## Gray Code

### 描述

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.

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

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


Note:

• For a given n, a gray code sequence is not uniquely defined.
• For example, [0,2,3,1] is also a valid gray code sequence according to the above definition.
• For now, the judge is able to judge based on one instance of gray code sequence. Sorry about that.

### 数学公式

// 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);
}
};


### Reflect-and-prefix method

// 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;
}
};