Program to find parity

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.

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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