 GFG App
Open App Browser
Continue

# Find all triplets with zero sum

Given an array of distinct elements. The task is to find triplets in the array whose sum is zero.

Examples :

Input: arr[] = {0, -1, 2, -3, 1}
Output: (0 -1 1), (2 -3 1)
Explanation: The triplets with zero sum are 0 + -1 + 1 = 0 and 2 + -3 + 1 = 0

Input: arr[] = {1, -2, 1, 0, 5}
Output: 1 -2  1
Explanation: The triplets with zero sum is 1 + -2 + 1 = 0

Recommended Practice

Naive approach: Below is the idea to solve the problem

Run three loops and check one by one whether the sum of the three elements is zero or not. If the sum of three elements is zero then print elements otherwise print not found.

Follow the below steps to Implement the Idea:

• Run three nested loops with loop counter i, j, k
• The first loops will run from 0 to n-3 and second loop from i+1 to n-2 and the third loop from j+1 to b. The loop counter represents the three elements of the triplet.
• Check if the sum of elements at i’th, j’th, k’th is equal to zero or not. If yes print the sum else continue.

Below is the implementation of the above approach:

## C++

 `// A simple C++ program to find three elements` `// whose sum is equal to zero` `#include ` `using` `namespace` `std;`   `// Prints all triplets in arr[] with 0 sum` `void` `findTriplets(``int` `arr[], ``int` `n)` `{` `    ``bool` `found = ``false``;` `    ``for` `(``int` `i = 0; i < n - 2; i++) {` `        ``for` `(``int` `j = i + 1; j < n - 1; j++) {` `            ``for` `(``int` `k = j + 1; k < n; k++) {` `                ``if` `(arr[i] + arr[j] + arr[k] == 0) {` `                    ``cout << arr[i] << ``" "` `<< arr[j] << ``" "` `                         ``<< arr[k] << endl;` `                    ``found = ``true``;` `                ``}` `            ``}` `        ``}` `    ``}`   `    ``// If no triplet with 0 sum found in array` `    ``if` `(found == ``false``)` `        ``cout << ``" not exist "` `<< endl;` `}`   `// Driver code` `int` `main()` `{` `    ``int` `arr[] = { 0, -1, 2, -3, 1 };` `    ``int` `n = ``sizeof``(arr) / ``sizeof``(arr);` `    ``findTriplets(arr, n);` `    ``return` `0;` `}`   `// This code is contributed by Aditya Kumar (adityakumar129)`

## C

 `// A simple C program to find three elements` `// whose sum is equal to zero` `#include ` `#include `   `// Prints all triplets in arr[] with 0 sum` `void` `findTriplets(``int` `arr[], ``int` `n)` `{` `    ``bool` `found = ``false``;` `    ``for` `(``int` `i = 0; i < n - 2; i++) {` `        ``for` `(``int` `j = i + 1; j < n - 1; j++) {` `            ``for` `(``int` `k = j + 1; k < n; k++) {` `                ``if` `(arr[i] + arr[j] + arr[k] == 0) {` `                    ``printf``(``"%d %d %d\n"``, arr[i], arr[j],` `                           ``arr[k]);` `                    ``found = ``true``;` `                ``}` `            ``}` `        ``}` `    ``}`   `    ``// If no triplet with 0 sum found in array` `    ``if` `(found == ``false``)` `        ``printf``(``" not exist \n"``);` `}`   `// Driver code` `int` `main()` `{` `    ``int` `arr[] = { 0, -1, 2, -3, 1 };` `    ``int` `n = ``sizeof``(arr) / ``sizeof``(arr);` `    ``findTriplets(arr, n);` `    ``return` `0;` `}`   `// This code is contributed by Aditya Kumar (adityakumar129)`

