Given four points, check whether they form Pythagorean Quadruple.
It is defined as a tuple of integers a, b, c, d such that 
. They are basically the solutions of Diophantine Equations. In the geometric interpretation it represents a cuboid with integer side lengths |a|, |b|, |c| and whose space diagonal is |d| .
The cuboids sides shown here are examples of pythagorean quadruples.
It is primitive when their greatest common divisor is 1. Every Pythagorean quadruple is an integer multiple of a primitive quadruple. We can generate the set of primitive pythagorean quadruples for which a is odd can be generated by formula :
a = m2 + n2 – p2 – q2,
b = 2(mq + np),
c = 2(nq – mp),
d = m2 + n2 + p2 + q2
where m, n, p, q are non-negative integers with greatest common divisor 1 such that m + n + p + q are odd. Thus, all primitive Pythagorean quadruples are characterized by Lebesgue’s identity.
(m2 + n2 + p2 + q2)2 = (2mq + 2nq)2 + 2(nq – mp)2 + (m2 + n2 – p2 – q2)m2 + n2 – p2 – q2
C++
// C++ code to detect Pythagorean Quadruples.#include <bits/stdc++.h>using namespace std;// function for checkingbool pythagorean_quadruple(int a, int b, int c, int d){ int sum = a * a + b * b + c * c; if (d * d == sum) return true; else return false;}// Driver Codeint main(){ int a = 1, b = 2, c = 2, d = 3; if (pythagorean_quadruple(a, b, c, d)) cout << "Yes" << endl; else cout << "No" << endl;} |
Java
// Java code to detect Pythagorean Quadruples.import java.io.*;import java.util.*;class GFG {// function for checkingstatic Boolean pythagorean_quadruple(int a, int b, int c, int d){ int sum = a * a + b * b + c * c; if (d * d == sum) return true; else return false;}// Driver function public static void main (String[] args) { int a = 1, b = 2, c = 2, d = 3; if (pythagorean_quadruple(a, b, c, d)) System.out.println("Yes"); else System.out.println("No" ); }}// This code is contributed by Gitanjali. |
Python3
# Python code to detect# Pythagorean Quadruples.import math# function for checkingdef pythagorean_quadruple(a,b, c, d): sum = a * a + b * b + c * c; if (d * d == sum): return True else: return False#driver codea = 1b = 2c = 2d = 3if (pythagorean_quadruple(a, b, c, d)): print("Yes")else: print("No" )# This code is contributed# by Gitanjali. |
C#
// C# code to detect // Pythagorean Quadruples.using System;class GFG { // function for checking static Boolean pythagorean_quadruple(int a, int b, int c, int d) { int sum = a * a + b * b + c * c; if (d * d == sum) return true; else return false; } // Driver function public static void Main () { int a = 1, b = 2, c = 2, d = 3; if (pythagorean_quadruple(a, b, c, d)) Console.WriteLine("Yes"); else Console.WriteLine("No" ); }}// This code is contributed by vt_M. |
PHP
<?php// php code to detect Pythagorean Quadruples.// function for checkingfunction pythagorean_quadruple($a, $b, $c, $d){ $sum = $a * $a + $b * $b + $c * $c; if ($d * $d == $sum) return true; else return false;}// Driver Code $a = 1; $b = 2; $c = 2; $d = 3; if (pythagorean_quadruple($a, $b, $c, $d)) echo "Yes" ; else echo "No" ; // This code is contributed by anuj_67.?> |
Javascript
<script>// JavaScript program to detect Pythagorean Quadruples.// function for checkingfunction pythagorean_quadruple(a, b, c, d){ let sum = a * a + b * b + c * c; if (d * d == sum) return true; else return false;} // Driver code let a = 1, b = 2, c = 2, d = 3; if (pythagorean_quadruple(a, b, c, d)) document.write("Yes"); else document.write("No" );</script> |
Output:
Yes
Time Complexity: O(1)
Auxiliary Space: O(1)
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