【LeetCode】Gray Code

最新推荐文章于 2019-07-29 00:39:02 发布

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最新推荐文章于 2019-07-29 00:39:02 发布

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分类专栏：动态规划位运算

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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].

题解：格雷码数列的生成一共2^n个数，可以用格雷码定义公式直接生成然而时间复杂度反而高因为是指数时间，所以不如O(n^2)，利用dp思想，即用ans记录前n-1位的格雷码数列，然后用镜像映射的方法生成当前，刚开始用map记录各个状态实际上，只用到前一个所以只需要一个ans即时更新即可(坑：ans+1<<i，这里必须加括号ans(1<<i)！！

代码：

class Solution {
public:
    vector<int> grayCode(int n) {
        vector<int> ans{0};
        for(int i = 0;i < n;i++){
            for(int j = ans.size()-1;j >= 0;j--){
                ans.push_back(ans[j]+(1<<i));
            }
         
        }
        return ans;
    }
};