5.9: Stack diagrams for recursive functions
- Page ID
- 41419
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.