[leetcode] 89. Gray Code 解题报告

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题目链接：https://leetcode.com/problems/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 - 001 - 111 - 310 - 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.

思路：利用模拟法来产生格雷码的时候有一个镜面定理，即当所有三位的格雷码可以由所有二位格雷码＋将二位所有格雷码从从最后一个到第一个依次最左边加１构成．例如二位的格雷码依次是00, 01, 11, 10．而三位的格雷码就是继承二位的格雷码＋逆序二位格雷码并在左边加１：110, 111, 101, 100．这样我们就可以得到所有的３位格雷为00, 01, 11, 10, 110, 111, 101, 100.

代码如下：

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

而实际上还有一种数学的方法来解决，不过并不是很推荐，因为面试不是考察你的数学，而是编程思维．

class Solution {public:    vector<int> grayCode(int n) {        int len = 1 << n;        vector<int> result;        for(int i = 0; i < len; i++)            result.push_back(i ^ (i>>1));        return result;    }};

参考：http://fisherlei.blogspot.com/2012/12/leetcode-gray-code.html

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