Find a triplet that sum to a given value

Given an array and a value, find if there is a triplet in array whose sum is equal to the given value. If there is such a triplet present in array, then print the triplet and return true. Else return false. For example, if the given array is {12, 3, 4, 1, 6, 9} and given sum is 24, then there is a triplet (12, 3 and 9) present in array whose sum is 24.

Method 1 (Naive)
A simple method is to generate all possible triplets and compare the sum of every triplet with the given value. The following code implements this simple method using three nested loops.

C

#include <stdio.h> 
  
// returns true if there is triplet with sum equal 
// to 'sum' present in A[]. Also, prints the triplet 
bool find3Numbers(int A[], int arr_size, int sum) 
{ 
    int l, r; 
  
    // Fix the first element as A[i] 
    for (int i = 0; i < arr_size - 2; i++) { 
  
        // Fix the second element as A[j] 
        for (int j = i + 1; j < arr_size - 1; j++) { 
  
            // Now look for the third number 
            for (int k = j + 1; k < arr_size; k++) { 
                if (A[i] + A[j] + A[k] == sum) { 
                    printf("Triplet is %d, %d, %d", 
                           A[i], A[j], A[k]); 
                    return true; 
                } 
            } 
        } 
    } 
  
    // If we reach here, then no triplet was found 
    return false; 
} 
  
/* Driver program to test above function */
int main() 
{ 
    int A[] = { 1, 4, 45, 6, 10, 8 }; 
    int sum = 22; 
    int arr_size = sizeof(A) / sizeof(A[0]); 
    find3Numbers(A, arr_size, sum); 
    return 0; 
} 

Java

// Java program to find a triplet 
class FindTriplet { 
  
    // returns true if there is triplet with sum equal 
    // to 'sum' present in A[]. Also, prints the triplet 
    boolean find3Numbers(int A[], int arr_size, int sum) 
    { 
        int l, r; 
  
        // Fix the first element as A[i] 
        for (int i = 0; i < arr_size - 2; i++) { 
  
            // Fix the second element as A[j] 
            for (int j = i + 1; j < arr_size - 1; j++) { 
  
                // Now look for the third number 
                for (int k = j + 1; k < arr_size; k++) { 
                    if (A[i] + A[j] + A[k] == sum) { 
                        System.out.print("Triplet is " + A[i] + ", " + A[j] + ", " + A[k]); 
                        return true; 
                    } 
                } 
            } 
        } 
  
        // If we reach here, then no triplet was found 
        return false; 
    } 
  
    // Driver program to test above functions 
    public static void main(String[] args) 
    { 
        FindTriplet triplet = new FindTriplet(); 
        int A[] = { 1, 4, 45, 6, 10, 8 }; 
        int sum = 22; 
        int arr_size = A.length; 
  
        triplet.find3Numbers(A, arr_size, sum); 
    } 
} 

Python3

# Python3 program to find a triplet  
# that sum to a given value 
  
# returns true if there is triplet with 
# sum equal to 'sum' present in A[].  
# Also, prints the triplet 
def find3Numbers(A, arr_size, sum): 
  
    # Fix the first element as A[i] 
    for i in range( 0, arr_size-2): 
  
        # Fix the second element as A[j] 
        for j in range(i + 1, arr_size-1):  
              
            # Now look for the third number 
            for k in range(j + 1, arr_size): 
                if A[i] + A[j] + A[k] == sum: 
                    print("Triplet is", A[i], 
                          ", ", A[j], ", ", A[k]) 
                    return True
      
    # If we reach here, then no  
    # triplet was found 
    return False
  
# Driver program to test above function  
A = [1, 4, 45, 6, 10, 8] 
sum = 22
arr_size = len(A) 
find3Numbers(A, arr_size, sum) 
  
# This code is contributed by Smitha Dinesh Semwal  

C#

// C# program to find a triplet 
// that sum to a given value 
using System; 
  
class GFG { 
    // returns true if there is 
    // triplet with sum equal 
    // to 'sum' present in A[]. 
    // Also, prints the triplet 
    static bool find3Numbers(int[] A, 
                             int arr_size, 
                             int sum) 
    { 
        // Fix the first 
        // element as A[i] 
        for (int i = 0; 
             i < arr_size - 2; i++) { 
  
