算法分析與設計課程（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：

我們先看幾個不同位數的格雷碼：

1）n=1時，序列爲：0、1

2）n=2時，序列爲：00、01、11、10

這裏我們可以考慮：異或轉換

二進制碼→格雷碼（編碼）：

此方法從對應的n位二進制碼字中直接得到n位格雷碼碼字，步驟如下：

1. 對n位二進制的碼字，從右到左，以0到n-1編號
2. 如果二進制碼字的第i位和i+1位相同，則對應的格雷碼的第i位爲0，否則爲1（當i+1=n時，二進制碼字的第n位被認爲是0，即第n-1位不變）[5]

代碼如下：

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