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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,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 grayCode(int n) { vector result(1, 0); for(int i = 0; i < n; i++) { int high = 1< =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 grayCode(int n) { int len = 1 << n; vector 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