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. Do this for a grid
# of 20 by 20


def gridRoutes(x, y, gs):
    res = 0

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

    else:
        if y > x:
            h = x
            x = y
            y = h
        if y == 1:
            res = x + 1
        else:
            res = gridRoutes(x - 1, y, gs) + gridRoutes(x, y - 1, gs)

        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")

    gss = [0] * 21
    for i in range(21):
        gss[i] = [0] * 21

    g = gridRoutes(20, 20, gss)
    # dg = dumbGridRoutes(3, 2)
    print(g)
    # print(gss)

if __name__ == "__main__":
    main()