leetcode - 191. Number of 1 Bits

Description

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

Note:

• Note that in some languages, such as Java, there is no unsigned integer type. In this case, the input will be given as a signed integer type. It should not affect your implementation, as the integer’s internal binary representation is the same, whether it is signed or unsigned.
• In Java, the compiler represents the signed integers using 2’s complement notation. Therefore, in Example 3, the input represents the signed integer. -3.

Example 1:

Input: n = 00000000000000000000000000001011
Output: 3
Explanation: The input binary string 00000000000000000000000000001011 has a total of three '1' bits.

Example 2:

Input: n = 00000000000000000000000010000000
Output: 1
Explanation: The input binary string 00000000000000000000000010000000 has a total of one '1' bit.

Example 3:

Input: n = 11111111111111111111111111111101
Output: 31
Explanation: The input binary string 11111111111111111111111111111101 has a total of thirty one '1' bits.

Constraints:

The input must be a binary string of length 32.

Follow up: If this function is called many times, how would you optimize it?

Solution

For each digit of the number, use logical AND with 1 to decide whether current digit is 1 or 0, after logical AND, move the number to right by 1 digit. Loop until the number is zero.

Time complexity: $o(\log n)$
Space complexity: $o(1)$

Code

class Solution:
    def hammingWeight(self, n: int) -> int:
        res = 0
        while n > 0:
            res += n & 1
            n >>= 1
        return res

Or use x & (x - 1) to remove the rightmost 1:

class Solution:
    def hammingWeight(self, n: int) -> int:
        res = 0
        while n > 0:
            res += 1
            n &= (n-1)
        return res