Add a gray_code_sequence.py file to the bit_manipulation folder (#5038)

* Added a gray_code_sequence.py file to the bit_manipulation folder

* Added a descriptive name for variable n changing it to bit count

* Update gray_code_sequence.py

Co-authored-by: krishchopra02 <krishchopra02@gmail.com>
Co-authored-by: John Law <johnlaw.po@gmail.com>

bit_manipulation/gray_code_sequence.py

@@ -0,0 +1,94 @@
+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
+
+    # 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
+    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()