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Recursion for Coding Interviews in JavaScript

Solution Review: Compute the Square of a Number

Understand how to compute the square of a number using two approaches: direct multiplication and recursion. Learn the mathematical foundation for the recursive method, how to define base and recursive cases, and implement both solutions in JavaScript.

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Solution #1: Multiplying Number with Itself

Javascript (babel-node)
function findSquare(testVariable) {
  return testVariable * testVariable;
}
// Driver Code
var testVariable = 5;
console.log(findSquare(testVariable));

Explanation

The solution to this problem is simple. We multiply the input variable with itself and return the result.

Solution #2: Recursive Method

Javascript (babel-node)
function findSquare(testVariable) {
  // Base case
  if (testVariable == 0) {
    return 0;
  }
  // Recursive case
  else {
    return findSquare(testVariable - 1) + (2 * testVariable) - 1;
  }
}
// Driver Code
var testVariable = 5;
console.log(findSquare(testVariable));

Explanation

Let’s break the problem down mathematically. We’ll compute the square of a number by direct recursion:

To implement the square operation as a recursive function, we need to first express the square operation in terms of itself:

Mathematically we know that:

(n−1)2=n2−2n+1(n-1)^2 = n^2 - 2n + 1 ...