A Pythagorean Triplet is a set of natural numbers such that a < b < c, for which **a^2 + b^2 = c^2**. For example, 3^2 + 4^2 = 5^2.

Given a number n, find a Pythagorean Triplet with sum as given n.

Examples :

Input : n = 12 Output : 3, 4, 5 Note that 3, 4 and 5 is a Pythagorean Triplet with sum equal to 12. Input : n = 4. Output : No Triplet There does not exist a Pythagorean Triplet with sum equal to 4.

A **simple solution **is to run three nested loops to generate all possible triplets and for every triplet, check if it is a Pythagorean Triplet and has given sum. Time complexity of this solution is O(n^{3}).

An **efficient solution** is to run two loops, where first loop runs from i = 1 to n/3, second loop runs from j = i+1 to n/2. In second loop, we check if (n – i – j) is equal to i * i + j * j.

## C++

// C++ program to find Pythagorean // Triplet of given sum. #include <bits/stdc++.h> using namespace std; void pythagoreanTriplet(int n) { // Considering triplets in // sorted order. The value // of first element in sorted // triplet can be at-most n/3. for (int i = 1; i <= n / 3; i++) { // The value of second // element must be less // than equal to n/2 for (int j = i + 1; j <= n / 2; j++) { int k = n - i - j; if (i * i + j * j == k * k) { cout << i << ", " << j << ", " << k; return; } } } cout << "No Triplet"; } // Driver Code int main() { int n = 12; pythagoreanTriplet(n); return 0; }

## Java

// Java program to find Pythagorean // Triplet of given sum. class GFG { static void pythagoreanTriplet(int n) { // Considering triplets in // sorted order. The value // of first element in sorted // triplet can be at-most n/3. for (int i = 1; i <= n / 3; i++) { // The value of second element // must be less than equal to n/2 for (int j = i + 1; j <= n / 2; j++) { int k = n - i - j; if (i * i + j * j == k * k) { System.out.print(i + ", "+ j + ", " + k); return; } } } System.out.print("No Triplet"); } // Driver Code public static void main(String arg[]) { int n = 12; pythagoreanTriplet(n); } } // This code is contributed by Anant Agarwal.

## Python3

# Python3 program to find # Pythagorean Triplet of # given sum. def pythagoreanTriplet(n): # Considering triplets in # sorted order. The value # of first element in sorted # triplet can be at-most n/3. for i in range(1, int(n / 3) + 1): # The value of second element # must be less than equal to n/2 for j in range(i + 1, int(n / 2) + 1): k = n - i - j if (i * i + j * j == k * k): print(i, ", ", j, ", ", k, sep = "") return print("No Triplet") # Driver Code n = 12 pythagoreanTriplet(n) # This code is contributed # by Smitha Dinesh Semwal

## C#

// C# program to find // Pythagorean Triplet // of given sum. using System; class GFG { static void pythagoreanTriplet(int n) { // Considering triplets in // sorted order. The value // of first element in sorted // triplet can be at-most n/3. for (int i = 1; i <= n / 3; i++) { // The value of second element // must be less than equal to n/2 for (int j = i + 1; j <= n / 2; j++) { int k = n - i - j; if (i * i + j * j == k * k) { Console.Write(i + ", "+ j + ", " + k); return; } } } Console.Write("No Triplet"); } // Driver Code public static void Main() { int n = 12; pythagoreanTriplet(n); } } // This code is contributed by Vt_m.

## PHP

<?php // PHP program to find // Pythagorean Triplet // of given sum. function pythagoreanTriplet($n) { // Considering triplets in // sorted order. The value // of first element in sorted // triplet can be at-most n/3. for ( $i = 1; $i <= $n / 3; $i++) { // The value of second // element must be less // than equal to n/2 for ( $j = $i + 1; $j <= $n / 2; $j++) { $k = $n - $i - $j; if ($i * $i + $j * $j == $k * $k) { echo $i , ", ", $j ,", ", $k; return; } } } echo "No Triplet"; } // Driver Code $n = 12; pythagoreanTriplet($n); // This code is contributed by anuj_67. ?>

**Output :**

3, 4, 5

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