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.
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
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.
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.
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.
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).