1. Description

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.

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.

2. Example

given n = 2, return [0,1,3,2]. Its gray code sequence is:
00 - 0
01 - 1
11 - 3
10 - 2

3. Code

import java.util.ArrayList;
import java.util.List;

public class LeetCode0089 {
    public List<Integer> grayCode(int n) {
        List<Integer> result = new ArrayList<Integer>();
        if (n < 0) {
            return result;
        }
        if (n == 0) {
            result.add(0);
            return result;
        }

        List<Integer> res = grayCode(n - 1);
        result.addAll(res);
        int num = 1 << (n - 1);
        for (int i = res.size() - 1; i >= 0; i--) {
            result.add(num + res.get(i));
        }
        return result;
    }

    public static void main(String[] args) {
        LeetCode0089 leetcode = new LeetCode0089();
        System.out.println(leetcode.grayCode(2));
    }
}