89. 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.

   

解题思路：

当n=3时，假设前4个元素使用n=2的gray code，即[000,001,011,010]，那么剩下的数字都是1xx，只要将前4个元素逆序，再加上4即可，即[110,111,101,100]。。。构造方法就是这样的过程。。

class Solution {

public:

    vector<int> grayCode(int n) {

        vector<int>res;

        res.push_back(0);

        if(n==0)return res;

        res.push_back(1);

        if(n==1)return res;

        int tmp=2;

        int num=(1<<n);

        while(tmp!=num){

            for(int i=tmp-1;i>=0;i--)res.push_back(res[i]+tmp);

            tmp<<=1;

        }

        return res;

    }

};