JavaScript Program to Find a triplet such that sum of two equals to third element

We will be writing a JavaScript program that finds a triplet where the sum of two elements equals the third element. This program will be implemented using arrays and loop structures. We will iterate through the array and check for each combination of three elements if two elements sum up to the third. If we find such a triplet, we will return it immediately.

Problem Understanding

Given an array, we need to find three elements (a triplet) where a + b = c. For example, in array [1, 4, 45, 6, 10, 8], the triplet [4, 6, 10] satisfies this condition since 4 + 6 = 10.

Approach

Here is the approach to solve this problem:

• Use three nested loops to generate all possible combinations of three elements

• For each triplet, check if the sum of any two elements equals the third

• Check all three possible combinations: arr[i] + arr[j] = arr[k], arr[i] + arr[k] = arr[j], and arr[j] + arr[k] = arr[i]

• Return the first valid triplet found

• If no triplet is found, return an appropriate message

Example

Here is a complete JavaScript program to find a triplet such that the sum of two elements equals the third element:

function findTriplet(arr) {
    for (let i = 0; i < arr.length; i++) {
        for (let j = i + 1; j < arr.length; j++) {
            for (let k = j + 1; k < arr.length; k++) {
                // Check all three possible combinations
                if (arr[i] + arr[j] === arr[k]) {
                    return [arr[i], arr[j], arr[k]];
                }
                if (arr[i] + arr[k] === arr[j]) {
                    return [arr[i], arr[k], arr[j]];
                }
                if (arr[j] + arr[k] === arr[i]) {
                    return [arr[j], arr[k], arr[i]];
                }
            }
        }
    }
    return "No such triplet found";
}

// Test the function
let arr = [1, 4, 45, 6, 10, 8];
let result = findTriplet(arr);
console.log("Array:", arr);
console.log("Triplet found:", result);

// Test with another array
let arr2 = [3, 34, 4, 12, 5, 2];
let result2 = findTriplet(arr2);
console.log("Array:", arr2);
console.log("Triplet found:", result2);

Array: [ 1, 4, 45, 6, 10, 8 ]
Triplet found: [ 4, 6, 10 ]
Array: [ 3, 34, 4, 12, 5, 2 ]
Triplet found: [ 3, 4, 12 ]

Optimized Approach Using Sorting

For better efficiency, we can sort the array first and use a more optimized approach:

function findTripletOptimized(arr) {
    // Sort array first
    arr.sort((a, b) => a - b);
    
    for (let i = arr.length - 1; i >= 2; i--) {
        let left = 0;
        let right = i - 1;
        
        while (left < right) {
            if (arr[left] + arr[right] === arr[i]) {
                return [arr[left], arr[right], arr[i]];
            } else if (arr[left] + arr[right] < arr[i]) {
                left++;
            } else {
                right--;
            }
        }
    }
    return "No such triplet found";
}

// Test the optimized function
let arr3 = [1, 4, 45, 6, 10, 8];
let result3 = findTripletOptimized([...arr3]); // Use spread to avoid modifying original
console.log("Optimized result:", result3);

Optimized result: [ 4, 6, 10 ]

Comparison

Key Points

• The brute force approach checks all possible combinations of three elements

• We need to check all three sum combinations: a+b=c, a+c=b, and b+c=a

• The optimized approach uses sorting and two-pointer technique for better performance

• Both methods return the first valid triplet found

Conclusion

This program successfully finds triplets where the sum of two elements equals the third. The brute force method is simple but has O(n³) complexity, while the optimized approach reduces this to O(n²) after sorting.