#### Gray Code Sequence

K
```def gray_code(bit_count: int) -> list:
"""
Takes in an integer n and returns a n-bit
gray code sequence
An n-bit gray code sequence is a sequence of 2^n
integers where:

a) Every integer is between [0,2^n -1] inclusive
b) The sequence begins with 0
c) An integer appears at most one times in the sequence
d)The binary representation of every pair of integers differ
by exactly one bit
e) The binary representation of first and last bit also
differ by exactly one bit

>>> gray_code(2)
[0, 1, 3, 2]

>>> gray_code(1)
[0, 1]

>>> gray_code(3)
[0, 1, 3, 2, 6, 7, 5, 4]

>>> gray_code(-1)
Traceback (most recent call last):
...
ValueError: The given input must be positive

>>> gray_code(10.6)
Traceback (most recent call last):
...
TypeError: unsupported operand type(s) for <<: 'int' and 'float'
"""

# bit count represents no. of bits in the gray code
if bit_count < 0:
raise ValueError("The given input must be positive")

# get the generated string sequence
sequence = gray_code_sequence_string(bit_count)
#
# convert them to integers
for i in range(len(sequence)):
sequence[i] = int(sequence[i], 2)

return sequence

def gray_code_sequence_string(bit_count: int) -> list:
"""
Will output the n-bit grey sequence as a
string of bits

>>> gray_code_sequence_string(2)
['00', '01', '11', '10']

>>> gray_code_sequence_string(1)
['0', '1']
"""

# The approach is a recursive one
# Base case achieved when either n = 0 or n=1
if bit_count == 0:
return ["0"]

if bit_count == 1:
return ["0", "1"]

seq_len = 1 << bit_count  # defines the length of the sequence
# 1<< n is equivalent to 2^n

smaller_sequence = gray_code_sequence_string(bit_count - 1)

sequence = []

# append 0 to first half of the smaller sequence generated
for i in range(seq_len // 2):
generated_no = "0" + smaller_sequence[i]
sequence.append(generated_no)

# append 1 to second half ... start from the end of the list
for i in reversed(range(seq_len // 2)):
generated_no = "1" + smaller_sequence[i]
sequence.append(generated_no)

return sequence

if __name__ == "__main__":
import doctest

doctest.testmod()
```  