Factorial (Recursive)

factorial(0) = 1, otherwise factorial(n) = n * factorial(n - 1). The smallest example of recursion with a single base case, used to visualise the call stack growing on descent and shrinking on unwind.

Algorithm

Canonical input n = 5 gives factorial(5) = 120. The replay shows six descent frames and five unwind frames (11 total).

descend then unwind Each non-base call awaits the result of the next call, then multiplies.

Visual walkthrough

The pinned run is factorial(5). The diagrams separate the descent, the base case, and the return values so the stack does not feel invisible.

Step 1 - Descend to the base case

Each call waits for one smaller call until f(0) returns 1.

Step 2 - Base value starts the unwind

The first finished frame is f(0) = 1; f(1) can now compute 1 * 1.

Step 3 - Unwind returns 120

Each frame multiplies its n by the completed smaller result.

Basic Implementation

                            basic.dart
                        

                            int factorial(int n) {
  if (n == 0) {
    return 1;
  }
  return n * factorial(n - 1);
}

void main() {
  final result = factorial(5);
  print(result);
}

                        

Complexity

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

Implementation notes

Dart: no need to grow the stack size at this depth; the standalone Dart VM handles n = 5 trivially.
The replay shows the call-stack contents on each frame and the computed n * factorial(n-1) value on each unwind, matching the lesson spec.