算法分析与设计课程（11）：【leetcode】Gray Code

Description:

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.

算法分析：

我们先看几个不同位数的格雷码：

1）n=1时，序列为：0、1

2）n=2时，序列为：00、01、11、10

这里我们可以考虑：异或转换

二进制码→格雷码（编码）： 此方法从对应的n位二进制码字中直接得到n位格雷码码字，步骤如下： 对n位二进制的码字，从右到左，以0到n-1编号 如果二进制码字的第i位和i+1位相同，则对应的格雷码的第i位为0，否则为1（当i+1=n时，二进制码字的第n位被认为是0，即第n-1位不变）[5] 代码如下： class Solution: # @param {int} n a number # @return {int[]} Gray code def grayCode(self, n): if n == 0: return [0] result = self.grayCode(n - 1) seq = list(result) for i in reversed(result): seq.append((1 << (n - 1)) | i) return seq