Factorial

Now that we understand both iteration and recursion, let's look at how both of them work.

As we know factorial of a number is defined as:

n! = n(n-1)(n-2)...1

or in other words:

n! = n(n-1)!

Let's now implement both an iterative and recursive solution for factorial in C++.

Both solutions look intuitive and easy to understand. The iterative version has a control variable i, which controls the loop so that the loop runs n times. For the iterative solution, we know in advance exactly how many times the loop would run.

The recursive version uses the second definition: n! = n * (n - 1)!, which is naturally a recursive definition. It defines the factorial of n in terms of the factorial of a smaller version (n - 1). We don't need to specify in advance, how many times the loop will run.

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// Iterative

function factorialIterative(n) {

  let result = 1;

  for (let i = n; i >= 1; i--) {

    result = result * i;

  }

  return result;

}

​

// Recursive

function factorialRecursive(n) {

  let result = 0;

​

  if (n == 1)

    // base case: n==1

    result = 1;

  // recursive case

  else result = n * factorialRecursive(n - 1);

​

  return result;

}

​

factorialIterative(4);

factorialRecursive(4);