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

06 Apr, 2022
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++
Java
Python
C#
PHP
Javascript
// 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 arrayvoid 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 programint 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 program to find three numbers// such that sum of two makes the// third element in arrayimport 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 program to find three numbers# such that sum of two makes the# third element in array # utility function for finding# triplet in arraydef 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 programarr = [ 5, 32, 1, 7, 10, 50, 19, 21, 2 ]n = len(arr)findTriplet(arr, n) # This code is contributed by Sachin Bisht
// C# program to find three numbers// such that sum of two makes the// third element in arrayusing 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 program to find three// numbers such that sum of// two makes the third// element in array // utility function for// finding triplet in arrayfunction 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.?>
<script> // Javascript program to find three numbers// such that sum of two makes the// third element in array  // Utility function for finding// triplet in arrayfunction 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.
Sort the given array.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).Take the sum of both the elements and search it in the remaining array using Binary Search.
Sort the given array.
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).
Take the sum of both the elements and search it in the remaining array using Binary Search.
C++
Java
Python3
Javascript
// 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 searchbool 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 tripletsvoid 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
// Java program to find three numbers// such that sum of two makes the// third element in arrayimport java.util.*; class GFG{ // Function to perform binary searchstatic boolean 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 tripletsstatic void findTriplet(int arr[], int n){         // Sorting the array    Arrays.sort(arr);     // 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                System.out.print("Numbers are: " + arr[i] + " " +                                   arr[j] + " " + (arr[i] + arr[j]));                return;            }        }    }         // If no such triplets are found    System.out.print("No such numbers exist");} // Driver codepublic 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 target_2
# Python program to find three numbers# such that sum of two makes the# third element in arrayfrom functools import cmp_to_key def mycmp(a, b):    return a - b def search(sum, start, end, arr):     while (start <= end):        mid = (start + end) // 2        if (arr[mid] == sum):            return True        elif (arr[mid] > sum):            end = mid - 1        else:            start = mid + 1     return False # Utility function for finding# triplet in arraydef findTriplet(arr, n):     # sort the array    arr.sort(key = cmp_to_key(mycmp))     # initialising nested loops    for i in range(n):        for j in range(i + 1,n):            if (search((arr[i] + arr[j]), j, n - 1, arr)):                print(f"numbers are {arr[i]} {arr[j]} {( arr[i] + arr[j] )}")                return     # No such triplet is found in array    print("No such triplet exists") # driver programarr = [ 5, 32, 1, 7, 10, 50, 19, 21, 2 ]n = len(arr) findTriplet(arr, n) # This code is contributed by shinjanpatra
<script> // Javascript program to find three numbers// such that sum of two makes the// third element in arraybool 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 arrayfunction 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); // This code is contributed by Sarthak Delori</script>
Time Complexity: O(N^2*log N)
Space Complexity:  O(1)
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