Pythagorean Triplet with given sum

06 Apr, 2021
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(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++
Java
Python3
C#
PHP
Javascript
// 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 Codeint main(){    int n = 12;    pythagoreanTriplet(n);    return 0;}
// 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 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 Coden = 12pythagoreanTriplet(n) # This code is contributed# by Smitha Dinesh Semwal
// 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 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.?>
<script> // JavaScript 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 (let i = 1; i <= n / 3; i++)        {                           // The value of second element            // must be less than equal to n/2            for (let j = i + 1; j <= n / 2; j++)            {                let k = n - i - j;                if (i * i + j * j == k * k)                {                    document.write(i + ", "+                                j + ", " + k);                    return;                }            }        }               document.write("No Triplet");    } // Driver Code        let n = 12;        pythagoreanTriplet(n); // This code is contributed by avijitmondal1998.</script>
3, 4, 5
 
vt_m
avijitmondal1998
programming-puzzle
Mathematical
Mathematical
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