            // Fix the second 
            // element as A[j] 
            for (int j = i + 1; 
                 j < arr_size - 1; j++) { 
  
                // Now look for 
                // the third number 
                for (int k = j + 1; 
                     k < arr_size; k++) { 
                    if (A[i] + A[j] + A[k] == sum) { 
                        Console.WriteLine("Triplet is " + A[i] + ", " + A[j] + ", " + A[k]); 
                        return true; 
                    } 
                } 
            } 
        } 
  
        // If we reach here, 
        // then no triplet was found 
        return false; 
    } 
  
    // Driver Code 
    static public void Main() 
    { 
        int[] A = { 1, 4, 45, 6, 10, 8 }; 
        int sum = 22; 
        int arr_size = A.Length; 
  
        find3Numbers(A, arr_size, sum); 
    } 
} 
  
// This code is contributed by m_kit 

PHP

<?php 
// PHP program to find a triplet  
// that sum to a given value 
  
// returns true if there is  
// triplet with sum equal to 
// 'sum' present in A[]. 
// Also, prints the triplet 
function find3Numbers($A, $arr_size, $sum) 
{ 
    $l; $r; 
  
    // Fix the first 
    // element as A[i] 
    for ($i = 0;  
         $i < $arr_size - 2; $i++) 
    { 
    // Fix the second  
    // element as A[j] 
    for ($j = $i + 1;  
         $j < $arr_size - 1; $j++) 
    { 
        // Now look for the 
        // third number 
        for ($k = $j + 1;  
             $k < $arr_size; $k++) 
        { 
            if ($A[$i] + $A[$j] +  
                $A[$k] == $sum) 
            { 
                echo "Triplet is", " ", $A[$i], 
                                  ", ", $A[$j],  
                                  ", ", $A[$k]; 
                return true; 
            } 
        } 
    } 
    } 
  
    // If we reach here, then 
    // no triplet was found 
    return false; 
} 
// Driver Code 
$A = array(1, 4, 45,  
           6, 10, 8); 
$sum = 22; 
$arr_size = sizeof($A); 
  
find3Numbers($A, $arr_size, $sum); 
  
// This code is contributed by ajit 
?> 

Output :

Triplet is 4, 10, 8

Time Complexity : O(n^3)

Method 2 (Use Sorting)
Time complexity of the method 1 is O(n^3). The complexity can be reduced to O(n^2) by sorting the array first, and then using method 1 of this post in a loop.
1) Sort the input array.
2) Fix the first element as A[i] where i is from 0 to array size – 2. After fixing the first element of triplet, find the other two elements using method 1 of this post.

C++

// C++ program to find a triplet 
#include <bits/stdc++.h> 
using namespace std; 
  
// returns true if there is triplet with sum equal 
// to 'sum' present in A[]. Also, prints the triplet 
bool find3Numbers(int A[], int arr_size, int sum) 
{ 
    int l, r; 
  
    /* Sort the elements */
    sort(A, A + arr_size); 
  
    /* Now fix the first element one by one and find the 
       other two elements */
    for (int i = 0; i < arr_size - 2; i++) { 
  
        // To find the other two elements, start two index 
        // variables from two corners of the array and move 
        // them toward each other 
        l = i + 1; // index of the first element in the 
        // remaining elements 
  
        r = arr_size - 1; // index of the last element 
        while (l < r) { 
            if (A[i] + A[l] + A[r] == sum) { 
                printf("Triplet is %d, %d, %d", A[i], 
                       A[l], A[r]); 
                return true; 
            } 
            else if (A[i] + A[l] + A[r] < sum) 
                l++; 
            else // A[i] + A[l] + A[r] > sum 
                r--; 
        } 
    } 
  
    // If we reach here, then no triplet was found 
    return false; 
} 
  
/* Driver program to test above function */
int main() 
{ 
    int A[] = { 1, 4, 45, 6, 10, 8 }; 
    int sum = 22; 
    int arr_size = sizeof(A) / sizeof(A[0]); 
  
    find3Numbers(A, arr_size, sum); 
  
    return 0; 
} 

Java

// Java program to find a triplet 
class FindTriplet { 
  
    // returns true if there is triplet with sum equal 
    // to 'sum' present in A[]. Also, prints the triplet 
    boolean find3Numbers(int A[], int arr_size, int sum) 
    { 
        int l, r; 
  