## Java

 `// A simple Java program to find three elements` `// whose sum is equal to zero` `import` `java.io.*;` `import` `java.util.*;` `class` `num {` `    ``// Prints all triplets in arr[] with 0 sum` `    ``static` `void` `findTriplets(``int``[] arr, ``int` `n)` `    ``{` `        ``boolean` `found = ``false``;` `        ``for` `(``int` `i = ``0``; i < n - ``2``; i++) {` `            ``for` `(``int` `j = i + ``1``; j < n - ``1``; j++) {` `                ``for` `(``int` `k = j + ``1``; k < n; k++) {` `                    ``if` `(arr[i] + arr[j] + arr[k] == ``0``) {` `                        ``System.out.println(arr[i] + ``" "` `                                           ``+ arr[j] + ``" "` `                                           ``+ arr[k]);` `                        ``found = ``true``;` `                    ``}` `                ``}` `            ``}` `        ``}`   `        ``// If no triplet with 0 sum found in array` `        ``if` `(found == ``false``)` `            ``System.out.println(``" not exist "``);` `    ``}`   `    ``// Driver code` `    ``public` `static` `void` `main(String[] args)` `    ``{` `        ``int` `arr[] = { ``0``, -``1``, ``2``, -``3``, ``1` `};` `        ``int` `n = arr.length;` `        ``findTriplets(arr, n);` `    ``}` `}`   `// This code is contributed by Aditya Kumar (adityakumar129)`

## Python3

 `# A simple Python 3 program` `# to find three elements whose` `# sum is equal to zero`   `# Prints all triplets in` `# arr[] with 0 sum`     `def` `findTriplets(arr, n):`   `    ``found ``=` `False` `    ``for` `i ``in` `range``(``0``, n``-``2``):`   `        ``for` `j ``in` `range``(i``+``1``, n``-``1``):`   `            ``for` `k ``in` `range``(j``+``1``, n):`   `                ``if` `(arr[i] ``+` `arr[j] ``+` `arr[k] ``=``=` `0``):` `                    ``print``(arr[i], arr[j], arr[k])` `                    ``found ``=` `True`   `    ``# If no triplet with 0 sum` `    ``# found in array` `    ``if` `(found ``=``=` `False``):` `        ``print``(``" not exist "``)`     `# Driver code` `arr ``=` `[``0``, ``-``1``, ``2``, ``-``3``, ``1``]` `n ``=` `len``(arr)` `findTriplets(arr, n)`   `# This code is contributed by Smitha Dinesh Semwal`

## C#

 `// A simple C# program to find three elements` `// whose sum is equal to zero` `using` `System;`   `class` `GFG {`   `    ``// Prints all triplets in arr[] with 0 sum` `    ``static` `void` `findTriplets(``int``[] arr, ``int` `n)` `    ``{` `        ``bool` `found = ``false``;` `        ``for` `(``int` `i = 0; i < n - 2; i++) {` `            ``for` `(``int` `j = i + 1; j < n - 1; j++) {` `                ``for` `(``int` `k = j + 1; k < n; k++) {` `                    ``if` `(arr[i] + arr[j] + arr[k] == 0) {` `                        ``Console.Write(arr[i]);` `                        ``Console.Write(``" "``);` `                        ``Console.Write(arr[j]);` `                        ``Console.Write(``" "``);` `                        ``Console.Write(arr[k]);` `                        ``Console.Write(``"\n"``);` `                        ``found = ``true``;` `                    ``}` `                ``}` `            ``}` `        ``}`   `        ``// If no triplet with 0 sum found in` `        ``// array` `        ``if` `(found == ``false``)` `            ``Console.Write(``" not exist "``);` `    ``}`   `    ``// Driver code` `    ``public` `static` `void` `Main()` `    ``{` `        ``int``[] arr = { 0, -1, 2, -3, 1 };` `        ``int` `n = arr.Length;` `        ``findTriplets(arr, n);` `    ``}` `}`   `// This code is contributed by nitin mittal.`

