(LeetCode 191) Number of 1 Bits

给定一个无符号整数,返回其二进制表示中1的个数。例如,输入32位整数11,由于其二进制形式为00000000000000000000000000001011,所以返回3。解决方案中需要注意将整数以long类型存储,以避免有符号整数的符号位问题。

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

For example, the 32-bit integer ’11’ has binary representation 00000000000000000000000000001011, so the function should return 3.

也是就输入一个无符号整数,对其二进制里面的1进行计数。

solution:
这道题主要一个陷阱就是,题目要求计算的是该整数无符号二进制中的1的个数,但是整数实际上在计算机中是按照有符号二进制补码存储会有一位符号位,所以当输入为 231 时,其无符号二进制是100000000000000000000000000000000,但是你转换出来是011111111111111111111111111111111,因为溢出了.
我们只需要把输入的32位无符号整数用long类型存储,这样可以避免数据位被转化成符号位。

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