JavaScript Program to Find Common Elements Between Two Sorted Arrays using Binary Search

Last Updated : 04 Jun, 2024

Given two sorted arrays, our task is to find common elements in two sorted arrays then the program should return an array that contains all the elements that are common to the two arrays. The arrays can contain duplicate elements, that is, values at one index in an array can be equal to the values at another index in the array.

Example:

Input: arr1 = [1, 1, 2, 2, 3, 3];
arr2 = [1, 1, 1, 2, 2, 4];
Output: [1, 2]

Approach

The "BSearch" function performs a binary search on a sorted array to find the element "x". It iteratively checks the middle element and adjusts the search range until it sees "x" or determines that "x" is not present.
The "BSearch" helper function is utilized to efficiently check for the presence of an element in an array, reducing the search time to logarithmic complexity.
In "findCommonEleBSearch", the arrays are swapped if necessary to ensure "arr1" is the smaller array. This reduces the number of binary searches needed, enhancing efficiency.
The function iterates through each element of "arr1", using "BSearch" to check if the element is in "arr2". If found and not a duplicate of the last added element, it adds the element to "commonelements".
The provided arrays "arr1" and "arr2" are compared, and the common elements [1, 4, 9] are correctly identified and printed using the "findCommonEleBSearch" function.

Example: The example below shows how to Find common elements in two sorted arrays using a Binary Search Algorithm.

JavaScript

function BSearch(arr, x) {
    let low = 0, high = arr.length - 1;
    while (low <= high) {
        let mid = Math.floor((low + high) / 2);
        if (arr[mid] === x) return true;
        else if (arr[mid] < x) low = mid + 1;
        else high = mid - 1;
    }
    return false;
}

// Function to find common elements using binary search
function findCommonEleBSearch(arr1, arr2) {
    // Ensure arr1 is the smaller array for efficiency
    if (arr1.length > arr2.length) {
        [arr1, arr2] = [arr2, arr1];
    }

    let commonElements = [];
    let lastAddedElement = null;
    for (let i = 0; i < arr1.length; i++) {
        if (arr1[i] !== lastAddedElement && 
                        BSearch(arr2, arr1[i])) {
            commonElements.push(arr1[i]);
            lastAddedElement = arr1[i];
        }
    }

    return commonElements;
}

let arr1 = [1, 3, 4, 6, 7, 9];
let arr2 = [1, 2, 4, 5, 9, 10];

let commonBSearch = findCommonEleBSearch(arr1, arr2);
console.log(commonBSearch);