Gray Code

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

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

For example, givenn = 2, return[0,1,3,2]. Its gray code sequence is:

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].

Reflect-and-prefix method

方法2，n比特的格雷码，可以递归地从n-1比特的格雷码生成。如下图所示。

// Gray Code
// reflect-and-prefix method
// 时间复杂度O(2^n)，空间复杂度O(1)
class Solution {
public:
    vector<int> grayCode(int n) {
        const int size = 1 << n;
        vector<int> result;
        result.reserve(size);

        result.push_back(0);
        for (int i = 0; i < n; i++) {
            const int highest_bit = 1 << i;
            for (int j = result.size() - 1; j >= 0; j--) // 要反着遍历，才能对称
                result.push_back(highest_bit | result[j]);
        }
        return result;
    }
};

Math Equation

// Gray Code
// 数学公式，时间复杂度O(2^n)，空间复杂度O(1)
class Solution {
public:
    vector<int> grayCode(int n) {
        const int size = 1 << n;  // 2^n
        vector<int> result;
        result.reserve(size);

        for (int i = 0; i < size; ++i)
            result.push_back(binary_to_gray(i));
        return result;
    }
private:
    static int binary_to_gray(int n) {
        return n ^ (n >> 1);
    }
};