        /* Sort the elements */
        quickSort(A, 0, arr_size - 1); 
  
        /* Now fix the first element one by one and find the 
           other two elements */
        for (int i = 0; i < arr_size - 2; i++) { 
  
            // To find the other two elements, start two index variables 
            // from two corners of the array and move them toward each 
            // other 
            l = i + 1; // index of the first element in the remaining elements 
            r = arr_size - 1; // index of the last element 
            while (l < r) { 
                if (A[i] + A[l] + A[r] == sum) { 
                    System.out.print("Triplet is " + A[i] + ", " + A[l] + ", " + A[r]); 
                    return true; 
                } 
                else if (A[i] + A[l] + A[r] < sum) 
                    l++; 
  
                else // A[i] + A[l] + A[r] > sum 
                    r--; 
            } 
        } 
  
        // If we reach here, then no triplet was found 
        return false; 
    } 
  
    int partition(int A[], int si, int ei) 
    { 
        int x = A[ei]; 
        int i = (si - 1); 
        int j; 
  
        for (j = si; j <= ei - 1; j++) { 
            if (A[j] <= x) { 
                i++; 
                int temp = A[i]; 
                A[i] = A[j]; 
                A[j] = temp; 
            } 
        } 
        int temp = A[i + 1]; 
        A[i + 1] = A[ei]; 
        A[ei] = temp; 
        return (i + 1); 
    } 
  
    /* Implementation of Quick Sort 
    A[] --> Array to be sorted 
    si  --> Starting index 
    ei  --> Ending index 
     */
    void quickSort(int A[], int si, int ei) 
    { 
        int pi; 
  
        /* Partitioning index */
        if (si < ei) { 
            pi = partition(A, si, ei); 
            quickSort(A, si, pi - 1); 
            quickSort(A, pi + 1, ei); 
        } 
    } 
  
    // Driver program to test above functions 
    public static void main(String[] args) 
    { 
        FindTriplet triplet = new FindTriplet(); 
        int A[] = { 1, 4, 45, 6, 10, 8 }; 
        int sum = 22; 
        int arr_size = A.length; 
  
        triplet.find3Numbers(A, arr_size, sum); 
    } 
} 

Python3

# Python3 program to find a triplet 
  
# returns true if there is triplet 
# with sum equal to 'sum' present 
# in A[]. Also, prints the triplet 
def find3Numbers(A, arr_size, sum): 
  
    # Sort the elements  
    A.sort() 
  
    # Now fix the first element  
    # one by one and find the 
    # other two elements  
    for i in range(0, arr_size-2): 
      
  
        # To find the other two elements, 
        # start two index variables from 
        # two corners of the array and 
        # move them toward each other 
          
        # index of the first element 
        # in the remaining elements 
        l = i + 1 
          
        # index of the last element 
        r = arr_size-1 
        while (l < r): 
          
            if( A[i] + A[l] + A[r] == sum): 
                print("Triplet is", A[i],  
                     ', ', A[l], ', ', A[r]); 
                return True
              
            elif (A[i] + A[l] + A[r] < sum): 
                l += 1
            else: # A[i] + A[l] + A[r] > sum 
                r -= 1
  
    # If we reach here, then 
    # no triplet was found 
    return False
  
# Driver program to test above function  
A = [1, 4, 45, 6, 10, 8] 
sum = 22
arr_size = len(A) 
  
find3Numbers(A, arr_size, sum) 
  
# This is contributed by Smitha Dinesh Semwal 

C#

// C# program to find a triplet 
using System; 
  
class GFG { 
  
    // returns true if there is triplet 
    // with sum equal to 'sum' present 
    // in A[]. Also, prints the triplet 
    bool find3Numbers(int[] A, int arr_size, 
                      int sum) 
    { 
        int l, r; 
  
        /* Sort the elements */
        quickSort(A, 0, arr_size - 1); 
  
        /* Now fix the first element  
    one by one and find the 
    other two elements */
        for (int i = 0; i < arr_size - 2; i++) { 
  
