【leetcode】89. Gray Code

一、题目描述

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.

思路：需要先找出规律，试着写几个用例就可以发现了。当n=0 时，[0]，当n=1 时， [0, 1]，当n=2时，[00, 01, 11, 10]，当n=3 时，[000, 001, 011, 010, 110, 111, 101, 100]。可以发现000, 001, 011, 010 正好是n=2 的数值在第一位加了一个0，而110, 111,
101, 100，正好是n=2 的数值按逆序在每个数的第一位加了一个1。

c++代码（3ms，100%）

class Solution {
public:
vector<int> grayCode(int n) {
vector<int> res;
if(n==0){
res.push_back(0);
return res;
}
vector<int> last_res = grayCode(n-1);
//获取之前的数值
res.insert(res.end(),last_res.begin(),last_res.end());
for(int i=(int)last_res.size()-1;i>=0; i--){
res.push_back(last_res[i]+(1<<n-1));
}
return res;
}
};