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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