            // To find the other two elements, 
            // start two index variables from 
            // two corners of the array and 
            // move them toward each other 
            l = i + 1; // index of the first element 
            // in the remaining elements 
            r = arr_size - 1; // index of the last element 
            while (l < r) { 
                if (A[i] + A[l] + A[r] == sum) { 
                    Console.Write("Triplet is " + A[i] + ", " + A[l] + ", " + A[r]); 
                    return true; 
                } 
                else if (A[i] + A[l] + A[r] < sum) 
                    l++; 
  
                else // A[i] + A[l] + A[r] > sum 
                    r--; 
            } 
        } 
  
        // If we reach here, then 
        // no triplet was found 
        return false; 
    } 
  
    int partition(int[] A, int si, int ei) 
    { 
        int x = A[ei]; 
        int i = (si - 1); 
        int j; 
  
        for (j = si; j <= ei - 1; j++) { 
            if (A[j] <= x) { 
                i++; 
                int temp = A[i]; 
                A[i] = A[j]; 
                A[j] = temp; 
            } 
        } 
        int temp1 = A[i + 1]; 
        A[i + 1] = A[ei]; 
        A[ei] = temp1; 
        return (i + 1); 
    } 
  
    /* Implementation of Quick Sort 
A[] --> Array to be sorted 
si --> Starting index 
ei --> Ending index 
*/
    void quickSort(int[] A, int si, int ei) 
    { 
        int pi; 
  
        /* Partitioning index */
        if (si < ei) { 
            pi = partition(A, si, ei); 
            quickSort(A, si, pi - 1); 
            quickSort(A, pi + 1, ei); 
        } 
    } 
  
    // Driver Code 
    static void Main() 
    { 
        GFG triplet = new GFG(); 
        int[] A = new int[] { 1, 4, 45, 6, 10, 8 }; 
        int sum = 22; 
        int arr_size = A.Length; 
  
        triplet.find3Numbers(A, arr_size, sum); 
    } 
} 
  
// This code is contributed by mits 

PHP

<?php 
// PHP program to find a triplet 
  
// returns true if there is  
// triplet with sum equal to 
// 'sum' present in A[]. Also, 
// prints the triplet 
function find3Numbers($A, $arr_size, $sum) 
{ 
    $l; $r; 
  
    /* Sort the elements */
    sort($A); 
  
    /* Now fix the first element  
    one by one and find the 
    other two elements */
    for ($i = 0; $i < $arr_size - 2; $i++)  
    { 
  
        // To find the other two elements,  
        // start two index variables from  
        // two corners of the array and  
        // move them toward each other 
        $l = $i + 1; // index of the first element  
                     // in the remaining elements 
  
        // index of the last element 
        $r = $arr_size - 1;  
        while ($l < $r)  
        { 
            if ($A[$i] + $A[$l] +  
                $A[$r] == $sum) 
            { 
                echo "Triplet is ", $A[$i], " ", 
                                    $A[$l], " ",  
                                    $A[$r], "
"; 
                return true; 
            } 
            else if ($A[$i] + $A[$l] + 
                     $A[$r] < $sum) 
                $l++; 
            else // A[i] + A[l] + A[r] > sum 
                $r--; 
        } 
    } 
  
    // If we reach here, then 
    // no triplet was found 
    return false; 
} 
  
// Driver Code 
$A = array (1, 4, 45, 6, 10, 8); 
$sum = 22; 
$arr_size = sizeof($A); 
  
find3Numbers($A, $arr_size, $sum); 
  
// This code is contributed by ajit 
?> 

Output :

Triplet is 4, 8, 10

Time Complexity : O(n^2)

Method 3 (Hashing Based Solution)

C++

// C++ program to find a triplet using Hashing 
#include <bits/stdc++.h> 
using namespace std; 
  
// returns true if there is triplet with sum equal 
// to 'sum' present in A[]. Also, prints the triplet 
bool find3Numbers(int A[], int arr_size, int sum) 
{ 
    // Fix the first element as A[i] 
    for (int i = 0; i < arr_size - 2; i++) { 
  
        // Find pair in subarray A[i+1..n-1] 
        // with sum equal to sum - A[i] 
        unordered_set<int> s; 
        int curr_sum = sum - A[i]; 
        for (int j = i + 1; j < arr_size; j++) { 
            if (s.find(curr_sum - A[j]) != s.end()) { 
                printf("Triplet is %d, %d, %d", A[i], 
                       A[j], curr_sum - A[j]); 
                return true; 
            } 
            s.insert(A[j]); 
        } 
    } 
  
