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Saturday, July 16, 2011

Count number of set bits in a number

Brian Kernighan’s Algorithm:
Subtraction of 1 from a number toggles all the bits (from right to left) till the rightmost set bit(including the righmost set bit). So if we subtract a number by 1 and do bitwise & with itself (n & (n-1)), we unset the righmost set bit. If we do n & (n-1) in a loop and count the no of times loop executes we get the set bit count.
Beauty of the this solution is number of times it loops is equal to the number of set bits in a given integer.

1 Initialize count: = 0
2 If integer n is not zero
(a) Do bitwise & with (n-1) and assign the value back to n
n: = n&(n-1)
(b) Increment count by 1
(c) go to step 2
3 Else return count
/* Function to get no of set bits in binary
representation of passed binary no. */
int countSetBits(int n)
{
unsigned int count = 0;
while (n)
{
n &= (n-1) ;
count++;
}
return count;
}


Method 2 :
int countSetBits(unsigned int n)
{
unsigned int count = 0;
while(n)
{
count += n & 1;
n >>= 1;
}
return count;
}

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