LeetCode-Number Complement

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Description：
Given a positive integer, output its complement number. The complement strategy is to flip the bits of its binary representation.

Note:

• The given integer is guaranteed to fit within the range of a 32-bit signed integer.
• You could assume no leading zero bit in the integer’s binary representation.

    Example 1:
    
    Input: 5
    Output: 2
    Explanation: The binary representation of 5 is 101 (no leading zero bits), and its complement is 010. So you need to output 2.

    Example 2:
    
    Input: 1
    Output: 0
    Explanation: The binary representation of 1 is 1 (no leading zero bits), and its complement is 0. 

题意：给定一个正整数，输出它的补数；其定义将正整数的无前导0的二进制取反（1变为0，0变为1）；

解法一：我们可以考虑异或操作，将这个数的无前导0二进制表示和其全1表示（长度为这个数的无前导0二进制表示）相异或，就可以得到其取反的数；

Java

class Solution {
    public int findComplement(int num) {
        int len = 0;
        int temp = num;
        while (temp > 0) {
            len++;
            temp /= 2;
        } 
        return num == 0 ? 1 : ((1 << len) - 1) ^ num;
    }
}

解法二：同样还是考虑用异或的操作，但是我们不去求这个数的无前导0二进制表示的长度，利用位操作直接得到其最后的表示；定义mask = ~0（全1表示）；将mask与num相与直到值为0，这个时候的mask的后n为即为num的无前导0二进制表示的长度，再将mask取反即得到解法一中的无前导0二进制全1表示；

Java

class Solution {
    public int findComplement(int num) {
        int mask = ~0;
        while ((num & mask) > 0) {
            mask <<= 1;
        }
        return num ^ ~mask;
    }
}