## PHP

 ``

## Javascript

 ``

Output

```0 -1 1
2 -3 1```

Time Complexity: O(n3), As three nested loops are required, so the time complexity is O(n3).
Auxiliary Space: O(1), Since no extra space is required, so the space complexity is constant.

## Find all  triplets with zero sum using Hashing

Below is the idea to solve the problem

This involves traversing through the array. For every element arr[i], find a pair with sum “-arr[i]”. This problem reduces to pair sum and can be solved in O(n) time using hashing.

Follow the steps below to implement the idea:

• Create a HashSet to store a unique element.
• Run a nested loop with two loops, the outer loop from 0 to n-2 and the inner loop from i+1 to n-1
• Check if the sum of ith and jth element multiplied with -1 is present in the HashSet or not
• If the element is present in the HashSet, print the triplet else insert the jth element in the HashSet.

Below is the implementation of the above approach:

## C++

 `// C++ program to find triplets in a given` `// array whose sum is zero` `#include ` `using` `namespace` `std;`   `// function to print triplets with 0 sum` `void` `findTriplets(``int` `arr[], ``int` `n)` `{` `    ``bool` `found = ``false``;`   `    ``for` `(``int` `i = 0; i < n - 1; i++) {` `        ``// Find all pairs with sum equals to` `        ``// "-arr[i]"` `        ``unordered_set<``int``> s;` `        ``for` `(``int` `j = i + 1; j < n; j++) {` `            ``int` `x = -(arr[i] + arr[j]);` `            ``if` `(s.find(x) != s.end()) {` `                ``printf``(``"%d %d %d\n"``, x, arr[i], arr[j]);` `                ``found = ``true``;` `            ``}` `            ``else` `                ``s.insert(arr[j]);` `        ``}` `    ``}`   `    ``if` `(found == ``false``)` `        ``cout << ``" No Triplet Found"` `<< endl;` `}`   `// Driver code` `int` `main()` `{` `    ``int` `arr[] = { 0, -1, 2, -3, 1 };` `    ``int` `n = ``sizeof``(arr) / ``sizeof``(arr);` `    ``findTriplets(arr, n);` `    ``return` `0;` `}`

## Java

 `// Java program to find triplets in a given` `// array whose sum is zero` `import` `java.io.*;` `import` `java.util.*;`   `class` `GFG {`   `    ``// function to print triplets with 0 sum` `    ``static` `void` `findTriplets(``int` `arr[], ``int` `n)` `    ``{` `        ``boolean` `found = ``false``;`   `        ``for` `(``int` `i = ``0``; i < n - ``1``; i++) {` `            ``// Find all pairs with sum equals to` `            ``// "-arr[i]"` `            ``HashSet s = ``new` `HashSet();` `            ``for` `(``int` `j = i + ``1``; j < n; j++) {` `                ``int` `x = -(arr[i] + arr[j]);` `                ``if` `(s.contains(x)) {` `                    ``System.out.printf(``"%d %d %d\n"``, x,` `                                      ``arr[i], arr[j]);` `                    ``found = ``true``;` `                ``}` `                ``else` `{` `                    ``s.add(arr[j]);` `                ``}` `            ``}` `        ``}`   `        ``if` `(found == ``false``) {` `            ``System.out.printf(``" No Triplet Found\n"``);` `        ``}` `    ``}`   `    ``// Driver code` `    ``public` `static` `void` `main(String[] args)` `    ``{` `        ``int` `arr[] = { ``0``, -``1``, ``2``, -``3``, ``1` `};` `        ``int` `n = arr.length;` `        ``findTriplets(arr, n);` `    ``}` `}`   `// This code contributed by Rajput-Ji`

## Python3

 `# Python3 program to find triplets` `# in a given array whose sum is zero`   `# function to print triplets with 0 sum`     `def` `findTriplets(arr, n):` `    ``found ``=` `False` `    ``for` `i ``in` `range``(n ``-` `1``):`   `        ``# Find all pairs with sum` `        ``# equals to "-arr[i]"` `        ``s ``=` `set``()` `        ``for` `j ``in` `range``(i ``+` `1``, n):` `            ``x ``=` `-``(arr[i] ``+` `arr[j])` `            ``if` `x ``in` `s:` `                ``print``(x, arr[i], arr[j])` `                ``found ``=` `True` `            ``else``:` `                ``s.add(arr[j])` `    ``if` `found ``=``=` `False``:` `        ``print``(``"No Triplet Found"``)`     `# Driver Code` `arr ``=` `[``0``, ``-``1``, ``2``, ``-``3``, ``1``]` `n ``=` `len``(arr)` `findTriplets(arr, n)`   `# This code is contributed by Shrikant13`

## C#

 `// C# program to find triplets in a given` `// array whose sum is zero` `using` `System;` `using` `System.Collections.Generic;`   `class` `GFG {`   `    ``// function to print triplets with 0 sum` `    ``static` `void` `findTriplets(``int``[] arr, ``int` `n)` `    ``{` `        ``bool` `found = ``false``;`   `        ``for` `(``int` `i = 0; i < n - 1; i++) {` `            ``// Find all pairs with sum equals to` `            ``// "-arr[i]"` `            ``HashSet<``int``> s = ``new` `HashSet<``int``>();` `            ``for` `(``int` `j = i + 1; j < n; j++) {` `                ``int` `x = -(arr[i] + arr[j]);` `                ``if` `(s.Contains(x)) {` `                    ``Console.Write(``"{0} {1} {2}\n"``, x,` `                                  ``arr[i], arr[j]);` `                    ``found = ``true``;` `                ``}` `                ``else` `{` `                    ``s.Add(arr[j]);` `                ``}` `            ``}` `        ``}`   `        ``if` `(found == ``false``) {` `            ``Console.Write(``" No Triplet Found\n"``);` `        ``}` `    ``}`   `    ``// Driver code` `    ``public` `static` `void` `Main(String[] args)` `    ``{` `        ``int``[] arr = { 0, -1, 2, -3, 1 };` `        ``int` `n = arr.Length;` `        ``findTriplets(arr, n);` `    ``}` `}`   `// This code has been contributed by 29AjayKumar`

## Javascript

 ``

Output

