# [LeetCode] Gray Code (Java)

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:

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.

## Analysis

To solve this problem, we need to look at the gray code sequence. Assuming n = 3, we have:

000
001
011
010
110
111
101
100

We can see that the last two digits of 4 codes at the bottom is just the descending sequence of the first 4 codes. The first 4 codes are 0, 1, 3, 2. So, we can easily get the last 4 codes: 2 + 4, 3 + 4, 1 + 4, 0 + 4, which is 6, 7, 5, 4. We can keep doing this until we reach n digits.

## Complexity

We need to generate $2^n$ numbers, so the complexity is $O(2^n)$.