【LeetCode】 1009. Complement of Base 10 Integer

Description

Every non-negative integer N has a binary representation. For example, 5 can be represented as "101" in binary, 11 as "1011" in binary, and so on. Note that except for N = 0, there are no leading zeroes in any binary representation.

The complement of a binary representation is the number in binary you get when changing every 1 to a 0 and 0 to a 1. For example, the complement of "101" in binary is "010" in binary.

For a given number N in base-10, return the complement of it's binary representation as a base-10 integer.

Note:

• 0 <= N < 10^9
  This question is the same as 476: https://leetcode.com/problems/number-complement/

每個非負整數N都有一個二進位代表數字。例如5在二進制可以表示成"101"，11則可以表示成"1011"等等。注意，除了N = 0以外，沒有其他以零當作開頭的數字。

一個二進制數字的補數是指把全部的1換成0然後0換成1。例如"101"的二進制補數就會是"010"。

給予一個十進制數字N，回傳它的二進制補數並換為十進制。

提示：

• 0 <= N < 10^9
  這個問題和476是一樣的：https://leetcode.com/problems/number-complement/

Example:

Example 1:

Input: 5
Output: 2
Explanation: 5 is "101" in binary, with complement "010" in binary, which is 2 in base-10.


Example 2:

Input: 7
Output: 0
Explanation: 7 is "111" in binary, with complement "000" in binary, which is 0 in base-10.


Example 3:

Input: 10
Output: 5
Explanation: 10 is "1010" in binary, with complement "0101" in binary, which is 5 in base-10.

Solution

• 這裡是一樣的題目的詳解
• 當一個數字和1做XOR運算後，就會變得相反。因此現在的問題變成要怎麼避免前面多餘的零也變成一。
• 最簡單的方法就是利用位移>>去計算N有幾個位元digits，再將digits個1去和N做XOR就是答案了。
  • 注意0是個特例，要另做判斷。

Code

class Solution {
public:
    int bitwiseComplement(int N) {
        if(N == 0) return 1;
        int digits = 0;
        int XOR = 0;
        while(N >> digits)
        {
            digits++;
            XOR = (XOR << 1) + 1;
        }
        return N ^ XOR;
    }
};

tags: LeetCode C++