Number of 1 Bits

Description

Write a function that takes 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?

Code

Time Complexity: $O(1)$, Space Complexity: $O(1)$

Bit manipulation trick，要去掉最右邊的 1 bit（drops the lowest set bit），使用 n = n & (n - 1)。

int hammingWeight(uint32_t n) {
    int count = 0;
    while(n > 0) {
        count++;
        n = n & (n - 1);
    } 
    return count;
}

class Solution {
public:
    int hammingWeight(uint32_t n) {
        int count = 0;
        while(n) {
            n = n & (n-1);
            count++;
        }
        return count;
    }
};

Source

• Number of 1 Bits - LeetCode