阶乘递归，答案在纸上没有意义？

Question

So I was on codingbat doing recursion excercises and I ran into this

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

I don't understand how this works on paper. as 1 returns 1 thats fine, 2 returns 2, thats fine, 3 returns 6 thats fine, but then factorial(4) returns 24? factorial(5) returns 120?

It doesn't make sense because it is doing it from the last answer of n I assume but not minusing 1? But passes all the tests. So it does 6*4 = 24, rather than 4x(n-1) which wouldn't equal 24? Help?

Answer 1

For any factorial(n), it is computed as nx (n-1) x (n-2) x ... x 1

So for factorial(4) that will be 4 x 3 x 2 x 1 = 24

Recursion is mostly introduced using factorial as an example, so to visualize it will look like

fact(4) = 4 x fact(3)
        = 4 x 3 x fact(2)
        = 4 x 3 x 2 x fact(1)
        = 4 x 3 x 2 x 1 = 24

The recursion repeats until it hits the "anchor" which is the base case of 1

Answer 2

When you're trying to understand recursion, it's good to picture a stack. Every time we're calling return n * factorial(n - 1) we are pushing a value down the stack so we can retrieve it after we're done computing the factorial(n - 1) call. And so on so forth.

factorial(5)
= 5 * factorial(4)
= 5 * 4 * factorial(3)
= 5 * 4 * 3 * factorial(2)
= 5 * 4 * 3 * 2 *factorial(1)
= 5 * 4 * 3 * 2 * 1
= 120