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

  • Difficulty Level : Medium
  • Last Updated : 08 Oct, 2021
Geek Week

Given an array of integers, you have to find three numbers such that the sum of two elements equals the third element.
Examples: 
 

Input : {5, 32, 1, 7, 10, 50, 19, 21, 2}
Output : 21, 2, 19

Input : {5, 32, 1, 7, 10, 50, 19, 21, 0}
Output : no such triplet exist

Question source: Arcesium Interview Experience | Set 7 (On campus for Internship)
 

Simple approach: Run three loops and check if there exists a triplet such that sum of two elements equals the third element.
Time complexity: O(n^3)
Efficient approach: The idea is similar to Find a triplet that sum to a given value. 
 

  • Sort the given array first.
  • Start fixing the greatest element of three from the back and traverse the array to find the other two numbers which sum up to the third element.
  • Take two pointers j(from front) and k(initially i-1) to find the smallest of the two number and from i-1 to find the largest of the two remaining numbers
  • If the addition of both the numbers is still less than A[i], then we need to increase the value of the summation of two numbers, thereby increasing the j pointer, so as to increase the value of A[j] + A[k].
  • If the addition of both the numbers is more than A[i], then we need to decrease the value of the summation of two numbers, thereby decrease the k pointer so as to decrease the overall value of A[j] + A[k].

Below image is a dry run of the above approach:
 



Below is the implementation of the above approach: 
 

C++




// CPP program to find three numbers
// such that sum of two makes the
// third element in array
#include <bits/stdc++.h>
using namespace std;
 
// Utility function for finding
// triplet in array
void findTriplet(int arr[], int n)
{
    // sort the array
    sort(arr, arr + n);
 
    // for every element in arr
    // check if a pair exist(in array) whose
    // sum is equal to arr element
    for (int i = n - 1; i >= 0; i--) {
        int j = 0;
        int k = i - 1;
 
        // Iterate forward and backward to find
        // the other two elements
        while (j < k) {
 
            // If the two elements sum is
            // equal to the third element
            if (arr[i] == arr[j] + arr[k]) {
 
                // pair found
                cout << "numbers are " << arr[i] << " "
                     << arr[j] << " " << arr[k] << endl;
                return;
            }
 
            // If the element is greater than
            // sum of both the elements, then try
            // adding a smaller number to reach the
            // equality
            else if (arr[i] > arr[j] + arr[k])
                j += 1;
 
            // If the element is smaller, then
            // try with a smaller number
            // to reach equality, so decrease K
            else
                k -= 1;
        }
    }
 
    // No such triplet is found in array
    cout << "No such triplet exists";
}
 
// driver program
int main()
{
    int arr[] = { 5, 32, 1, 7, 10, 50, 19, 21, 2 };
    int n = sizeof(arr) / sizeof(arr[0]);
 
    findTriplet(arr, n);
    return 0;
}

Java




// Java program to find three numbers
// such that sum of two makes the
// third element in array
import java.util.Arrays;
 
public class GFG {
 
    // utility function for finding
    // triplet in array
    static void findTriplet(int arr[], int n)
    {
        // sort the array
        Arrays.sort(arr);
 
        // for every element in arr
        // check if a pair exist(in array) whose
        // sum is equal to arr element
        for (int i = n - 1; i >= 0; i--) {
            int j = 0;
            int k = i - 1;
            while (j < k) {
                if (arr[i] == arr[j] + arr[k]) {
 
                    // pair found
                    System.out.println("numbers are " + arr[i] + " "
                                       + arr[j] + " " + arr[k]);
 
                    return;
                }
                else if (arr[i] > arr[j] + arr[k])
                    j += 1;
                else
                    k -= 1;
            }
        }
 
        // no such triplet is found in array
        System.out.println("No such triplet exists");
    }
 
    // driver program
    public static void main(String args[])
    {
        int arr[] = { 5, 32, 1, 7, 10, 50, 19, 21, 2 };
        int n = arr.length;
        findTriplet(arr, n);
    }
}
// This code is contributed by Sumit Ghosh

