# 

## 

### 

a=0^a=a^0

0=a^a

a=a^b^b

### 

a=a^b

b=a^b

a=a^b

###  1

a=n&(n-1)

###  1

diff=(n&(n-1))^n

## 

[single-number](https://leetcode-cn.com/problems/single-number/)

> ****

```c++
int singleNumber(vector& nums) {
    // 10 ^10 == 00
    // 0
    auto result = 0;
    for (const auto &num : nums) {
        result ^= num;
    }
    return result;
}
```

[single-number-ii](https://leetcode-cn.com/problems/single-number-ii/)

> ****

```c++
// 13
// 0
int singleNumber(vector& nums) {
    auto ret = 0;
    for (int i = 0; i < 32; ++i) {
        auto sumOne = 0;
        for (const auto &item : nums) {
            sumOne += (item >> i) & 1;
        }
        ret ^= (sumOne % 3)   `nums` 

```c++
vector singleNumber(vector& nums) {
    auto diff = 0;
    // 
    for (const auto &item : nums) {
        diff ^= item;
    }
    vector result(2);
    //  1
    //  '1'
    diff &= (-diff);
    // 10
    for (const auto &num : nums) {
        if ((diff & num) == 0) {
            result[0] ^= num;
        } else {
            result[1] ^= num;
        }
    }
    return result;
}
```
>  x & (-x)  
>   
>  x  -x '1' x  '1'  
>   
> 1  
> 10-108  
>  10: 0000 1010  
> -10: 1111 1010
> x & (-x) x'1'

[number-of-1-bits](https://leetcode-cn.com/problems/number-of-1-bits/)

>  1 [](https://baike.baidu.com/item/%E6%B1%89%E6%98%8E%E9%87%8D%E9%87%8F)

```c++
int hammingWeight(int n) {
    auto ret = 0;
    while (n != 0) {
        n = n & (n - 1);
        ++ret;
    }
    return ret;
}
```

[counting-bits](https://leetcode-cn.com/problems/counting-bits/)

>  **num** 0  i  num  i 1 

```c++
vector countBits(int num) {
    vector ret(num+1);
    for (int i = 0; i = 1;
        --pow;
    }
    return ret;
}
```

[bitwise-and-of-numbers-range](https://leetcode-cn.com/problems/bitwise-and-of-numbers-range/)

>  [m, n] 0 >= 1;
        ++zeroNum;
    }
    return m