Related Articles
Pythagorean Triplet with given sum using single loop
• Last Updated : 22 Mar, 2021

A Pythagorean Triplet is a set of natural numbers such that a < b < c, for which Given a number N, find a Pythagorean Triplet with sum as given N or return -1.

Examples:

```Input: 12
Output: 3 4 5
Explanation:
As 32 + 42 = 52

Input: 82
Output: -1```

Approach: The idea is to find the value of b and c in terms of a and iterate a from 1 to N. To find the value of b and c in terms of a we have to do following:

We have two equations, [Tex] a + b + c = N    [/Tex]

We will find the value of c in term of a and b Then put this value in equation 1 to solve for b.

From equation 2, Now, put this value in equation 1. After solving the above equation we will get, [Tex]c = N – b – a    [/Tex]

Now, iterate a from 1 to N and calculate respectively the value of b and c Then, check if ## C++

 `// C++ program to find the Pythagorean``// Triplet with given sum``#include ``using` `namespace` `std;` `// Function to calculate the``// Pythagorean triplet in O(n)``void` `PythagoreanTriplet(``int` `n)``{``    ``int` `flag = 0;` `    ``// Iterate a from 1 to N-1.``    ``for` `(``int` `a = 1; a < n; a++)``    ``{``        ``// Calculate value of b``        ``int` `b = (n * n - 2 * n * a)``                ``/ (2 * n - 2 * a);` `        ``// The value of c = n - a - b``        ``int` `c = n - a - b;` `        ``if` `(a * a + b * b == c * c``            ``&& b > 0 && c > 0)``        ``{``            ``cout << a << ``" "` `<< b << ``" "` `<< c;``            ``flag = 1;``            ``break``;``        ``}``    ``}` `    ``if` `(flag == 0) {``        ``cout << ``"-1"``;``    ``}` `    ``return``;``}` `// Driver Code``int` `main()``{``    ``int` `N = 12;` `    ``// Function call``    ``PythagoreanTriplet(N);` `    ``return` `0;``}`

## Java

 `// Java program to find the Pythagorean``// Triplet with given sum` `class` `GFG {` `    ``// Function to calculate the``    ``// Pythagorean triplet in O(n)``    ``static` `void` `PythagoreanTriplet(``int` `n)``    ``{``        ``int` `flag = ``0``;` `        ``// Iterate a from 1 to N-1.``        ``for` `(``int` `a = ``1``; a < n; a++)``        ``{``            ``// Calculate value of b``            ``int` `b = (n * n - ``2` `* n * a)``              ``/ (``2` `* n - ``2` `* a);` `            ``// The value of c = n - a - b``            ``int` `c = n - a - b;` `            ``if` `(a * a + b * b == c * c``                ``&& b > ``0` `&& c > ``0``)``            ``{``                ``System.out``                  ``.print(a + ``" "` `+ b + ``" "` `+ c);``                ``flag = ``1``;``                ``break``;``            ``}``        ``}` `        ``if` `(flag == ``0``)``        ``{``            ``System.out.print(``"-1"``);``        ``}` `        ``return``;``    ``}``  ` `    ``// Driver Code``    ``public` `static` `void` `main(String[] args)``    ``{``        ``int` `N = ``12``;` `        ``// Function call``        ``PythagoreanTriplet(N);``    ``}``}` `// This code contributed by sapnasingh4991`

## Python3

 `# Python3 program to find the Pythagorean``# Triplet with a given sum` `# Function to calculate the``# Pythagorean triplet in O(n)`  `def` `PythagoreanTriplet(n):``    ``flag ``=` `0` `    ``# Iterate a from 1 to N-1.``    ``for` `a ``in` `range``(``1``, n, ``1``):` `        ``# Calculate value of b``        ``b ``=` `(n ``*` `n ``-` `2` `*` `n ``*` `a) ``/``/` `(``2` `*` `n ``-` `2` `*` `a)` `        ``# The value of c = n - a - b``        ``c ``=` `n ``-` `a ``-` `b` `        ``if` `(a ``*` `a ``+` `b ``*` `b ``=``=` `c ``*` `c``            ``and` `b > ``0` `and` `c > ``0``):``            ``print``(a, b, c)``            ``flag ``=` `1``            ``break` `    ``if``(flag ``=``=` `0``):``        ``print``(``"-1"``)` `    ``return`  `# Driver code``if` `__name__ ``=``=` `'__main__'``:``    ``N ``=` `12` `    ``# Function call``    ``PythagoreanTriplet(N)` `# This code is contributed by Bhupendra_Singh`

## C#

 `// C# program to find the Pythagorean``// Triplet with given sum``using` `System;` `class` `GFG {` `    ``// Function to calculate the``    ``// Pythagorean triplet in O(n)``    ``static` `void` `PythagoreanTriplet(``int` `n)``    ``{``        ``int` `flag = 0;` `        ``// Iterate a from 1 to N-1.``        ``for` `(``int` `a = 1; a < n; a++)``        ``{``            ``// Calculate value of b``            ``int` `b = (n * n - 2 * n * a)``              ``/ (2 * n - 2 * a);` `            ``// The value of c = n - a - b``            ``int` `c = n - a - b;``            ``if` `(a * a + b * b == c * c``                ``&& b > 0 && c > 0)``            ``{``                ``Console.Write(a + ``" "` `+ b + ``" "` `+ c);``                ``flag = 1;``                ``break``;``            ``}``        ``}` `        ``if` `(flag == 0) {``            ``Console.Write(``"-1"``);``        ``}``        ``return``;``    ``}` `    ``// Driver code``    ``public` `static` `void` `Main(String[] args)``    ``{``        ``int` `N = 12;` `        ``// Function call``        ``PythagoreanTriplet(N);``    ``}``}` `// This code is contributed by shivanisinghss2110`

## Javascript

 ``
Output
`3 4 5`

Time Complexity: O(N)

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.  To complete your preparation from learning a language to DS Algo and many more,  please refer Complete Interview Preparation Course.

In case you wish to attend live classes with industry experts, please refer Geeks Classes Live and Geeks Classes Live USA

My Personal Notes arrow_drop_up