
from __future__ import annotations





def        lowerCAmelCase       (				snake_case__   :      list[int] )->			Tuple:
    if not list_of_ints:
        return []

    if min(_SCREAMING_SNAKE_CASE ) < 0:
        raise ValueError("All numbers must be positive" )

    A_								=					max(len(bin(_SCREAMING_SNAKE_CASE )[2:] ) for x in list_of_ints )
    return _msd_radix_sort(_SCREAMING_SNAKE_CASE				,					_SCREAMING_SNAKE_CASE )





def        lowerCAmelCase       (				snake_case__   :      list[int]				,					snake_case__   :      int )->			str:
    if bit_position == 0 or len(_SCREAMING_SNAKE_CASE ) in [0, 1]:
        return list_of_ints

    A_								=					[]
    A_								=					[]
    # Split numbers based on bit at bit_position from the right
    for number in list_of_ints:
        if (number >> (bit_position - 1)) & 1:
            # number has a one at bit bit_position
            ones.append(_SCREAMING_SNAKE_CASE )
        else:
            # number has a zero at bit bit_position
            zeros.append(_SCREAMING_SNAKE_CASE )

    # recursively split both lists further
    A_								=					_msd_radix_sort(_SCREAMING_SNAKE_CASE				,					bit_position - 1 )
    A_								=					_msd_radix_sort(_SCREAMING_SNAKE_CASE				,					bit_position - 1 )

    # recombine lists
    A_								=					zeros
    res.extend(_SCREAMING_SNAKE_CASE )

    return res





def        lowerCAmelCase       (				snake_case__   :      list[int] )->			Union[str, Any]:
    A_								=					len(_SCREAMING_SNAKE_CASE )
    if not list_of_ints or length == 1:
        return

    if min(_SCREAMING_SNAKE_CASE ) < 0:
        raise ValueError("All numbers must be positive" )

    A_								=					max(len(bin(_SCREAMING_SNAKE_CASE )[2:] ) for x in list_of_ints )
    _msd_radix_sort_inplace(_SCREAMING_SNAKE_CASE				,					_SCREAMING_SNAKE_CASE				,					0				,					_SCREAMING_SNAKE_CASE )





def        lowerCAmelCase       (				snake_case__   :      list[int]				,					snake_case__   :      int				,					snake_case__   :      int				,					snake_case__   :      int )->			Any:
    if bit_position == 0 or end_index - begin_index <= 1:
        return

    bit_position -= 1

    A_								=					begin_index
    A_								=					end_index - 1
    while i <= j:
        A_								=					False
        if not (list_of_ints[i] >> bit_position) & 1:
            # found zero at the beginning
            i += 1
            A_								=					True
        if (list_of_ints[j] >> bit_position) & 1:
            # found one at the end
            j -= 1
            A_								=					True

        if changed:
            continue

        A_	,	A_								=					list_of_ints[j], list_of_ints[i]
        j -= 1
        if j != i:
            i += 1

    _msd_radix_sort_inplace(_SCREAMING_SNAKE_CASE				,					_SCREAMING_SNAKE_CASE				,					_SCREAMING_SNAKE_CASE				,					_SCREAMING_SNAKE_CASE )
    _msd_radix_sort_inplace(_SCREAMING_SNAKE_CASE				,					_SCREAMING_SNAKE_CASE				,					_SCREAMING_SNAKE_CASE				,					_SCREAMING_SNAKE_CASE )


if __name__ == "__main__":
     import doctest

     doctest.testmod()








'''simple docstring'''







import logging

# standard libraries
import sys

import numpy as np
import pytest  # type: ignore

# Custom/local libraries
from matrix import matrix_operation as matop

_snake_case					: List[str]     			=					[[12, 10], [3, 9]]
_snake_case					: Any     			=					[[3, 4], [7, 4]]
_snake_case					: List[str]     			=					[[3, 0, 2], [2, 0, -2], [0, 1, 1]]
_snake_case					: Any     			=					[[3, 0, -2], [2, 0, 2], [0, 1, 1]]
_snake_case					: Any     			=					[[3, 0, 2], [2, 0, -2], [0, 1, 1], [2, 0, -2]]
_snake_case					: Optional[Any]     			=					[1]
_snake_case					: str     			=					[2]

_snake_case					: Optional[int]     			=					logging.getLogger()
_snake_case					: Optional[Any]     			=					logging.DEBUG
_snake_case					: Tuple     			=					logging.StreamHandler(sys.stdout)
logger.addHandler(stream_handler)



@pytest.mark.mat_ops
@pytest.mark.parametrize(
    ("mat1", "mat2")						,      [(mat_a, mat_b), (mat_c, mat_d), (mat_d, mat_e), (mat_f, mat_h)]	)
def       _a		(						_SCREAMING_SNAKE_CASE		: List[Any]						,      _SCREAMING_SNAKE_CASE		: Tuple	):
						if (np.array(_SCREAMING_SNAKE_CASE	)).shape < (2, 2) or (np.array(_SCREAMING_SNAKE_CASE	)).shape < (2, 2):
												with pytest.raises(_SCREAMING_SNAKE_CASE	):
																		logger.info(F'\n\t{test_addition.__name__} returned integer'	)
																		matop.add(_SCREAMING_SNAKE_CASE						,      _SCREAMING_SNAKE_CASE	)
						elif (np.array(_SCREAMING_SNAKE_CASE	)).shape == (np.array(_SCREAMING_SNAKE_CASE	)).shape:
												logger.info(F'\n\t{test_addition.__name__} with same matrix dims'	)
												_SCREAMING_SNAKE_CASE					=			(np.array(_SCREAMING_SNAKE_CASE	) + np.array(_SCREAMING_SNAKE_CASE	)).tolist()
												_SCREAMING_SNAKE_CASE					=			matop.add(_SCREAMING_SNAKE_CASE						,      _SCREAMING_SNAKE_CASE	)
												assert theo == act
						else:
												with pytest.raises(_SCREAMING_SNAKE_CASE	):
																		logger.info(F'\n\t{test_addition.__name__} with different matrix dims'	)
																		matop.add(_SCREAMING_SNAKE_CASE						,      _SCREAMING_SNAKE_CASE	)



