Counting Set Bits

Problem: Count the number of $1$ bits in an integer (population count).

Method 1: Loop and check each bit. $O(\log n)$.

count = 0
while n > 0:
    count = count + (n & 1)
    n = n >> 1
return count

Method 2: Clear lowest set bit repeatedly. $O(k)$ where $k$ is the number of $1$ bits.

count = 0
while n > 0:
    n = n & (n - 1)
    count = count + 1
return count

Method 3: Built-in functions.

• C++: __builtin_popcount(n)
• Python: bin(n).count('1')
• Java: Integer.bitCount(n)

Built-ins use hardware instructions and are fastest.