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 an odd number of 1-bits and is “even parity” if it contains an even number of 1-bits. 
The 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 = 7;
        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.
?>

Javascript

<script>

// Javascript program to find parity
// of an 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)
{
    var parity = false;
    while(n != 0)
    {
        parity = !parity;
        n = n & (n - 1);
    }
    return parity;
}

// Driver code
var n = 7;
document.write("Parity of no " + n + " = " +
              (getParity(n) ? "odd": "even"));

// This code is contributed by Kirti

</script>

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).
Auxiliary Space: O(1)

Another approach: (Using built-in-function)

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)
{
    return __builtin_parity(n);
}

// Driver code
int main()
{
    unsigned int n = 7;
    cout<<"Parity of no "<<n<<" = "<<(getParity(n)? "odd": "even");

    getchar();
    return 0;
}

// This code is contributed by Kasina Dheeraj

Output

Parity of no 7 = odd

Time Complexity: O(1)

Auxiliary Space: O(1)

Another Approach: Mapping numbers with the bit 

We can use a map or an array of the number of bits to form a nibble (a nibble consists of 4 bits, so a 16 – length array would be required). Then, we can get the nibbles of a given number.

This approach can be summarized into the following steps:

1. Build the 16 length array of the number of bits to form a nibble – { 0, 1, 1, 2, 1, 2, 2, 3, 1, 2, 2, 3, 2, 3, 3, 4 }

2. Recursively count the set of the bits by taking the last nibble (4 bits) from the array using the formula num & 0xf and then getting each successive nibble by discarding the last 4 bits using >> operator.

3. Check the parity: if the number of set bits is even, ie numOfSetBits % 2 == 0, then the number is of even parity. Else, it is of odd parity.

C++

// C++ program to get the parity of the
// binary representation of a number

#include <bits/stdc++.h>
using namespace std;

int nibble_to_bits[16]
    = { 0, 1, 1, 2, 1, 2, 2, 3, 1, 2, 2, 3, 2, 3, 3, 4 };

// Function to recursively get the nibble
// of a given number and map them in the array

unsigned int countSetBits(unsigned int num)
{
    int nibble = 0;
    if (0 == num)
        return nibble_to_bits[0];

    // Find last nibble
    nibble = num & 0xf;

    // Use pre-stored values to find count
    // in last nibble plus recursively add
    // remaining nibbles.
    return nibble_to_bits[nibble] + countSetBits(num >> 4);
}

// Function to get the parity of a number
bool getParity(int num) { return countSetBits(num) % 2; }

// Driver code
int main()
{
    unsigned int n = 7;

    // Function call
    cout << "Parity of no " << n << " = "
         << (getParity(n) ? "odd" : "even");

    return 0;
}

// This code is contributed by phasing17

Java

// Java program to get the parity of the
// binary representation of a number
import java.util.*;

class GFG{

    static int[] nibble_to_bits = {
        0, 1, 1, 2, 1, 2, 2, 3, 1, 2, 2, 3, 2, 3, 3, 4
    };

    // Function to recursively get the nibble
    // of a given number and map them in the array

    static int countSetBits(int num)
    {
        int nibble = 0;
        if (0 == num)
            return nibble_to_bits[0];

        // Find last nibble
        nibble = num & 0xf;

        // Use pre-stored values to find count
        // in last nibble plus recursively add
        // remaining nibbles.
        return nibble_to_bits[nibble]
            + countSetBits(num >> 4);
    }

    // Function to get the parity of a number
    static boolean getParity(int num)
    {
        return countSetBits(num) % 2 == 1;
    }

// Driver code
public static void main(String[] args)
{
        int n = 7;

        // Function call
        System.out.print(
            "Parity of no " + n + " = "
            + (getParity(n) ? "odd" : "even"));
}
}

// This code is contributed by sanjoy_62.

Python3

# Python3 program to get the parity of the
# binary representation of a number
nibble_to_bits = [0, 1, 1, 2, 1, 2, 2, 3, 1, 2, 2, 3, 2, 3, 3, 4]

# Function to recursively get the nibble
# of a given number and map them in the array
def countSetBits(num):
    nibble = 0
    if (0 == num):
        return nibble_to_bits[0]

    # Find last nibble
    nibble = num & 0xf

    # Use pre-stored values to find count
    # in last nibble plus recursively add
    # remaining nibbles.
    return nibble_to_bits[nibble] + countSetBits(num >> 4)

# Function to get the parity of a number
def getParity(num):
    return countSetBits(num) % 2

# Driver code
n = 7

# Function call
print("Parity of no", n, " = ", ["even", "odd"][getParity(n)])

# This code is contributed by phasing17

C#

// C# program to get the parity of the
// binary representation of a number
using System;

class GFG {

    static int[] nibble_to_bits = {
        0, 1, 1, 2, 1, 2, 2, 3, 1, 2, 2, 3, 2, 3, 3, 4
    };

    // Function to recursively get the nibble
    // of a given number and map them in the array

    static int countSetBits(int num)
    {
        int nibble = 0;
        if (0 == num)
            return nibble_to_bits[0];

        // Find last nibble
        nibble = num & 0xf;

        // Use pre-stored values to find count
        // in last nibble plus recursively add
        // remaining nibbles.
        return nibble_to_bits[nibble]
            + countSetBits(num >> 4);
    }

    // Function to get the parity of a number
    static bool getParity(int num)
    {
        return countSetBits(num) % 2 == 1;
    }

    // Driver code
    public static void Main(string[] args)
    {
        int n = 7;

        // Function call
        Console.WriteLine(
            "Parity of no " + n + " = "
            + (getParity(n) ? "odd" : "even"));
    }
}

// This code is contributed by phasing17

Javascript

// JavaScript program to get the parity of the
// binary representation of a number

let nibble_to_bits
    = [ 0, 1, 1, 2, 1, 2, 2, 3, 1, 2, 2, 3, 2, 3, 3, 4 ];

// Function to recursively get the nibble
// of a given number and map them in the array

function countSetBits(num)
{
    let nibble = 0;
    if (0 == num)
        return nibble_to_bits[0];

    // Find last nibble
    nibble = num & 0xf;

    // Use pre-stored values to find count
    // in last nibble plus recursively add
    // remaining nibbles.
    return nibble_to_bits[nibble] + countSetBits(num >> 4);
}

// Function to get the parity of a number
function getParity(num) { return countSetBits(num) % 2; }


// Driver code
let n = 7;

// Function call
console.log("Parity of no " + n + " = "+ (getParity(n) ? "odd" : "even"));


// This code is contributed by phasing17

Output

Parity of no 7 = odd

Time Complexity: O(1)

Auxiliary Space: O(1)

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.