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

Given an array of integers you have to find three numbers such that 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 back and traverse the array to find other two numbers which sum upto 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 increase 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++

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// 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;
}

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Java

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// 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

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Python

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# 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

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C#

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// 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.

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PHP

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<?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.
?>

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Output:

numbers are 21 2 19

Time complexity: O(N^2)

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

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Improved By : vt_m