How to avoid using a global variable in this recursion function and improve my code?

Question

I made the next function to solve the problem of rat maze, where the rat only can move to forward and down, and i needed to find the number of ways possibles. I did it but i want to avoid the global variable "possible_ways". What are the way to improve my code ?

possible_ways = 0

def solve(n,x,y):
  if x == n-1 and y == n-1:
    global possible_ways
    possible_ways = possible_ways+1
    return True
  if x<=n-1 and y<=n-1:
    solve(n,x+1,y)
    solve(n,x,y+1)

solve(4,0,0)

print(possible_ways)

Answer 1

In this case you can make the function return a value (for all possible code paths in it — your code returned None whenever the first if condition was untrue):

def solve(n,x,y):
    if x == n-1 and y == n-1:
        return 1

    if x <= n-1 and y <= n-1:
        return solve(n,x+1,y) + solve(n,x,y+1)

    return 0

possible_ways = solve(4,0,0)
print(possible_ways)