[leedcode 89] 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.

public class Solution {
    public List<Integer> grayCode(int n) {
       //自然数（二进制表示）转化为格雷码的公式是：i>>1^i
       //例如：Binary Code ：1011 要转换成Gray Code 
       //(1011 >> 1)^1011 = 1110
        int size=1<<n;//先求出二进制一共的个数
        List<Integer> res=new ArrayList<Integer>();
        for(int i=0;i<size;i++){
            res.add(i>>1^i);
        }
        return res;
    }
        /*格雷码的规律是 将格雷码看成是上下两部分 n=1 

        上 0  下 1

        当n=2

        上为n=1时的格雷码 

        下为n=1时的格雷码的倒序再加上最前面的1*/
}