gray_code_sequence.py

defgray_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
ifbit_count<0:
raiseValueError("The given input must be positive")

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

returnsequence


defgray_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
ifbit_count==0:
return ["0"]

ifbit_count==1:
return ["0", "1"]

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

# recursive answer will generate answer for n-1 bits
smaller_sequence=gray_code_sequence_string(bit_count-1)

sequence= []

# append 0 to first half of the smaller sequence generated
foriinrange(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
foriinreversed(range(seq_len//2)):
generated_no="1"+smaller_sequence[i]
sequence.append(generated_no)

returnsequence


if__name__=="__main__":
importdoctest

doctest.testmod()