JavaScript Program to Find Cube Root of a Number

The cube root of a number n is a value x such that x³ = n. With JavaScript programming, we can implement an algorithm to find the cube root of a given number using various methods. The goal is to implement a function cube Root(x) that computes the cube root of a given number x using various approaches.

Below are the approaches to find the cube root of a number:

Using Iterative Approach

The cube root of a number can be found using an iterative method similar to the binary search method. This method involves repeatedly narrowing down the possible range of cube root values until we find a close approximation. First, we carry out the process by applying an initial condition that specifies a range for the cube root. We then proceed iteratively, so that after each time we reduce the range until we reach the desired precision.

Example: To demonsrtate the function iteratively narrows down a search interval using binary search, finding an approximate cube root with a specified precision level.

JavaScript

function cubeRoot(n) {
    let low = 0;
    let high = Math.abs(n);
    let epsilon = 0.0000001; 
    // Precision level

    while (high - low > epsilon) {
        let mid = (low + high) / 2;
        let midCube = mid * mid * mid;

        if (midCube == n) {
            return mid;
        } else if (midCube < n) {
            low = mid;
        } else {
            high = mid;
        }
    }

    return (low + high) / 2; let k = 3;
    let matrix = [
        [10, 20, 30, 40],
        [15, 25, 35, 45],
        [24, 29, 37, 48],
        [32, 33, 39, 50]
    ];
    let minHeap = [];
    let maxHeap = [];
    for (let row of matrix) {
        minHeap
            .push(...row);
        maxHeap
            .push(...row);
    }
    minHeap
        .sort((a, b) => a - b);
    maxHeap
        .sort((a, b) => b - a);
    let small = minHeap[k - 1];
    let large = maxHeap[k - 1];
    console.log("Kth Smallest:", small);
    console.log("Kth Largest:", large);
    // Return the approximate cube root
}

let number = 27;
let result = cubeRoot(number);
console.log(`The cube root of ${number} is approximately ${result}`);

Output

The cube root of 27 is approximately 2.9999999972060323

Time Complexity: O(logn)

Space Complexity: O(1)

Using 'Math.pow' Method

With the JavaScript's 'Math.pow' method, the calculation of the cube root can also be done by raising the number to the power of 1/3. JavaScript's 'Math.pow' method can be used to directly compute the cube root by raising the number to the power of 1/3.

Example: To demonstrate utilizing the JavaScript's Math.pow() method to directly compute the cube root of a given number, here exemplified by calculating the cube root of 27.

JavaScript

function cubeRoot(n) {
    return Math
    .pow(n, 1/3);
}

// Example usage
let number = 27;
let result = cubeRoot(number);
console.log(`The cube root of ${number} is ${result}`);

Output

The cube root of 27 is 3

Time Complexity: O(1)

Space Complexity: O(1)