gray-code——找规律

Posted 2020-09-24 鸭子船长

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。

 1 class Solution {
 2 public:
 3     vector<int> grayCode(int n) {
 4         vector<int> res;
 5         if(n<0) return res;
 6         res.push_back(0);
 7         for(int i=1;i<=n;i++){
 8             int size=res.size();
 9                 for(int j=size-1;j>=0;j--){
10                     int tmp=1<<(i-1);
11                     tmp|=res[j];
12                     res.push_back(tmp);
13                 }
14             }
15       
16     return res;
17     }
18 };