DSAverse

Recursion

Loading Recursion Visualizer...

Recursion Tree

depth: 1

f(n) = f(n-1) + f(n-2)

Back to Recursion

Factorial Recursion

Watch the call stack grow as factorial calls itself, then see values return as the stack unwinds.

Call Stack: O(n)

Time: O(n)

Result: 120

Controls

Number (n): 5

factorial(5) = 120

Recursive calls: 5

Speed: 1000ms

Medium

Show execution trace

Step Information

Progress1 / 0

Phase:Making Calls

Pending:0 waiting

Adjust n and click Play to begin.

Call Stack

Calling

Depth: 0

Adjust n and click Play to begin

Legend

Making callReturnedActive

Execution Trace

Trace will appear here

Test Yourself

Q1/3

What is the base case of factorial recursion?

Python

def factorial(n):
    # Base case: factorial of 0 or 1 is 1
    if n <= 1:
        return 1
    # Recursive case: n * factorial(n-1)
    return n * factorial(n - 1)

# factorial(5) = 120

JavaScript

function factorial(n) {
    if (n <= 1) return 1;
    return n * factorial(n - 1);
}
// factorial(5) = 120

Complexity Analysis

Time Complexity: O(n)

Exactly n recursive calls, each O(1). For n=5: 5 calls.

Space Complexity: O(n)

Call stack grows to depth n. For n=5: max 5 frames.

Key Patterns