Given four points, check whether they form Pythagorean Quadruple.
It is defined as a tuple of integers a, b, c, d such that
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++ code to detect Pythagorean Quadruples. #include <bits/stdc++.h> using namespace std;
// function for checking bool 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 Code int 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 code to detect Pythagorean Quadruples. import java.io.*;
import java.util.*;
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 (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. |
# Python code to detect # Pythagorean Quadruples. import math
# function for checking def 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)):
print ( "Yes" )
else :
print ( "No" )
# This code is contributed # by Gitanjali. |
// 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 code to detect Pythagorean Quadruples. // function for checking function 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. ?> |
<script> // JavaScript program to detect Pythagorean Quadruples. // function for checking function 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)