【leetcode】Gray Code

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.

观察可以发现，

n位的格雷码前一半元素与n-1的格雷码元素完全相同

后半部分等于前半部分逆序，在加上最高位，即1<<(n-1);

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