Problem:

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, find the sequence of gray code. A gray code sequence must begin with 0 and with cover all 2n integers.

Have you met this question in a real interview? Yes
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.

[0,2,3,1] is also a valid gray code sequence according to the above definition.

Challenge
O(2n) time.

Leetcode link
Lintcode link

Solution:

Use recursion to generate a new gray code from the (n-1) as the picture shown in the Figure below.

/*************************************************************************
    > File Name: GrayCode.java
    > Author: Yao Zhang 
    > Mail: psyyz10@163.com 
    > Created Time: Fri 13 Nov 17:22:56 2015
 ************************************************************************/

public class GrayCode{
    List<Integer> grayCode(int n){
        ArrayList<Integer> result = new ArrayList<Integer>();
        result.add(0);
        if (n == 0)
            return result;
        if (n == 1){
            result.add(1);
            return result;
        }
        result = (ArrayList<Integer>) grayCode(n - 1);
        ArrayList<Integer> temp = reverse(result);
        for (int i = 0; i < temp.size(); i++){
            temp.set(i,(1 << (n - 1)) + temp.get(i));
        }
        result.addAll(temp);

        return result;
    }

    public ArrayList<Integer> reverse(ArrayList<Integer> result){
        ArrayList<Integer> newResult = new ArrayList<Integer>();
        for (int i = result.size() - 1; i >= 0; i--){
            newResult.add(result.get(i));
        }
        return newResult;
    }
}