#ProjectEuler/Python/Problem15.py
#Matthew Ellison
# Created: 01-31-19
#Modified: 03-28-19
#How many routes from the top left corner to the bottom right corner are there through a 20×20 grid if you can only move right and down?
#Unless otherwise listed, all of my non-standard imports can be gotten from my pyClasses repository at https://bitbucket.org/Mattrixwv/pyClasses
#There must be a better way than this. This is untested. I let it run for about 14 hours and it still hadn't spit an answer out for me
#But it is programed exactly as I programmed the C++ solution, so the eventual answer should be correct
"""
	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

__gridWidth = 20	#The height of the grid
__gridHeight = 20	#The width of the grid


def movement(currentX: int, currentY: int) -> int:
	#Return 1 if you are at the finish location
	if((currentX == __gridWidth) and (currentY == __gridHeight)):
		return 1

	numberMoves = 0
	#Otherwise move one right if you can and recurse
	if(currentX < __gridWidth):
		numberMoves = movement(currentX + 1, currentY)

	#Then move one down and recurse
	if(currentY < __gridHeight):
		numberMoves += movement(currentX, currentY + 1)

	return numberMoves

def Problem15():
	#Start the recursion at the right location and catch what is returned
	numberMoves = movement(0, 0)
	#Print the results
	print("The number of paths from 1 corner of a " + str(__gridWidth) + " x " + str(__gridHeight) + " grid to the opposite corner is " + str(numberMoves))

#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
	Problem15()		#Call the function that answers the question
	timer.stop()	#Stop the timer
	#Print the results of the timer
	print("It took " + timer.getString() + " to run this algorithm")

"""Results:

"""