# 89 Gray Code

## 89. [Gray Code](https://leetcode.com/problems/gray-code/description/)

## 1. Question

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:

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

**Note:**\
For a givenn, 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.

## 2. Implementation

**(1) Backtracking**

思路: 本质上和320 Generalized Abbreviation一样，对每个bit，我们有两种选择，要么不改变原有的bit，要么反转现有的bit

```java
class Solution {
    public List<Integer> grayCode(int n) {
        List<Integer> res = new ArrayList<>();
        int[] num = new int[1];
        getGrayCode(n, num, res);
        return res;
    }

    public void getGrayCode(int n, int[] num, List<Integer> res) {
        if (n == 0) {
            res.add(num[0]);
            return;
        }
        // For each bit of the num, we either leave it alone or invert the current bit
        // Leave the current bit alone
        getGrayCode(n - 1, num, res);

        // Invert the current bit
        num[0] ^= (1 << (n -1));
        getGrayCode(n - 1, num, res);
    }
}
```

## 3. Time & Space Complexity

**Backtracking:** 时间复杂度O(2^n), 空间复杂度O(2^n)
