#ProjectEuler/Python/Problem1.py
#Matthew Ellison
# Created: 01-26-19
#Modified: 10-26-20
#What is the sum of all the multiples of 3 or 5 that are less than 1000
#Unless otherwise listed, all of my non-standard imports can be gotten from my pyClasses repository at https://bitbucket.org/Mattrixwv/pyClasses
"""
	Copyright (C) 2020  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 Problems.Problem import Problem
from Unsolved import Unsolved
import math


class Problem1(Problem):
	#Variables
	__topNum = 999	#The largest number to be checked

	#Functions
	#Constructor
	def __init__(self):
		super().__init__("What is the sum of all the multiples of 3 or 5 that are less than 1000")
		self.fullSum = 0	#The sum of all the numbers

	#Operational functions
	#Solve the problem
	def solve(self):
		#If the problem has already been solved do nothing and end the function
		if(self.solved):
			return

		#Start the timer
		self.timer.start()

		#Get the sum of the progressions of 3 and 5 and remove the sum of progressions of the overlap
		self.fullSum = self.sumOfProgression(3) + self.sumOfProgression(5) - self.sumOfProgression(3 * 5)

		#Stop the timer
		self.timer.stop()

		#Throw a flag to show the problem is solved
		self.solved = True

		#Save the results
		self.result = "The sum of all numbers < " + str(self.__topNum + 1) + " is " + str(self.fullSum)

	#Reset the problem so it can be run again
	def reset(self):
		super().reset()
		self.fullSum = 0
	#Gets
	#Returns the requested sum
	def getSum(self) -> int:
		#If the problem hasn't been solved throw an exception
		if(not self.solved):
			raise Unsolved("You must solve the problem before can you see the sum")
		return self.fullSum
	#Gets the sum of the progression of the multiple
	def sumOfProgression(self, multiple: int) -> int:
		numTerms = math.floor(self.__topNum / multiple)	#Get the sum of the progressions of 3 and 5 and remove the sum of progressions of the overlap
		#The sum of progression formula is (n / 2)(a + l). n = number of terms, a = multiple, l = last term
		return int((numTerms / 2) * (multiple + (numTerms * multiple)))


#If you are running this file, automatically start the correct function
if(__name__ == "__main__"):
	problem = Problem1()
	print(problem.getDescription())	#Print the description
	problem.solve()		#Call the function that answers the problem
	#Print the results
	print(problem.getResult())
	print("It took " + problem.getTime() + " to solve this algorithm")

"""Results:
The sum of all numbers < 1000 is 233168
It took an average of 2.293 microseconds to run this problem through 100 iterations
"""