Python




# Python program to find three numbers
# such that sum of two makes the
# third element in array
 
# utility function for finding
# triplet in array
def findTriplet(arr, n):
     
    # sort the array
    arr.sort()
  
    # for every element in arr
    # check if a pair exist(in array) whose
    # sum is equal to arr element
    i = n - 1
    while(i >= 0):
        j = 0
        k = i - 1
        while (j < k):
            if (arr[i] == arr[j] + arr[k]):
                
                # pair found
                print "numbers are ", arr[i], arr[j], arr[k]
                return
            elif (arr[i] > arr[j] + arr[k]):
                j += 1
            else:
                k -= 1
        i -= 1
         
    # no such triplet is found in array
    print "No such triplet exists"
  
# driver program
arr = [ 5, 32, 1, 7, 10, 50, 19, 21, 2 ]
n = len(arr)
findTriplet(arr, n)
 
# This code is contributed by Sachin Bisht

C#




// C# program to find three numbers
// such that sum of two makes the
// third element in array
using System;
 
public class GFG {
 
    // utility function for finding
    // triplet in array
    static void findTriplet(int[] arr, int n)
    {
 
        // sort the array
        Array.Sort(arr);
 
        // for every element in arr
        // check if a pair exist(in
        // array) whose sum is equal
        // to arr element
        for (int i = n - 1; i >= 0; i--) {
            int j = 0;
            int k = i - 1;
            while (j < k) {
                if (arr[i] == arr[j] + arr[k]) {
 
                    // pair found
                    Console.WriteLine("numbers are "
                                      + arr[i] + " " + arr[j]
                                      + " " + arr[k]);
 
                    return;
                }
                else if (arr[i] > arr[j] + arr[k])
                    j += 1;
                else
                    k -= 1;
            }
        }
 
        // no such triplet is found in array
        Console.WriteLine("No such triplet exists");
    }
 
    // driver program
    public static void Main()
    {
        int[] arr = { 5, 32, 1, 7, 10, 50,
                      19, 21, 2 };
        int n = arr.Length;
 
        findTriplet(arr, n);
    }
}
 
// This code is contributed by vt_m.

PHP




<?php
// PHP program to find three
// numbers such that sum of
// two makes the third
// element in array
 
// utility function for
// finding triplet in array
function findTriplet($arr, $n)
{
    // sort the array
    sort($arr);
 
    // for every element in
    // arr check if a pair
    // exist(in array) whose
    // sum is equal to arr element
    for ($i = $n - 1; $i >= 0; $i--)
    {
        $j = 0;
        $k = $i - 1;
        while ($j < $k)
        {
            if ($arr[$i] == $arr[$j] + $arr[$k])
            {
                 
                // pair found
                echo "numbers are ", $arr[$i], " ",
                                      $arr[$j], " ",
                                      $arr[$k];
                return;
            }
            else if ($arr[$i] > $arr[$j] +
                                $arr[$k])
                $j += 1;
            else
                $k -= 1;
        }
    }
 
    // no such triplet
    // is found in array
    echo "No such triplet exists";
}
 
// Driver Code
$arr = array(5, 32, 1, 7, 10,
             50, 19, 21, 2 );
$n = count($arr);
 
findTriplet($arr, $n);
 
// This code is contributed by anuj_67.
?>

Javascript




<script>
 
// Javascript program to find three numbers
// such that sum of two makes the
// third element in array
 
 
// Utility function for finding
// triplet in array
function findTriplet(arr, n)
{
    // sort the array
    arr.sort((a,b) => a-b);
 
    // for every element in arr
    // check if a pair exist(in array) whose
    // sum is equal to arr element
    for (let i = n - 1; i >= 0; i--) {
        let j = 0;
        let k = i - 1;
 
        // Iterate forward and backward to find
        // the other two elements
        while (j < k) {
 
            // If the two elements sum is
            // equal to the third element
            if (arr[i] == arr[j] + arr[k]) {
 
