5.9: Stack diagrams for recursive functions

In Section 3.9, we used a stack diagram to represent the state of a program during a function call. The same kind of diagram can help interpret a recursive function.

Every time a function gets called, Python creates a frame to contain the function’s local variables and parameters. For a recursive function, there might be more than one frame on the stack at the same time.

Figure \(\PageIndex{1}\) shows a stack diagram for countdown called with n = 3.

As usual, the top of the stack is the frame for __main__. It is empty because we did not create any variables in __main__ or pass any arguments to it.

The four countdown frames have different values for the parameter n. The bottom of the stack, where n=0, is called the base case. It does not make a recursive call, so there are no more frames.

As an exercise, draw a stack diagram for print_n called with s = 'Hello' and n=2. Then write a function called do_n that takes a function object and a number, n, as arguments, and that calls the given function n times.

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