LeetCode89. Gray Code（C++）

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本文介绍了一种生成格雷码序列的有效算法，通过异或运算实现，详细解释了算法原理，并提供了完整的C++代码实现。格雷码是一种二进制数系统，其中任意两个连续的数值仅在一个位上不同。

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The gray code is a binary numeral system where two successive values differ in only one bit.

Given a non-negative integer n representing the total number of bits in the code, print the sequence of gray code. A gray code sequence must begin with 0.

Example 1:

Input: 2
Output: [0,1,3,2]

Explanation:
00 - 0
01 - 1
11 - 3
10 - 2

For a given n, a gray code sequence may not be uniquely defined.
For example, [0,2,3,1] is also a valid gray code sequence.

00 - 0
10 - 2
11 - 3
01 - 1

Example 2:

Input: 0
Output: [0]
Explanation: 
We define the gray code sequence to begin with 0.A gray code sequence of n has size = 2n, which for n = 0 the size is 20 = 1.Therefore, for n = 0 the gray code sequence is [0].

解题思路：首先用 n = 7的情况来简单认识一下格雷码的编码过程：

G(0) = 000 ^ 000 = 000
G(1) = 001 ^ 000 = 001
G(2) = 010 ^ 001 = 011
G(3) = 011 ^ 001 = 010
G(4) = 100 ^ 010 = 110
G(5) = 101 ^ 010 = 111
G(6) = 110 ^ 011 = 101
G(7) = 111 ^ 011 = 100

不难发现第 i 个的格雷码，就是 i 本身的二进制与该二进制的右移一位的异或。

class Solution {
public:
    vector<int> grayCode(int n) {
        n = 1 << n;
        vector<int>ans(n, 0);
        for(int i = 0; i < n; ++ i )
            ans[i] = i^(i >> 1);
        return ans;
    }
};