Recursion and Dynamic Programming

Factorial (Recursive)

factorial(0) = 1, otherwise factorial(n) = n * factorial(n - 1). The smallest example of recursion with a single base case.

Algorithm

Canonical input n = 5 descends through six call frames and unwinds through five multiplications. Final result 120.

Basic Implementation

basic.js 
function factorial(n) {
    if (n === 0) {
        return 1;
    }
    return n * factorial(n - 1);
}

const result = factorial(5);
console.log(result);

Complexity

  • Time: O(n)
  • Space: O(n) call stack

Implementation notes

  • JavaScript: same recursive shape as the other languages.
  • The replay treats the call stack as a vertical list of frames; descent pushes, unwind pops with the computed multiplication shown.
base case `if (n === 0) return 1;`
recursive call `return n * factorial(n - 1);`