import os
import math
import numpy as np


# Given a grid with start in one corner and goal in opposite corner, find 
# the number of paths you can take from start to goal


gs = [[0] * 21] * 21

def gridRoutes(x, y):
    res = 0

    if gs[x][y] > 0:
        res = gs[x][y]

    else:
        if x == 1:
            res = y + 1
        elif y == 1:
            res = x + 1
        else:
            res = gridRoutes(x - 1, y) + gridRoutes(x, y - 1)

        gs[x][y] = res
    print(x, y, res)
    return res

def dumbGridRoutes(x, y):
    if x == 1:
        return y + 1
    elif y == 1:
        return x + 1
    else:
        return dumbGridRoutes(x, y - 1) + dumbGridRoutes(x - 1, y)


def main():
    print("Hello, this is Patrick")

    g = gridRoutes(3, 2)
    gd = dumbGridRoutes(3, 2)
    print(g, gd)

if __name__ == "__main__":
    main()