# Question

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.

# Solution

A valid gray code sequence of length `n`

can be generated by prepending `0`

to the gray code sequence of length `n - 1`

in order, followed by prepending `1`

to the gray code sequence of length `n - 1`

in reverse order.

```
class Solution:
def grayCode(self, n):
"""
:type n: int
:rtype: List[int]
"""
if n == 0:
return [0]
elif n == 1:
return[0, 1]
else:
results = self.grayCode(n - 1)
length = len(results)
leading_bit = 2 ** (n - 1)
for i in range(length - 1, -1, -1):
results.append(leading_bit + results[i])
return results
```