Visualizing recursive call stacks#

Recursive functions build up a stack as they work. Consider the sumup function we defined:

As sumup runs, each addition is pending on the call stack, as we wrote before:

sumup(10) — since 10 > 0, we go to the recursive case, computing…
10 + sumup(9) — since 9 > 0, we go to the recursive case, computing…
10 + 9 + sumup(8) — since 8 > 0, we go to the recursive case, computing…
10 + 9 + 8 + sumup(7) — since 7 > 0, we go to the recursive case, computing…
…and so on, until we have…
10 + 9 + 8 + 7 + 6 + 5 + 4 + 3 + 2 + sumup(1) — since 1 > 0, we go to the recursive case, computing…
10 + 9 + 8 + 7 + 6 + 5 + 4 + 3 + 2 + 1 + sumup(0) — and it’s not the case that 0 > 0, so sumup(0) returns 0, and we have…
10 + 9 + 8 + 7 + 6 + 5 + 4 + 3 + 2 + 1 + 0 which is 55.

It’s important to understand that each addition is waiting in its own stack frame. Using PythonTutor, it’s easy to see this in the progressive return values through each frame.

In order to understand, write, and debug recursive functions, you need to be able to picture the call stack in your mind. The best way to do this is to practice, by drawing how recursive functions are working on the board. Here’s a program with an interesting recursion: it sums up all of the numbers in arbitrarily nested lists. Notice how it uses isinstance to decide how to work:

Try drawing the stack of this program as it executes the function call at the bottom.