191. Number of 1 Bits

Description

Write a function that takes an unsigned integer and return 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 signed integer type and should not affect your implementation, as the internal binary representation of the integer 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 above the input represents the signed integer -3.

Follow up:

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

Constraints

Approach

Links

• GeeksforGeeks

• Leetcode

• ProgramCreek

• YouTube

Examples

Example 1

Input: 00000000000000000000000000001011

Output: 3

Explanation: The input binary string 00000000000000000000000000001011 has a total of three '1' bits.

Example 2

Input: 00000000000000000000000010000000

Output: 1

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

Example 3

Input: 11111111111111111111111111111101

Output: 31

Explanation: The input binary string 11111111111111111111111111111101 has a total of thirty one '1' bits.

Solutions

Solution 1

/**
 * Time complexity : The run time depends on the number of bits in n. 
 *    Because n in this piece of code is a 32-bit integer, 
 *    the time complexity is O(1).
 * Space complexity : O(1), since no additional space is allocated.
 */

public class Solution {
    // you need to treat n as an unsigned value
    public int hammingWeight(int n) {
        if(n == 0) return 0;
        
        int bits = 0;
        int mask = 1;
        for(int i = 0; i < 32; i++) {
            if((n&mask) != 0) {
                bits++;
            }
            mask <<= 1;
        }
        return bits;
    }
}

Solution 2

/**
 * Time complexity : The run time depends on the number of 11-bits in n. 
 *    In the worst case, all bits in nn are 11-bits. 
 *    In case of a 32-bit integer, the run time is O(1).
 * Space complexity : O(1), since no additional space is allocated.
 */
 
 public class Solution {
    // you need to treat n as an unsigned value
    public int hammingWeight(int n) {
        if(n == 0) return 0;
        
        int bits = 0;
        while(n != 0) {
            bits++;
            n &= (n-1);
        }
        
        return bits;
    }
}

Follow up