Leetcode 89: Gray Code

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 - 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.

 

Code

class Solution(object):
    def grayCode(self, n):
        """
        :type n: int
        :rtype: List[int]
        """
        if n<0:
            return []
        
        res = [0]
        for i in xrange(n):
            for j in xrange(len(res)-1, -1, -1):
                res.append(res[j] + (1 << i))
        return res

 

Idea

Say we have already had the gray codes for n. Then, the gray codes for n+1 are constituted from:

1. ‘0’ followed by the gray codes for n
2. ‘1’ followed by the gray codes for n in the reversed order