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LeetCode89 Gray Code

题目:

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(Medium)

For example, given n = 2, return [0,1,3,2]. Its gray code sequence is: 

00 - 0
01 - 1
11 - 3
10 - 2

分析:

考察三位的格雷码和两位的格雷码如下:

00 01 11 10;

000 001 011 010 110 111 101 100;

可以看出如下规律,三位的格雷码是二位的格雷码前面加上0,和倒序二维格雷码前面加上1得到的。

所以要求n为格雷码,只需要在所有n-1位格雷码前面加0,并在倒序的所有n-1位格雷码前面加1即可。

代码:

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

 

 

 

LeetCode89 Gray Code