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#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:
"""