[Leetcode]-- Gray Code

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 - 0
01 - 1
11 - 3
10 - 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.

000
001
011
010
110
111 
101
100

public class Solution {
    public ArrayList<Integer> grayCode(int n) {
        ArrayList<Integer> result = new ArrayList<Integer>();
        
        if(n <= 1){
          result.add(0);
          if(n == 1)
            result.add(1);
            return result;
        }
        
        ArrayList<Integer> pre = grayCode(n-1);
        int highest = 1<<(n-1);
        result.addAll(pre);
        for(int i = pre.size()-1; i>= 0; i--){
            result.add(pre.get(i)+ highest); 
        }
        
        return result;
    }
}

二进制码->格雷码（编码）：从最右边一位起，依次将每一位与左边一位异或（XOR），作为对应格雷码该位的值，最左边一位不变（相当于左边是0）；
格雷码->二进制码（解码）：从左边第二位起，将每位与左边一位解码后的值异或，作为该位解码后的值（最左边一位依然不变）。

public ArrayList<Integer> grayCode(int n) {
        ArrayList<Integer> result = new ArrayList<Integer>();
        int count = 1 << n;
        for(int i = 0; i < count; i++){
            result.add(i^(i >> 1));
        }   
        return result;
    }

ref: http://www.cnblogs.com/feiling/p/3252084.html