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Recursion: Conceptual

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Base Case of a Recursive Function

A recursive function should have a base case with a condition that stops the function from recursing indefinitely. In the example, the base case is a condition evaluating a negative or zero value to be true.

function countdown(value) if value is negative or zero print "done" otherwise if value is greater than zero print value call countdown with (value-1)

Recursive Step in Recursive Function

A recursive function should have a recursive step which calls the recursive function with some input that brings it closer to its base case. In the example, the recursive step is the call to countdown() with a decremented value.

def countdown(value): if value <= 0: print("done") else: print(value) countdown(value-1) #recursive step

What is Recursion

Recursion is a strategy for solving problems by defining the problem in terms of itself. A recursive function consists of two basic parts: the base case and the recursive step.

Call Stack in Recursive Function

Programming languages use a facility called a call stack to manage the invocation of recursive functions. Like a stack, a call stack for a recursive function calls the last function in its stack when the base case is met.

An animation showing how to calculate the factorial of 4 using a call stack.

Big-O Runtime for Recursive Functions

The big-O runtime for a recursive function is equivalent to the number of recursive function calls. This value varies depending on the complexity of the algorithm of the recursive function. For example, a recursive function of input N that is called N times will have a runtime of O(N). On the other hand, a recursive function of input N that calls itself twice per function may have a runtime of O(2^N).

Weak Base Case in Recursive Function

A recursive function with a weak base case will not have a condition that will stop the function from recursing, causing the function to run indefinitely. When this happens, the call stack will overflow and the program will generate a stack overflow error.

Execution Context of a Recursive Function

An execution context of a recursive function is the set of arguments to the recursive function call. Programming languages use execution contexts to manage recursive functions.

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