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; } |
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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; } |
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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*/ |
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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 = 7print ("Parity of no ", n," = ", ( "odd" if getParity(n) else "even")) # This code is contributed by "Sharad_Bhardwaj". |
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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. |
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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. ?> |
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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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