[Leetcode Series] [algorithm] [medium] Gray code

topic:

Topic links:  https://leetcode-cn.com/problems/gray-code/

 

Problem-solving ideas:

N + 1 of Gray coded order, in fact, can be divided into the following two parts:

1. N Gray-coded order, preceded by a 0
2. Gray coded order n, in reverse order, preceded by a 1

Illustrated as follows:

n = 0	n = 1	n = 2	n = 3	n = 4
0	0	0 0	0 00	...
	1	0 1	0 01	...
		1 1	0 11	...
		1 0	0 10	...
			1 10	...
			1 11	...
			1 01	...
			1 00	...

 

Therefore, according to Gray coding 0-order, it can be introduced at any stage of the Gray code

 

Code:

class Solution:
    def grayCode(self, n: int) -> List[int]:
        res, head = [0], 1
        for i in range(n):
            for j in range(len(res) - 1, -1, -1):
                res.append(head + res[j])
                
            head <<= 1
        
        return res