

from __future__ import annotations

from typing import TypedDict






class 						__magic_name__					(							snake_case				):
     UpperCamelCase_	:str
     UpperCamelCase_	:int




def 			lowerCAmelCase(      SCREAMING_SNAKE_CASE_			)->						list[str]:



    """simple docstring"""






    if not isinstance(SCREAMING_SNAKE_CASE_			,						SCREAMING_SNAKE_CASE_			):
        raise TypeError("The parameter s type must be str."			)

    return [s[i:] + s[:i] for i in range(len(SCREAMING_SNAKE_CASE_			)			)]




def 			lowerCAmelCase(      SCREAMING_SNAKE_CASE_			)->						BWTTransformDict:



    """simple docstring"""






    if not isinstance(SCREAMING_SNAKE_CASE_			,						SCREAMING_SNAKE_CASE_			):
        raise TypeError("The parameter s type must be str."			)
    if not s:
        raise ValueError("The parameter s must not be empty."			)

    UpperCamelCase_			  =						all_rotations(SCREAMING_SNAKE_CASE_			)
    rotations.sort()  # sort the list of rotations in alphabetically order
    # make a string composed of the last char of each rotation
    UpperCamelCase_			  =						{
        "bwt_string": "".join([word[-1] for word in rotations]			),
        "idx_original_string": rotations.index(SCREAMING_SNAKE_CASE_			),
    }
    return response




def 			lowerCAmelCase(      SCREAMING_SNAKE_CASE_			,						SCREAMING_SNAKE_CASE_			)->						str:



    """simple docstring"""






    if not isinstance(SCREAMING_SNAKE_CASE_			,						SCREAMING_SNAKE_CASE_			):
        raise TypeError("The parameter bwt_string type must be str."			)
    if not bwt_string:
        raise ValueError("The parameter bwt_string must not be empty."			)
    try:
        UpperCamelCase_			  =						int(SCREAMING_SNAKE_CASE_			)
    except ValueError:
        raise TypeError(
            "The parameter idx_original_string type must be int or passive"
            " of cast to int."			)
    if idx_original_string < 0:
        raise ValueError("The parameter idx_original_string must not be lower than 0."			)
    if idx_original_string >= len(SCREAMING_SNAKE_CASE_			):
        raise ValueError(
            "The parameter idx_original_string must be lower than" " len(bwt_string)."			)

    UpperCamelCase_			  =						[""] * len(SCREAMING_SNAKE_CASE_			)
    for _ in range(len(SCREAMING_SNAKE_CASE_			)			):
        for i in range(len(SCREAMING_SNAKE_CASE_			)			):
            UpperCamelCase_			  =						bwt_string[i] + ordered_rotations[i]
        ordered_rotations.sort()
    return ordered_rotations[idx_original_string]


if __name__ == "__main__":
 SCREAMING_SNAKE_CASE		:str						=     """Provide a string that I will generate its BWT transform: """
 SCREAMING_SNAKE_CASE		:Tuple						=     input(entry_msg).strip()
 SCREAMING_SNAKE_CASE		:List[Any]						=     bwt_transform(s)
 print(
     F'''Burrows Wheeler transform for string \'{s}\' results '''
     F'''in \'{result['bwt_string']}\''''
 )
 SCREAMING_SNAKE_CASE		:Dict						=     reverse_bwt(result["""bwt_string"""], result["""idx_original_string"""])
 print(
     F'''Reversing Burrows Wheeler transform for entry \'{result['bwt_string']}\' '''
     F'''we get original string \'{original_string}\''''
 )



def 			lowerCAmelCase(      SCREAMING_SNAKE_CASE_			)->						list:



    """simple docstring"""






    if bit_count < 0:
        raise ValueError("The given input must be positive"			)

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

    return sequence




def 			lowerCAmelCase(      SCREAMING_SNAKE_CASE_			)->						list:



    """simple docstring"""






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

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

    UpperCamelCase_			  =						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
    UpperCamelCase_			  =						gray_code_sequence_string(bit_count - 1			)

    UpperCamelCase_			  =						[]

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

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

    return sequence


if __name__ == "__main__":
 import doctest

 doctest.testmod()