@pytest.mark.mat_ops
@pytest.mark.parametrize(
    ("mat1", "mat2")						,      [(mat_a, mat_b), (mat_c, mat_d), (mat_d, mat_e), (mat_f, mat_h)]	)
def       _a		(						_SCREAMING_SNAKE_CASE		: Optional[Any]						,      _SCREAMING_SNAKE_CASE		: List[str]	):
						if (np.array(_SCREAMING_SNAKE_CASE	)).shape < (2, 2) or (np.array(_SCREAMING_SNAKE_CASE	)).shape < (2, 2):
												with pytest.raises(_SCREAMING_SNAKE_CASE	):
																		logger.info(F'\n\t{test_subtraction.__name__} returned integer'	)
																		matop.subtract(_SCREAMING_SNAKE_CASE						,      _SCREAMING_SNAKE_CASE	)
						elif (np.array(_SCREAMING_SNAKE_CASE	)).shape == (np.array(_SCREAMING_SNAKE_CASE	)).shape:
												logger.info(F'\n\t{test_subtraction.__name__} with same matrix dims'	)
												_SCREAMING_SNAKE_CASE					=			(np.array(_SCREAMING_SNAKE_CASE	) - np.array(_SCREAMING_SNAKE_CASE	)).tolist()
												_SCREAMING_SNAKE_CASE					=			matop.subtract(_SCREAMING_SNAKE_CASE						,      _SCREAMING_SNAKE_CASE	)
												assert theo == act
						else:
												with pytest.raises(_SCREAMING_SNAKE_CASE	):
																		logger.info(F'\n\t{test_subtraction.__name__} with different matrix dims'	)
																		assert matop.subtract(_SCREAMING_SNAKE_CASE						,      _SCREAMING_SNAKE_CASE	)



@pytest.mark.mat_ops
@pytest.mark.parametrize(
    ("mat1", "mat2")						,      [(mat_a, mat_b), (mat_c, mat_d), (mat_d, mat_e), (mat_f, mat_h)]	)
def       _a		(						_SCREAMING_SNAKE_CASE		: Any						,      _SCREAMING_SNAKE_CASE		: List[str]	):
						if (np.array(_SCREAMING_SNAKE_CASE	)).shape < (2, 2) or (np.array(_SCREAMING_SNAKE_CASE	)).shape < (2, 2):
												logger.info(F'\n\t{test_multiplication.__name__} returned integer'	)
												with pytest.raises(_SCREAMING_SNAKE_CASE	):
																		matop.add(_SCREAMING_SNAKE_CASE						,      _SCREAMING_SNAKE_CASE	)
						elif (np.array(_SCREAMING_SNAKE_CASE	)).shape == (np.array(_SCREAMING_SNAKE_CASE	)).shape:
												logger.info(F'\n\t{test_multiplication.__name__} meets dim requirements'	)
												_SCREAMING_SNAKE_CASE					=			(np.matmul(_SCREAMING_SNAKE_CASE						,      _SCREAMING_SNAKE_CASE	)).tolist()
												_SCREAMING_SNAKE_CASE					=			matop.multiply(_SCREAMING_SNAKE_CASE						,      _SCREAMING_SNAKE_CASE	)
												assert theo == act
						else:
												with pytest.raises(_SCREAMING_SNAKE_CASE	):
																		logger.info(
																		    F'\n\t{test_multiplication.__name__} does not meet dim requirements'	)
																		assert matop.subtract(_SCREAMING_SNAKE_CASE						,      _SCREAMING_SNAKE_CASE	)



@pytest.mark.mat_ops
def       _a		(						):
						_SCREAMING_SNAKE_CASE					=			(3.5 * np.array(_SCREAMING_SNAKE_CASE	)).tolist()
						_SCREAMING_SNAKE_CASE					=			matop.scalar_multiply(_SCREAMING_SNAKE_CASE						,      3.5	)
						assert theo == act



@pytest.mark.mat_ops
def       _a		(						):
						_SCREAMING_SNAKE_CASE					=			(np.identity(5	)).tolist()
						_SCREAMING_SNAKE_CASE					=			matop.identity(5	)
						assert theo == act




@pytest.mark.mat_ops
@pytest.mark.parametrize("mat"						,      [mat_a, mat_b, mat_c, mat_d, mat_e, mat_f]	)
def       _a		(						_SCREAMING_SNAKE_CASE		: Tuple	):
						if (np.array(_SCREAMING_SNAKE_CASE	)).shape < (2, 2):
												with pytest.raises(_SCREAMING_SNAKE_CASE	):
																		logger.info(F'\n\t{test_transpose.__name__} returned integer'	)
																		matop.transpose(_SCREAMING_SNAKE_CASE	)
						else:
												_SCREAMING_SNAKE_CASE					=			(np.transpose(_SCREAMING_SNAKE_CASE	)).tolist()
												_SCREAMING_SNAKE_CASE					=			matop.transpose(_SCREAMING_SNAKE_CASE						,      return_map=_SCREAMING_SNAKE_CASE	)
												assert theo == act