89. Gray Code.py

"""
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.

Example 1:

Input: 2
Output: [0,1,3,2]
Explanation:
00 - 0
01 - 1
11 - 3
10 - 2

For a given n, a gray code sequence may not be uniquely defined.
For example, [0,2,3,1] is also a valid gray code sequence.

00 - 0
10 - 2
11 - 3
01 - 1
Example 2:

Input: 0
Output: [0]
Explanation: We define the gray code sequence to begin with 0.
             A gray code sequence of n has size = 2n, which for n = 0 the size is 20 = 1.
             Therefore, for n = 0 the gray code sequence is [0].
"""
class Solution:
    def grayCode(self, n: int) -> List[int]:
        result = []
        def backtrack(n,path):
            if n == 0:
                result.append(int(''.join(path),2))
                return
            backtrack(n-1,path+['0'])
            backtrack(n-1,path+['1'])
        backtrack(n,[])
        return result

# This solution doesn't preserve the condition : two successive values differ in only one bit. but it is a backtracking solution.