# How can I count the number of cases in recursive functions?

One of the ways to solve this is by adding the count you get from each recursive function's return. When you call the recursive function, take the count that is returned and add it to the count variable in the current scope. For example:

def calcPath(trace_map, x, y):
n = len(trace_map)
count = 0
if x > n - 1 or y > n - 1:
pass
elif x < n and y < n:
if x + trace_map[x][y] == (n - 1) and y == (n - 1):
count += 1
elif x == (n - 1) and y + trace_map[x][y] == (n - 1):
count += 1
else:
count += calcPath(trace_map, x + trace_map[x][y], y)
count += calcPath(trace_map, x, y + trace_map[x][y])
return count


An alternative solution would be to create a global variable and reset it to 0 every time the function is called (although I don't recommend this since it requires ceremony everytime the function is called).

That might look something like this:

count = 0 # Global variable

def calcPath(trace_map, x, y):
global count
n = len(trace_map)
if x > n - 1 or y > n - 1:
pass
elif x < n and y < n:
if x + trace_map[x][y] == (n - 1) and y == (n - 1):
count += 1
elif x == (n - 1) and y + trace_map[x][y] == (n - 1):
count += 1
else:
calcPath(trace_map, x + trace_map[x][y], y)
calcPath(trace_map, x, y + trace_map[x][y])

if __name__ == "__main__":
trace_map = [
[1, 2, 9, 4, 9],
[9, 9, 9, 9, 9],
[9, 3, 9, 9, 2],
[9, 9, 9, 9, 9],
[9, 9, 9, 1, 0],
]
print(calcPath(trace_map, 0, 0))

# Use count in some way

count = 0 # Reset the count

trace_map = [[1, 1, 1], [1, 1, 2], [1, 2, 0]]
print(calcPath(trace_map, 0, 0))