Program to find parity - GeeksforGeeks

Parity: Parity of a number refers to whether it contains an odd or even number of 1-bits. The number has “odd parity”, if it contains odd number of 1-bits and is “even parity” if it contains even number of 1-bits.
Main idea of the below solution is – Loop while n is not 0 and in loop unset one of the set bits and invert parity.

Recommended: Please solve it on “PRACTICE” first, before moving on to the solution.

Algorithm: getParity(n)
1. Initialize parity = 0
2. Loop while n != 0      
      a. Invert parity 
             parity = !parity
      b. Unset rightmost set bit
             n = n & (n-1)
3. return parity

Example:
 Initialize: n = 13 (1101)   parity = 0

n = 13 & 12  = 12 (1100)   parity = 1
n = 12 & 11 = 8  (1000)   parity = 0
n = 8 & 7 = 0  (0000)    parity = 1

Program:

C++

// C++ program to find parity 
// of an integer 
# include<bits/stdc++.h> 
# define bool int 
using namespace std; 
  
// Function to get parity of number n. It returns 1 
// if n has odd parity, and returns 0 if n has even 
// parity  
bool getParity(unsigned int n) 
{ 
    bool parity = 0; 
    while (n) 
    { 
        parity = !parity; 
        n     = n & (n - 1); 
    }      
    return parity; 
} 
  
/* Driver program to test getParity() */
int main() 
{ 
    unsigned int n = 7; 
    cout<<"Parity of no "<<n<<" = "<<(getParity(n)? "odd": "even"); 
      
    getchar(); 
    return 0; 
} 

C

// C program to find parity 
// of an integer 
# include <stdio.h> 
# define  bool int 
  
/* Function to get parity of number n. It returns 1 
   if n has odd parity, and returns 0 if n has even 
   parity */
bool getParity(unsigned int n) 
{ 
    bool parity = 0; 
    while (n) 
    { 
        parity = !parity; 
        n      = n & (n - 1); 
    }         
    return parity; 
} 
  
/* Driver program to test getParity() */
int main() 
{ 
    unsigned int n = 7; 
    printf("Parity of no %d = %s",  n,  
             (getParity(n)? "odd": "even")); 
      
    getchar(); 
    return 0; 
} 

Java

// Java program to find parity 
// of an integer 
import java.util.*; 
import java.lang.*; 
import java.io.*; 
import java.math.BigInteger; 
  
class GFG 
 { 
    /* Function to get parity of number n. 
    It returns 1 if n has odd parity, and 
    returns 0 if n has even parity */
    static boolean getParity(int n) 
    { 
        boolean parity = false; 
        while(n != 0) 
        { 
            parity = !parity; 
            n = n & (n-1); 
        } 
        return parity; 
          
    } 
      
    /* Driver program to test getParity() */
    public static void main (String[] args) 
    { 
        int n = 12; 
        System.out.println("Parity of no " + n + " = " + 
                         (getParity(n)? "odd": "even"));  
    } 
} 
/* This code is contributed by Amit khandelwal*/ 

Python3

# Python3 code to get parity. 
  
# Function to get parity of number n.  
# It returns 1 if n has odd parity,  
# and returns 0 if n has even parity 
def getParity( n ): 
    parity = 0
    while n: 
        parity = ~parity 
        n = n & (n - 1) 
    return parity 
  
# Driver program to test getParity() 
n = 7
print ("Parity of no ", n," = ", 
     ( "odd" if getParity(n) else "even")) 
  
# This code is contributed by "Sharad_Bhardwaj". 

C#

// C# program to find parity of an integer 
using System; 
  
class GFG { 
      
    /* Function to get parity of number n. 
    It returns 1 if n has odd parity, and 
    returns 0 if n has even parity */
    static bool getParity(int n) 
    { 
        bool parity = false; 
        while(n != 0) 
        { 
            parity = !parity; 
            n = n & (n-1); 
        } 
        return parity; 
          
    } 
      
    // Driver code 
    public static void Main () 
    { 
        int n = 7; 
        Console.Write("Parity of no " + n  
                 + " = " + (getParity(n)? 
                          "odd": "even"));  
    } 
} 
  
// This code is contributed by nitin mittal. 

PHP

<?php 
// PHP program to find the parity 
// of an unsigned integer 
  
// Function to get parity of  
// number n. It returns 1 
// if n has odd parity, and 
// returns 0 if n has even 
// parity 
function getParity( $n) 
{ 
    $parity = 0; 
    while ($n) 
    { 
        $parity = !$parity; 
        $n = $n & ($n - 1); 
    }  
    return $parity; 
} 
  
    // Driver Code 
    $n = 7; 
    echo "Parity of no ",$n ," = " ,  
          getParity($n)? "odd": "even"; 
      
// This code is contributed by anuj_67. 
?> 

Output:

Parity of no 7 = odd

Above solution can be optimized by using lookup table. Please refer to Bit Twiddle Hacks[1st reference] for details.

Time Complexity: The time taken by above algorithm is proportional to the number of bits set. Worst case complexity is O(Log n).

Uses: Parity is used in error detection and cryptography.

Compute the parity of a number using XOR and table look-up

References:
http://graphics.stanford.edu/~seander/bithacks.html#ParityNaive – last checked on 30 May 2009.

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My Personal Notes

Recommended: Please solve it on “PRACTICE” first, before moving on to the solution.

C++

C

Java

Python3

C#

PHP

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