gray-code——找规律

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.

 

n=0    0

n=1    0    0+1<<(1-1)

n=2    n=1: 0  1   1+1<<(2-1)   0+1<<(2-1)

 

找到规律，第n次增加的序列为n-1序列的倒序+（高位+1）形成。

class Solution {
public:
    vector<int> grayCode(int n) {
        vector<int> res;
        if(n<0) return res;
        res.push_back(0);
        for(int i=1;i<=n;i++){
            int size=res.size();
                for(int j=size-1;j>=0;j--){
                    int tmp=1<<(i-1);
                    tmp|=res[j];
                    res.push_back(tmp);
                }
            }
      
    return res;
    }
};