8.1 recursion.js

// *****************************Replace Loops using Recursion*********************

// Recursion is the concept that a function can be expressed in terms of itself.
//  To help understand this, start by thinking about the following task: multiply the first n elements
//   of an array to create the product of those elements. Using a for loop, you could do this:

  function multiply(arr, n) {
    let product = 1;
    for (let i = 0; i < n; i++) {
      product *= arr[i];
    }
    return product;
  }
// However, notice that multiply(arr, n) == multiply(arr, n - 1) * arr[n - 1]. That means you can rewrite multiply in terms of itself and never need to use a loop.

  function multiply(arr, n) {
    if (n <= 0) {
      return 1;
    } else {
      return multiply(arr, n - 1) * arr[n - 1];
    }
  }
// The recursive version of multiply breaks down like this. In the base case, where n <= 0, 
// it returns 1. For larger values of n, it calls itself, but with n - 1. That function call 
// is evaluated in the same way, calling multiply again until n <= 0. At this point, all the 
// functions can return and the original multiply returns the answer.

// Note: Recursive functions must have a base case when they return without calling 
// the function again (in this example, when n <= 0), otherwise they can never finish executing.