#Project Euler/Python/Problem9.py
#Matthew Ellison
# Created: 01-29-19
#Modified: 03-28-19
#There exists exactly one Pythagorean triplet for which a + b + c = 1000. Find the product abc.
#Unless otherwise listed, all of my non-standard 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 math


def Problem9():
	#Setup the variables
	foundTriplet = False
	sideA = 1

	#Start with the lowest possible a , 1, and search for the b and c to complete the triplet
	while((sideA <= (1000 / 3)) and (not foundTriplet)):
		#Setup b and c
		sideB = sideA + 1	#b must be > a to be a triplet
		sideC = math.hypot(sideA, sideB)	#C is the hyp
		#Loop through possible b's and calculate c's until you find the numbers or the sum gets too large
		while((sideA + sideB + sideC) < 1000):
			sideB += 1
			sideC = math.hypot(sideA, sideB)
			#If c is an integer make it one
			if((sideC % 1) == 0):
				sideC = int(round(sideC))
		#Check if the correct sides were found
		if((sideA + sideB + sideC) == 1000):
			foundTriplet = True
		#Otherwise increment a to the next possible number
		else:
			sideA += 1

	#Print the results
	if(foundTriplet):
		print("The Pythagorean triplet where a + b + c = 1000 is " + str(sideA) + " " + str(sideB) + " " + str(int(sideC)))
		print("The product of those numbers is " + str(int(sideA * sideB * sideC)))
	else:
		print("Could not find the triplet where a + b + c = 1000")

#If you are running this file, automatically start the correct function
if __name__ == "__main__":
	timer = Stopwatch()	#Determines the algorithm's run time
	timer.start()	#Start the timer
	Problem9()		#Call the function that answers the question
	timer.stop()	#Start the timer
	#Print the results of the timer
	print("It took " + timer.getString() + " to run this algorithm")

"""Results:
The Pythagorean triplet where a + b + c = 1000 is 200 375 425
The product of those numbers is 31875000
It took 22.106 milliseconds to run this algorithm
"""