt)
		if(len(div) > 1):
			div.remove(div[len(div) - 1])
		divisorSums[cnt] = sum(div)

	#Get the abundant numbers
	abund = []
	for cnt in range(0, len(divisorSums)):
		if(divisorSums[cnt] > cnt):
			abund.append(cnt)

	#Check if each number can be the sum of 2 abundant numbers and add to the sum if no
	sumOfNums = 0
	for cnt in range(1, __maxNum):
		if(not isSum(abund, cnt)):
			sumOfNums += cnt

	#Print the results
	print("The answer is " + str(sumOfNums))


if __name__ == "__main__":
	timer = Stopwatch()
	timer.start()
	Problem23()
	timer.stop()
	print("It took " + timer.getString() + " to run this algorithm")

""" Results:
The answer is 4179871
It took 27.738 minutes to run this algorithm
"""