LooetCode Q191: Number of 1 Bits

Write a function that takes an unsigned integer and returns the number of ’1' bits it has (also known as the Hamming weight).

For example, the 32-bit integer ’11' has binary representation 00000000000000000000000000001011, so the function should return 3.

My solution: Time complexity O(1) it counts entire 32 bits.
Optimal solution: Although the time complexity is also O(1), it takes k steps to finish, where k is the number of 1s in int. The idea is to remove an 1 at a time. The trick is: An elegant way to check is an integer has exactly one bit set to 1. Given integer say int i=k, we could check if (i & (i-1))==0, if true then only one bit is 1 in i. In the same time (i & (i-1))==0 actually check if number i is a power of 2.