    // If we reach here, then no triplet was found 
    return false; 
} 
  
/* Driver program to test above function */
int main() 
{ 
    int A[] = { 1, 4, 45, 6, 10, 8 }; 
    int sum = 22; 
    int arr_size = sizeof(A) / sizeof(A[0]); 
  
    find3Numbers(A, arr_size, sum); 
  
    return 0; 
} 

Java

// Java program to find a triplet using Hashing 
import java.util.*; 
  
class GFG { 
  
    // returns true if there is triplet 
    // with sum equal to 'sum' present 
    // in A[]. Also, prints the triplet 
    static boolean find3Numbers(int A[], 
                                int arr_size, int sum) 
    { 
        // Fix the first element as A[i] 
        for (int i = 0; i < arr_size - 2; i++) { 
  
            // Find pair in subarray A[i+1..n-1] 
            // with sum equal to sum - A[i] 
            HashSet<Integer> s = new HashSet<Integer>(); 
            int curr_sum = sum - A[i]; 
            for (int j = i + 1; j < arr_size; j++) { 
                if (s.contains(curr_sum - A[j]) && curr_sum - A[j] != (int)s.toArray()[s.size() - 1]) { 
                    System.out.printf("Triplet is %d, %d, %d", A[i], 
                                      A[j], curr_sum - A[j]); 
                    return true; 
                } 
                s.add(A[j]); 
            } 
        } 
  
        // If we reach here, then no triplet was found 
        return false; 
    } 
  
    /* Driver code */
    public static void main(String[] args) 
    { 
        int A[] = { 1, 4, 45, 6, 10, 8 }; 
        int sum = 22; 
        int arr_size = A.length; 
  
        find3Numbers(A, arr_size, sum); 
    } 
} 
  
// This code has been contributed by 29AjayKumar 

Python3

# Python3 program to find a triplet using Hashing 
# returns true if there is triplet with sum equal 
# to 'sum' present in A[]. Also, prints the triplet 
def find3Numbers(A, arr_size, sum): 
    for i in range(0, arr_size-1): 
        # Find pair in subarray A[i + 1..n-1]  
        # with sum equal to sum - A[i] 
        s = set() 
        curr_sum = sum - A[i] 
        for j in range(i + 1, arr_size): 
            if (curr_sum - A[j]) in s: 
                print("Triplet is", A[i],  
                        ", ", A[j], ", ", curr_sum-A[j]) 
                return True
            s.add(A[j]) 
      
    return False
  
# Driver program to test above function  
A = [1, 4, 45, 6, 10, 8]  
sum = 22
arr_size = len(A)  
find3Numbers(A, arr_size, sum)  
  
# This is contributed by Yatin gupta 

C#

// C# program to find a triplet using Hashing 
using System; 
using System.Collections.Generic; 
public class GFG { 
  
    // returns true if there is triplet 
    // with sum equal to 'sum' present 
    // in A[]. Also, prints the triplet 
    static bool find3Numbers(int[] A, 
                             int arr_size, int sum) 
    { 
        // Fix the first element as A[i] 
        for (int i = 0; i < arr_size - 2; i++) { 
  
            // Find pair in subarray A[i+1..n-1] 
            // with sum equal to sum - A[i] 
            HashSet<int> s = new HashSet<int>(); 
            int curr_sum = sum - A[i]; 
            for (int j = i + 1; j < arr_size; j++) { 
                if (s.Contains(curr_sum - A[j])) { 
                    Console.Write("Triplet is {0}, {1}, {2}", A[i], 
                                  A[j], curr_sum - A[j]); 
                    return true; 
                } 
                s.Add(A[j]); 
            } 
        } 
  
        // If we reach here, then no triplet was found 
        return false; 
    } 
  
    /* Driver code */
    public static void Main() 
    { 
        int[] A = { 1, 4, 45, 6, 10, 8 }; 
        int sum = 22; 
        int arr_size = A.Length; 
  
        find3Numbers(A, arr_size, sum); 
    } 
} 
  
/* This code contributed by PrinciRaj1992 */

Output :

Triplet is 4, 8, 10

How to print all triplets with given sum?
Please refer Find all triplets with zero sum

Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above.

Find a triplet that sum to a given value

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