【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.
![](http://images0.cnblogs.com/blog/250006/201501/192223588754396.png)
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 };