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

• Last Updated : 11 Jan, 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:

## 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 code``arr ``=` `[``5``, ``32``, ``1``, ``7``, ``10``, ``50``, ``19``, ``21``, ``2``]``n ``=` `len``(arr)``findTriplet(arr, n)``# This code is contributed by Sachin Bisht`

Output:

`numbers are 21 2 19`

Time complexity: O(N^2)
Please refer complete article on Find a triplet such that sum of two equals to third element for more details!

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