```-1 0 1
-3 2 1```

Time Complexity: O(n2), Since two nested loops are required, so the time complexity is O(n2).
Auxiliary Space: O(n), Since a HashSet is required, so the space complexity is linear.

## Find all triplets with zero sum using Sorting:

The idea is based on the above discussed approach using Hashmap of this post. For every element check that there is a pair whose sum is equal to the negative value of that element.

Follow the steps below to implement the idea:

• Sort the array in ascending order.
• Traverse the array from start to end.
• For every index i, create two variables l = i + 1 and r = n – 1
• Run a loop until l is less than r if the sum of array[i], array[l] and array[r] is equal to zero then print the triplet and break the loop
• If the sum is less than zero then increment the value of l, by increasing the value of l the sum will increase as the array is sorted, so array[l+1] > array [l]
• If the sum is greater than zero then decrement the value of r, by decreasing the value of r the sum will decrease as the array is sorted, so array[r-1] < array [r].

Below is the implementation of the above approach:

## C++

 `// C++ program to find triplets in a given` `// array whose sum is zero` `#include ` `using` `namespace` `std;`   `// function to print triplets with 0 sum` `void` `findTriplets(``int` `arr[], ``int` `n)` `{` `    ``bool` `found = ``false``;`   `    ``// sort array elements` `    ``sort(arr, arr + n);`   `    ``for` `(``int` `i = 0; i < n - 1; i++) {` `        ``// initialize left and right` `        ``int` `l = i + 1;` `        ``int` `r = n - 1;` `        ``int` `x = arr[i];` `        ``while` `(l < r) {` `            ``if` `(x + arr[l] + arr[r] == 0) {` `                ``// print elements if it's sum is zero` `                ``printf``(``"%d %d %d\n"``, x, arr[l], arr[r]);` `                ``l++;` `                ``r--;` `                ``found = ``true``;` `                ``//   break;` `            ``}`   `            ``// If sum of three elements is less` `            ``// than zero then increment in left` `            ``else` `if` `(x + arr[l] + arr[r] < 0)` `                ``l++;`   `            ``// if sum is greater than zero then` `            ``// decrement in right side` `            ``else` `                ``r--;` `        ``}` `    ``}`   `    ``if` `(found == ``false``)` `        ``cout << ``" No Triplet Found"` `<< endl;` `}`   `// Driven source` `int` `main()` `{` `    ``int` `arr[] = { 0, -1, 2, -3, 1 };` `    ``int` `n = ``sizeof``(arr) / ``sizeof``(arr);` `    ``findTriplets(arr, n);` `    ``return` `0;` `}`

## Java

 `// Java  program to find triplets in a given` `// array whose sum is zero` `import` `java.io.*;` `import` `java.util.Arrays;`   `class` `GFG {` `    ``// function to print triplets with 0 sum` `    ``static` `void` `findTriplets(``int` `arr[], ``int` `n)` `    ``{` `        ``boolean` `found = ``false``;`   `        ``// sort array elements` `        ``Arrays.sort(arr);`   `        ``for` `(``int` `i = ``0``; i < n - ``1``; i++) {` `            ``// initialize left and right` `            ``int` `l = i + ``1``;` `            ``int` `r = n - ``1``;` `            ``int` `x = arr[i];` `            ``while` `(l < r) {` `                ``if` `(x + arr[l] + arr[r] == ``0``) {` `                    ``// print elements if it's sum is zero` `                    ``System.out.print(x + ``" "``);` `                    ``System.out.print(arr[l] + ``" "``);` `                    ``System.out.println(arr[r] + ``" "``);`   `                    ``l++;` `                    ``r--;` `                    ``found = ``true``;` `                ``}`   `                ``// If sum of three elements is less` `                ``// than zero then increment in left` `                ``else` `if` `(x + arr[l] + arr[r] < ``0``)` `                    ``l++;`   `                ``// if sum is greater than zero then` `                ``// decrement in right side` `                ``else` `                    ``r--;` `            ``}` `        ``}`   `        ``if` `(found == ``false``)` `            ``System.out.println(``" No Triplet Found"``);` `    ``}`   `    ``// Driven source` `    ``public` `static` `void` `main(String[] args)` `    ``{`   `        ``int` `arr[] = { ``0``, -``1``, ``2``, -``3``, ``1` `};` `        ``int` `n = arr.length;` `        ``findTriplets(arr, n);` `    ``}` `    ``// This code is contributed by Tushil..` `}`

