Pythagorean Triple

A Pythagorean triple consists of three positive integers a,b, and,c such that . Such a triple is commonly written as (a,b,c). This term comes from the Pythagorean theorem, which says that a Pythagorean Triple will be the lengths of the sides of a right-angled triangle.

You have been given an integer that represents the length of one of the catheti of a right-angle triangle.

You need to find the lengths of the remaining sides. There may be multiple possible answers; anyone will be accepted.

Hints:

• Every odd number  can be represented as .
• If  and  are integers and , then .

Example:

Input:  a = 5
Output: 5 12 13

Approach

Java

import java.util.Arrays;

public class PythagoreanTriplet {
    public static void main(String[] args) {

        long a = 5;

        long[] triple = pythagoreanTriple(a);

        System.out.println(Arrays.toString(triple));

    }

    static long[] pythagoreanTriple(long a) {
        long b, c;
        if (a % 2 != 0) {
            b = (a * a - 1) / 2;
            c = b + 1;
        } else {
            b = (a / 2) * (a / 2) - 1;
            c = b + 2;
        }
        long[] res = new long[3];
        res[0] = a;
        res[1] = b;
        res[2] = c;

        return res;
    }

}

C++

#include <bits/stdc++.h>
using namespace std;

vector<long long int> pythagoreanTriple(long long int a)
{
    long long int b, c;
    if (a % 2 != 0)
    {
        b = (a * a - 1) / 2;
        c = b + 1;
    }
    else
    {
        b = (a / 2) * (a / 2) - 1;
        c = b + 2;
    }
    vector<long long int> res;
    res.push_back(a);
    res.push_back(b);
    res.push_back(c);

    return res;
}

int main()
{

    long long int a = 5;

    vector<long long int> triple = pythagoreanTriple(a);
    for (int i = 0; i < triple.size(); i++)
    {
        cout << triple[i];
        if (i != triple.size() - 1)
        {
            cout << " ";
        }
    }
    return 0;
}