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Initializing Sorting Algorithms...

Sorting Algorithm

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Graph Traversal

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Factorial Recursion Visualizer

Watch how factorial function calls itself recursively and see the call stack in action.

Call Stack: O(n)

Time: O(n)

Result: 120

Controls

Number (n): 5

factorial(5) = 120

Calls needed: 5

Speed: 1000ms

Medium

Show execution trace

Step Information

Progress:1 / 0

Phase:📞 Making Calls

Pending:0 calls waiting

Click Start to begin the factorial visualization

Call Stack Visualization

Calling

Stack size: 0

Click Start to see the call stack in action

Execution Trace

Execution trace will appear here

Legend

Making function call

Returning value

Currently active

Stack level

Python Implementation

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)

# Example usage
result = factorial(5)  # Returns 120

JavaScript Implementation

function factorial(n) {
    // Base case
    if (n <= 1) {
        return 1;
    }
    
    // Recursive case
    return n * factorial(n - 1);
}

// Example usage
const result = factorial(5); // Returns 120

Complexity Analysis & Key Insights

Time Complexity: O(n)

The function makes exactly n recursive calls. Each call performs constant time operations (comparison and multiplication), so total time is proportional to n.

For n=5: 5 function calls needed

Space Complexity: O(n)

The recursion depth equals n, meaning the call stack grows to size n. Each stack frame stores the parameter and return address.

Max stack depth: 5 frames

Key Patterns

• 🎯 Base case: factorial(1) = 1
• 🔄 Recursive: n × factorial(n-1)
• 📞 Stack grows during calls
• 🔙 Values computed on return
• ⏳ Calls wait for subcalls
• 🧮 Final result: 120