LeetCode 191. Number of 1 Bits

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.

分析:题目大意是编写一个函数,函数接收一个无符号整数,并返回该数字二进制表示下“1”的个数。

注意:java中默认是有符号数,在对数字操作时需要注意!

Java代码:

解法一:有两点需要注意

1. 位运算 & 的优先级 低于 比较运算符 == ,括号不能少,为了代码可读性,多写括号偷笑

Java常用符号优先级:

优先级 运算符 结合性
1 () [] . 从左到右
2 ! +(正)  -(负) ~ ++ -- 从右向左
3 * / % 从左向右
4 +(加) -(减) 从左向右
5 << >> >>> 从左向右
6 < <= > >= instanceof 从左向右
7 ==   != 从左向右
8 &(按位与) 从左向右
9 ^ 从左向右
10 | 从左向右
11 && 从左向右
12 || 从左向右
13 ?: 从右向左
14 = += -= *= /= %= &= |= ^=  ~=  <<= >>=   >>>= 从右向左

2. 由于对无符号数操作,用无符号右移 >>>而不是>>

public class Solution {
    // you need to treat n as an unsigned value
    public int hammingWeight(int n) {
        int cnt = 0;
        while(n != 0){
            // 记得括号,==优先级高于&
            if((n & 1) == 1) cnt++;// 也可写作 cnt += n & 1;
            n = n >>> 1;// 右移时要采用无符号右移,用 >> 会报错。 
        }
        
        return cnt;
    }
}
解法2:

public class Solution {
    // you need to treat n as an unsigned value
    public int hammingWeight(int n) {
        int cnt = 0;
        while(n != 0){           
            // 解法2
            cnt++;
            n = n & (n-1);
        }        
        return cnt;
    }
}



### 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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