Find parity of an unsigned integer

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

Code:

# include <stdio.h> # define  bool int bool getParity(unsigned int n) {     bool parity = 0;     while (n)     {         parity = !parity;         n      = n & (n - 1);     }            return parity; } int main() {     unsigned int n = 7;     printf("Parity of no %d = %s",  n,              (getParity(n)? "odd": "even"));           getchar();     return 0; }

Above solution can be optimized by using lookup table.
Time Complexity: The time taken by above algorithm is proportional to the number of bits set. Worst case complexity is O(Logn).
Uses: Parity is used in error detection and cryptography.