                // pair found
                document.write("numbers are " + arr[i] +
                " " + arr[j] + " " + arr[k] + "<br>");
                return;
            }
 
            // If the element is greater than
            // sum of both the elements, then try
            // adding a smaller number to reach the
            // equality
            else if (arr[i] > arr[j] + arr[k])
                j += 1;
 
            // If the element is smaller, then
            // try with a smaller number
            // to reach equality, so decrease K
            else
                k -= 1;
        }
    }
 
    // No such triplet is found in array
    document.write("No such triplet exists");
}
 
// driver program
 
    let arr = [ 5, 32, 1, 7, 10, 50, 19, 21, 2 ];
    let n = arr.length;
 
    findTriplet(arr, n);
 
// This code is contributed by Mayank Tyagi
 
</script>

Output:  

numbers are 21 2 19

Time complexity: O(N^2)

Another Approach: The idea is similar to previous approach.

  1. Sort the given array.
  2. Start a nested loop, fixing the first element i(from 0 to n-1) and moving the other one j (from i+1 to n-1).
  3. Take the sum of both the elements and search it in the remaining array using Binary Search.

C++




// CPP program to find three numbers
// such that sum of two makes the
// third element in array
#include <bits/stdc++.h>
#include <iostream>
using namespace std;
 
// function to perform binary search
bool search(int sum, int start, int end, int arr[])
{
    while (start <= end) {
        int mid = (start + end) / 2;
        if (arr[mid] == sum) {
            return true;
        }
        else if (arr[mid] > sum) {
            end = mid - 1;
        }
        else {
            start = mid + 1;
        }
    }
    return false;
}
 
// function to find the triplets
void findTriplet(int arr[], int n)
{
    // sorting the array
    sort(arr, arr + n);
 
    // initialising nested loops
    for (int i = 0; i < n; i++) {
        for (int j = i + 1; j < n; j++) {
 
            // finding the sum of the numbers
            if (search((arr[i] + arr[j]), j, n - 1, arr)) {
 
                // printing out the first triplet
                cout << "Numbers are: " << arr[i] << " "
                     << arr[j] << " " << (arr[i] + arr[j]);
                return;
            }
        }
    }
    // if no such triplets are found
    cout << "No such numbers exist" << endl;
}
 
int main()
{
    int arr[] = { 5, 32, 1, 7, 10, 50, 19, 21, 2 };
    int n = sizeof(arr) / sizeof(arr[0]);
    findTriplet(arr, n);
    return 0;
}
 
// This code is contributed by Sarthak Delori

Javascript




<script>
 
// Javascript program to find three numbers
// such that sum of two makes the
// third element in array
 
bool search(sum, start, end, arr)
{
    while (start <= end) {
        let mid = (start + end) / 2;
        if (arr[mid] == sum) {
            return true;
        }
        else if (arr[mid] > sum) {
            end = mid - 1;
        }
        else {
            start = mid + 1;
        }
    }
    return false;
}
 
 
// Utility function for finding
// triplet in array
function findTriplet(arr, n)
{
    // sort the array
    arr.sort((a,b) => a-b);
 
    // initialising nested loops
    for (let i = 0; i < n; i++) {
        for (let j = i + 1; j < n; j++) {
            if (search((arr[i] + arr[j]), j, n - 1, arr)) {
                document.write("numbers are " + arr[i] +
                " " + arr[j] + " " + ( arr[i] + arr[j] ) + "<br>");
            }
        }
    }
    // No such triplet is found in array
    document.write("No such triplet exists");
}
 
// driver program
 
    let arr = [ 5, 32, 1, 7, 10, 50, 19, 21, 2 ];
    let n = arr.length;
 
    findTriplet(arr, n);
 
 
</script>
 
 
// This code is contributed by Sarthak Delori

Time Complexity: O(N^2*log N)

Space Complexity:  O(1)

This article is contributed by Mandeep Singh. If you like GeeksforGeeks and would like to contribute, you can also write an article using write.geeksforgeeks.org or mail your article to review-team@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.
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