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 with as given n.

Examples:

3;
Input : n = 23;
Output : 3, 4, 53;
Note that 3, 4 and 5 is a Pythagorean Triplet3;
with sum equal to 2.3;
3;
Input : n = 4.3;
Output : No Triplet3;
There does not exist a Pythagorean Triplet3;
with sum equal to 4.3;

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++ program to find Pythagorean Triplet 
// 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 function
int ()
{
    int n = 12;
    pythagoreanTriplet(n);
    return 0;
}



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