Finding the Parity of a number Efficiently

Given an integer N. The task is to write a program to find the parity of the given number.

Note: Parity of a number is used to define if the total number of set-bits(1-bit in binary representation) in a number is even or odd. If the total number of set-bits in the binary representation of a number is even then the number is said to have even parity, otherwise, it will have odd parity.

Examples:

Input : N = 13 
Output : Odd Parity
Binary representation of 13 is (1101)

Input : N = 9 (1001)
Output : Even Parity

Recommended: Please try your approach on {IDE} first, before moving on to the solution.

The parity of a number represented by 32-bits can be efficiently calculated by performing the following operations.

Let the given number be x, then perform the below operations:

y = x^(x>>1)
y = y^(y>>2)
y = y^(y>>4)
y = y^(y>>8)
y = y^(y>>16)

Now, the rightmost bit in y will represent the parity of x. If the rightmost bit is 1, then x will have odd parity and if it is 0 then x will have even parity.

So, in order to extract the last bit of y, perform bit-wise AND operation of y with 1.

if(y&1==1)
    odd Parity
else
    even Parity

Below is the implementation of the above approach:

C++

// Program to find the parity of a given number 
#include <bits/stdc++.h> 
  
using namespace std; 
  
// Function to find the parity 
bool findParity(int x) 
{ 
    int y = x ^ (x >> 1); 
    y = y ^ (y >> 2); 
    y = y ^ (y >> 4); 
    y = y ^ (y >> 8); 
    y = y ^ (y >> 16); 
  
    // Rightmost bit of y holds the parity value 
    // if (y&1) is 1 then parity is odd else even 
    if (y & 1) 
        return 1; 
    return 0; 
} 
  
// Driver code 
int main() 
{ 
    (findParity(9)==0)?cout<<"Even Parity\n": 
                            cout<<"Odd Parity\n"; 
      
    (findParity(13)==0)?cout<<"Even Parity\n": 
                            cout<<"Odd Parity\n"; 
      
    return 0; 
} 

Java

// Program to find the 
// parity of a given number 
import java.io.*; 
  
class GFG  
{ 
  
// Function to find the parity 
static boolean findParity(int x) 
{ 
    int y = x ^ (x >> 1); 
        y = y ^ (y >> 2); 
        y = y ^ (y >> 4); 
        y = y ^ (y >> 8); 
        y = y ^ (y >> 16); 
  
    // Rightmost bit of y holds 
    // the parity value 
    // if (y&1) is 1 then parity  
    // is odd else even 
    if ((y & 1) > 0) 
        return true; 
    return false; 
} 
  
// Driver code 
public static void main (String[] args)  
{ 
    if((findParity(9) == false)) 
        System.out.println("Even Parity"); 
    else
        System.out.println("Odd Parity"); 
      
    if(findParity(13) == false) 
        System.out.println("Even Parity"); 
    else
        System.out.println("Odd Parity"); 
} 
} 
  
// This Code is Contributed by chandan_jnu. 

Python3

# Program to find the 
# parity of a given number 
  
# Function to find the parity 
def findParity(x): 
    y = x ^ (x >> 1); 
    y = y ^ (y >> 2); 
    y = y ^ (y >> 4); 
    y = y ^ (y >> 8); 
    y = y ^ (y >> 16); 
  
    # Rightmost bit of y holds  
    # the parity value if (y&1) 
    # is 1 then parity is odd 
    # else even 
    if (y & 1): 
        return 1; 
    return 0; 
  
# Driver code 
if(findParity(9) == 0): 
    print("Even Parity"); 
else: 
    print("Odd Parity\n"); 
  
if(findParity(13) == 0): 
    print("Even Parity"); 
else: 
    print("Odd Parity"); 
      
# This code is contributed by mits 

C#

// Program to find the 
// parity of a given number 
using System; 
  
class GFG  
{ 
  
// Function to find the parity 
static bool findParity(int x) 
{ 
    int y = x ^ (x >> 1); 
        y = y ^ (y >> 2); 
        y = y ^ (y >> 4); 
        y = y ^ (y >> 8); 
        y = y ^ (y >> 16); 
  
    // Rightmost bit of y holds 
    // the parity value 
    // if (y&1) is 1 then parity  
    // is odd else even 
    if ((y & 1) > 0) 
        return true; 
    return false; 
} 
  
// Driver code 
public static void Main ()  
{ 
    if((findParity(9) == false)) 
        Console.WriteLine("Even Parity"); 
    else
        Console.WriteLine("Odd Parity"); 
      
    if(findParity(13) == false) 
        Console.WriteLine("Even Parity"); 
    else
        Console.WriteLine("Odd Parity"); 
} 
} 
  
// This Code is Contributed  
// by chandan_jnu 

PHP

<?php 
// Program to find the 
// parity of a given number 
  
// Function to find the parity 
function findParity($x) 
{ 
    $y = $x ^ ($x >> 1); 
    $y = $y ^ ($y >> 2); 
    $y = $y ^ ($y >> 4); 
    $y = $y ^ ($y >> 8); 
    $y = $y ^ ($y >> 16); 
  
    // Rightmost bit of y holds  
    // the parity value if (y&1) 
    // is 1 then parity is odd 
    // else even 
    if ($y & 1) 
        return 1; 
    return 0; 
} 
  
// Driver code 
(findParity(9) == 0) ?  
 print("Even Parity\n"): 
 print("Odd Parity\n"); 
  
(findParity(13) == 0) ?  
print("Even Parity\n"): 
print("Odd Parity\n"); 
      
// This Code is Contributed by mits 
?> 

Output:

Even Parity
Odd Parity

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My Personal Notes

Recommended: Please try your approach on {IDE} first, before moving on to the solution.

C++

Java

Python3

C#

PHP

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