## Python3

 `# python program to find triplets in a given` `# array whose sum is zero`   `# function to print triplets with 0 sum`     `def` `findTriplets(arr, n):`   `    ``found ``=` `False`   `    ``# sort array elements` `    ``arr.sort()`   `    ``for` `i ``in` `range``(``0``, n``-``1``):`   `        ``# initialize left and right` `        ``l ``=` `i ``+` `1` `        ``r ``=` `n ``-` `1` `        ``x ``=` `arr[i]` `        ``while` `(l < r):`   `            ``if` `(x ``+` `arr[l] ``+` `arr[r] ``=``=` `0``):` `                ``# print elements if it's sum is zero` `                ``print``(x, arr[l], arr[r])` `                ``l ``+``=` `1` `                ``r ``-``=` `1` `                ``found ``=` `True`   `            ``# If sum of three elements is less` `            ``# than zero then increment in left` `            ``elif` `(x ``+` `arr[l] ``+` `arr[r] < ``0``):` `                ``l ``+``=` `1`   `            ``# if sum is greater than zero then` `            ``# decrement in right side` `            ``else``:` `                ``r ``-``=` `1`   `    ``if` `(found ``=``=` `False``):` `        ``print``(``" No Triplet Found"``)`     `# Driven source` `arr ``=` `[``0``, ``-``1``, ``2``, ``-``3``, ``1``]` `n ``=` `len``(arr)` `findTriplets(arr, n)`   `# This code is contributed by Smitha Dinesh Semwal`

## C#

 `// C#  program to find triplets in a given` `// array whose sum is zero` `using` `System;`   `public` `class` `GFG {` `    ``// function to print triplets with 0 sum` `    ``static` `void` `findTriplets(``int``[] arr, ``int` `n)` `    ``{` `        ``bool` `found = ``false``;`   `        ``// sort array elements` `        ``Array.Sort(arr);`   `        ``for` `(``int` `i = 0; i < n - 1; i++) {` `            ``// initialize left and right` `            ``int` `l = i + 1;` `            ``int` `r = n - 1;` `            ``int` `x = arr[i];` `            ``while` `(l < r) {` `                ``if` `(x + arr[l] + arr[r] == 0) {` `                    ``// print elements if it's sum is zero` `                    ``Console.Write(x + ``" "``);` `                    ``Console.Write(arr[l] + ``" "``);` `                    ``Console.WriteLine(arr[r] + ``" "``);`   `                    ``l++;` `                    ``r--;` `                    ``found = ``true``;` `                ``}`   `                ``// If sum of three elements is less` `                ``// than zero then increment in left` `                ``else` `if` `(x + arr[l] + arr[r] < 0)` `                    ``l++;`   `                ``// if sum is greater than zero then` `                ``// decrement in right side` `                ``else` `                    ``r--;` `            ``}` `        ``}`   `        ``if` `(found == ``false``)` `            ``Console.WriteLine(``" No Triplet Found"``);` `    ``}`   `    ``// Driven source` `    ``static` `public` `void` `Main()` `    ``{`   `        ``int``[] arr = { 0, -1, 2, -3, 1 };` `        ``int` `n = arr.Length;` `        ``findTriplets(arr, n);` `    ``}` `    ``// This code is contributed by akt_mit..` `}`

## PHP

 ``

## Javascript

 ``

Output

```-3 1 2
-1 0 1```

Time Complexity: O(n2), Only two nested loops are required, so the time complexity is O(n2).
Auxiliary Space: O(1), no extra space is required, so the space complexity is constant.

This article is contributed by DANISH_RAZA. 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.