Number of 1 Bits - LeetCodee

Problem 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.

Examples

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.

Jump to Solution: Python Java C++ JavaScript C#

Python Solution


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

Alternative Solution (Brian Kernighan's Algorithm):


def hammingWeight(n: int) -> int:
    count = 0
    while n:
        n &= (n - 1)  # Clear the least significant 1 bit
        count += 1
    return count

Java Solution


public class Solution {
    public int hammingWeight(int n) {
        int count = 0;
        while (n != 0) {
            count += n & 1;
            n >>>= 1;  // Unsigned right shift
        }
        return count;
    }
}

C++ Solution


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

JavaScript Solution


/**
 * @param {number} n - a positive integer
 * @return {number}
 */
var hammingWeight = function(n) {
    let count = 0;
    while (n !== 0) {
        count += n & 1;
        n >>>= 1;  // Unsigned right shift
    }
    return count;
};

C# Solution


public class Solution {
    public int HammingWeight(uint n) {
        int count = 0;
        while (n != 0) {
            count += (int)(n & 1);
            n >>= 1;
        }
        return count;
    }
}

Complexity Analysis

Time Complexity: O(1) as we process at most 32 bits
Space Complexity: O(1) as we only use a constant amount of extra space

Solution Explanation

There are two main approaches to solve this problem:

Loop and Count:
- Check each bit using AND operation
- Right shift to move to next bit
- Count the 1s
Brian Kernighan's Algorithm:
- Uses n & (n-1) to clear least significant 1
- More efficient for sparse numbers
- Fewer iterations needed

Key points:

Bit manipulation
Unsigned integers
Language specifics
Optimization techniques

Alternative approaches:

Built-in functions
Lookup tables
Divide and conquer