# Pythagorean Triplet with given sum

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.
```

## Recommended: Please try your approach on {IDE} first, before moving on to the solution.

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(n3).

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 ` `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

 ` `

Output :

```3, 4, 5
```

Attention reader! Don’t stop learning now. Get hold of all the important DSA concepts with the DSA Self Paced Course at a student-friendly price and become industry ready.

My Personal Notes arrow_drop_up Check out this Author's contributed articles.

If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.

Please Improve this article if you find anything incorrect by clicking on the "Improve Article" button below.

Improved By : vt_m