leetcode 191. Number of 1 Bits(bit中1的个数)

本文介绍了一种高效算法,用于计算32位整型数中1的比特位数量,即Hamming权重。该算法通过巧妙的位操作减少计算步骤,实现了快速统计。

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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.

Hamming距离,input是32位整型,统计其中bit位为1的个数。

思路:
有个著名的并行统计bit为1的算法,
先是相邻2位,然后4位,8位,具体参考并行bit count算法

    public int hammingWeight(int n) {
        n = n - ((n >> 1) & 0x55555555);               
        n = (n & 0x33333333) + ((n >> 2) & 0x33333333); 
        int c = ((n + (n >> 4) & 0xF0F0F0F) * 0x1010101) >> 24;
        
        return c;
    }
### LeetCode Problems Involving Counting the Number of 1s in Binary Representation #### Problem Description from LeetCode 191. Number of 1 Bits A task involves writing a function that receives an unsigned integer and returns the quantity of '1' bits within its binary form. The focus lies on identifying and tallying these specific bit values present in any given input number[^1]. ```python class Solution: def hammingWeight(self, n: int) -> int: count = 0 while n: count += n & 1 n >>= 1 return count ``` This Python code snippet demonstrates how to implement the solution using bitwise operations. #### Problem Description from LeetCode 338. Counting Bits Another related challenge requires generating an output list where each element represents the amount of set bits ('1') found in the binary notation for integers ranging from `0` up to a specified value `n`. This problem emphasizes creating an efficient algorithm capable of handling ranges efficiently[^4]. ```python def countBits(num): result = [0] * (num + 1) for i in range(1, num + 1): result[i] = result[i >> 1] + (i & 1) return result ``` Here, dynamic programming principles are applied alongside bitwise shifts (`>>`) and AND (`&`) operators to optimize performance during computation. #### Explanation Using Brian Kernighan Algorithm For optimizing further especially with large inputs, applying algorithms like **Brian Kernighan** offers significant advantages due to reduced iterations needed per operation compared against straightforward methods iterating through all possible positions or dividing repeatedly until reaching zero. The core idea behind this method relies upon subtracting powers-of-two corresponding only to those places holding actual ‘ones’ thereby skipping over zeroes entirely thus reducing unnecessary checks: ```python def hammingWeight(n): count = 0 while n != 0: n &= (n - 1) count += 1 return count ``` --related questions-- 1. How does the Hamming weight calculation differ between signed versus unsigned integers? 2. Can you explain why shifting right works effectively when determining counts of one-bits? 3. What optimizations exist beyond basic iteration techniques for calculating bit counts? 4. Is there any difference in implementation logic required across various programming languages supporting similar syntaxes? 5. Why might someone choose the Brian Kernighan approach over other strategies?
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