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 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 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 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# 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 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.
?>
<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>
OutputParity 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
// Java program to implement approach
import java.util.*;
class Main {
// Function to get parity of number n. It returns 1
// if n has odd parity, and returns 0 if n has even
// parity
public static boolean getParity(int n) {
return Integer.bitCount(n) % 2 == 1;
}
// Driver code
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 phasing17
# Python 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
def getParity(n):
return (bin(n).count("1"))%2
# Driver code
n=7
print("Parity of no {0} = ".format(n),end="")
print("odd" if getParity(n) else "even")
# This code is contributed by Pushpesh Raj
// C# code to implement the approach
using System;
using System.Linq;
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
public static bool GetParity(int n)
{
return Convert.ToInt32(Convert.ToString(n, 2).Count(x => x == '1')) % 2 == 1;
}
// Driver code
public static void Main()
{
int n = 7;
Console.WriteLine("Parity of no " + n + " = " + (GetParity(n) ? "odd" : "even"));
}
}
// This code is contributed by phasing17
// JS program to implement the above approach
// Function to get parity of number n. It returns 1
// if n has odd parity, and returns 0 if n has even parity
const getParity = (n) => {
return (n.toString(2).split("1").length - 1) % 2;
};
// Driver code
const n = 7;
console.log(`Parity of no ${n} =`, getParity(n) ? "odd" : "even");
// This code is implemented by Phasing17
OutputParity 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 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 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# 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 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
OutputParity 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.
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