# 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 - 001 - 111 - 310 - 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)public class Solution {    public ArrayList<Integer> grayCode(int n) {        final int size = 1 << n;  // 2^n        ArrayList<Integer> result = new ArrayList<>(size);        for (int i = 0; i < size; ++i)            result.add(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)public class Solution {    public ArrayList<Integer> grayCode(int n) {        final int size = 1 << n;        ArrayList<Integer> result = new ArrayList<>(size);        result.add(0);        for (int i = 0; i < n; i++) {            final int highest_bit = 1 << i;            for (int j = result.size() - 1; j >= 0; j--) // 要反着遍历，才能对称                result.add(highest_bit | result.get(j));        }        return result;    }}