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.

 解法1 dp＋非位运算

  规律：

public class Solution {
    public List<Integer> grayCode(int n) {
        if(n == 0) {
            List<Integer> l1 = new ArrayList<>();
            l1.add(0);
            return l1;
        }
        List<List<String>> list = new ArrayList<>();
        List<String> l1 = new ArrayList<>();
        List<Integer> res = new ArrayList<>();
        l1.add("0");
        l1.add("1");
        list.add(l1);
        for(int i = 1 ; i < n ; i++){
            List<String> member = list.get(i-1);
            List<String> next = new ArrayList<>();
            for(String s : member){
                String newS = "0"+ s;
                next.add(newS);
            }
            
            for(int j = member.size() -1 ; j >= 0; j--){
                String newS = "1"+ member.get(j);
                next.add(newS);
            }
            list.add(next);
        }
         List<String> l = list.get(n-1);
         for(String str : l){
             res.add(getValueofBit(str));
         }
         return res;
    }
    public int getValueofBit(String s){
        int res = 0;
        for(int i = 0 ; i < s.length() ; i++){
            res += Math.pow(2, s.length()-1-i) * (s.charAt(i) -'0');
        }
        return res;
    }
}

bit运算

public class Solution {
    public List<Integer> grayCode(int n) {
        int count = (int) Math.pow(2, n);
        List<Integer> res = new ArrayList<>();
        for(int i = 0; i < count ; i++){
            res.add(i ^ (i >> 1));
        }
        return res;
    }
}