LeetCode刷题笔记--89. Gray Code

中间停了几天没有刷题，因为种种原因。今天开始恢复刷题，加油！

89. Gray Code

Medium

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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.

Example 1:

Input: 2
Output: [0,1,3,2]
Explanation:
00 - 0
01 - 1
11 - 3
10 - 2

For a given n, a gray code sequence may not be uniquely defined.
For example, [0,2,3,1] is also a valid gray code sequence.

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

Example 2:

Input: 0
Output: [0]
Explanation: We define the gray code sequence to begin with 0.
             A gray code sequence of n has size = 2n, which for n = 0 the size is 20 = 1.
             Therefore, for n = 0 the gray code sequence is [0].

这道题初看好像没有什么规律，于是我在自己的本子上挨个写下了n=1,2,3,4几种情况，写完发现是有规律可循的，找到规律后整理了一下思路，写代码只是分分钟的事，稍微调试一下就OK了。

规律如下：

从n=1可以通过如下变化得到n=2，就是从last数组vector[1]到vector[0]，逐个加上2，加入vector中。同理，从2可以得到3，从3可以得到4。（用到递归）

下面是AC的代码：

class Solution {
public:
    vector<int> cal(vector<int> last,int n,int now)
    {
        if(now==n)
        {
            return last;
        }
        else
        {
            int len=last.size();
            for(int i=len-1;i>=0;i--)
            {
                last.push_back(last[i]+pow(2,now));
            }
            now++;
            return cal(last,n,now);
        }
        
    }
    
    vector<int> grayCode(int n) {
        vector<int> ans;
        ans.clear();
        ans.push_back(0);
        if(n==0)return ans;
        ans.push_back(1);
        if(n==1)return ans;
        return cal(ans,n,1);
    }
};