## DEV Community

Abhishek Chaudhary

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# Gray Code

An n-bit gray code sequence is a sequence of `2n` integers where:

• Every integer is in the inclusive range `[0, 2n - 1]`,
• The first integer is `0`,
• An integer appears no more than once in the sequence,
• The binary representation of every pair of adjacent integers differs by exactly one bit, and
• The binary representation of the first and last integers differs by exactly one bit.

Given an integer `n`, return any valid n-bit gray code sequence.

Example 1:

Input: n = 2
Output: [0,1,3,2]
Explanation:
The binary representation of [0,1,3,2] is [00,01,11,10].

• 00 and 01 differ by one bit
• 01 and 11 differ by one bit
• 11 and 10 differ by one bit
• 10 and 00 differ by one bit [0,2,3,1] is also a valid gray code sequence, whose binary representation is [00,10,11,01].
• 00 and 10 differ by one bit
• 10 and 11 differ by one bit
• 11 and 01 differ by one bit
• 01 and 00 differ by one bit

Example 2:

Input: n = 1
Output: [0,1]

Constraints:

• `1 <= n <= 16`

SOLUTION:

``````class Solution:
def grayCode(self, n: int) -> List[int]:
if n == 1:
return [0, 1]
prev = self.grayCode(n - 1)
k = 1 << (n - 1)
return prev + [prev[i] + k for i in range(k - 1, -1, -1)]
``````