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.

[解题思路]

000
001
011
010
110
111 
101
100

public class Solution {
    public ArrayList<Integer> grayCode(int n) {
        // Start typing your Java solution below
        // DO NOT write main() function
        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;
    }
}

解2：

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) {
        // Start typing your Java solution below
        // DO NOT write main() function
        ArrayList<Integer> result = new ArrayList<Integer>();
        int count = 1 << n;
        for(int i = 0; i < count; i++){
            result.add(i^(i >> 1));
        }
        
        return result;
    }