



def    _lowerCAmelCase  (	):


    '''simple docstring'''


    return [list(range(1000 - i						,		-1000 - i						,		-1						)						) for i in range(1000						)]


__magic_name__  	=    generate_large_matrix()
__magic_name__  	=    (
    [[4, 3, 2, -1], [3, 2, 1, -1], [1, 1, -1, -2], [-1, -1, -2, -3]],
    [[3, 2], [1, 0]],
    [[7, 7, 6]],
    [[7, 7, 6], [-1, -2, -3]],
    grid,
)




def    _lowerCAmelCase  (	A__:      list[list[int]]						):


    '''simple docstring'''


    assert all(row == sorted(__UpperCAmelCase						,		reverse=__UpperCAmelCase						) for row in grid						)
    assert all(list(__UpperCAmelCase						) == sorted(__UpperCAmelCase						,		reverse=__UpperCAmelCase						) for col in zip(*__UpperCAmelCase						)						)




def    _lowerCAmelCase  (	A__:      list[int]						):


    '''simple docstring'''


    UpperCAmelCase      =       0
    UpperCAmelCase      =       len(__UpperCAmelCase						) - 1

    # Edge cases such as no values or all numbers are negative.
    if not array or array[0] < 0:
        return 0

    while right + 1 > left:
        UpperCAmelCase      =       (left + right) // 2
        UpperCAmelCase      =       array[mid]

        # Num must be negative and the index must be greater than or equal to 0.
        if num < 0 and array[mid - 1] >= 0:
            return mid

        if num >= 0:
            UpperCAmelCase      =       mid + 1
        else:
            UpperCAmelCase      =       mid - 1
    # No negative numbers so return the last index of the array + 1 which is the length.
    return len(__UpperCAmelCase						)




def    _lowerCAmelCase  (	A__:      list[list[int]]						):


    '''simple docstring'''


    UpperCAmelCase      =       0
    UpperCAmelCase      =       len(grid[0]						)

    for i in range(len(__UpperCAmelCase						)						):
        UpperCAmelCase      =       find_negative_index(grid[i][:bound]						)
        total += bound
    return (len(__UpperCAmelCase						) * len(grid[0]						)) - total




def    _lowerCAmelCase  (	A__:      list[list[int]]						):


    '''simple docstring'''


    return len([number for row in grid for number in row if number < 0]						)




def    _lowerCAmelCase  (	A__:      list[list[int]]						):


    '''simple docstring'''


    UpperCAmelCase      =       0
    for row in grid:
        for i, number in enumerate(__UpperCAmelCase						):
            if number < 0:
                total += len(__UpperCAmelCase						) - i
                break
    return total




def    _lowerCAmelCase  (	):


    '''simple docstring'''


    from timeit import timeit

    print('''Running benchmarks'''						)
    UpperCAmelCase      =       (
        """from __main__ import count_negatives_binary_search, """
        """count_negatives_brute_force, count_negatives_brute_force_with_break, grid"""
    )
    for func in (
        "count_negatives_binary_search",  # took 0.7727 seconds
        "count_negatives_brute_force_with_break",  # took 4.6505 seconds
        "count_negatives_brute_force",  # took 12.8160 seconds
    ):
        UpperCAmelCase      =       timeit(F"""{func}(grid=grid)"""						,		setup=__UpperCAmelCase						,		number=500						)
        print(F"""{func}() took {time:0.4f} seconds"""						)


if __name__ == "__main__":
    import doctest

    doctest.testmod()
    benchmark()












"""simple docstring"""





from random import randint
from tempfile import TemporaryFile

import numpy as np



def   a    (     __UpperCAmelCase      :    Optional[Any]      ,   __UpperCAmelCase      :    Optional[int]      ,   __UpperCAmelCase      :    Optional[int]  )    ->							int:
						__magic_name__:	Optional[int]							=       0
						if start < end:
												__magic_name__:	Union[str, Any]							=       randint(__UpperCAmelCase      ,   __UpperCAmelCase  )
												__magic_name__:	int							=       a[end]
												__magic_name__:	Optional[int]							=       a[pivot]
												__magic_name__:	Tuple							=       temp

												__magic_name__,			__magic_name__:	int							=       _in_place_partition(__UpperCAmelCase      ,   __UpperCAmelCase      ,   __UpperCAmelCase  )
												count += _in_place_quick_sort(__UpperCAmelCase      ,   __UpperCAmelCase      ,   p - 1  )
												count += _in_place_quick_sort(__UpperCAmelCase      ,   p + 1      ,   __UpperCAmelCase  )
						return count



def   a    (     __UpperCAmelCase      :    Optional[Any]      ,   __UpperCAmelCase      :    str      ,   __UpperCAmelCase      :    List[Any]  )    ->							Union[str, Any]:
						__magic_name__:	Union[str, Any]							=       0
						__magic_name__:	str							=       randint(__UpperCAmelCase      ,   __UpperCAmelCase  )
						__magic_name__:	Optional[int]							=       a[end]
						__magic_name__:	Optional[int]							=       a[pivot]
						__magic_name__:	Optional[int]							=       temp
						__magic_name__:	Dict							=       start - 1
						for index in range(__UpperCAmelCase      ,   __UpperCAmelCase  ):
												count += 1
												if a[index] < a[end]:  # check if current val is less than pivot value
																		__magic_name__:	List[Any]							=       new_pivot_index + 1
																		__magic_name__:	Any							=       a[new_pivot_index]
																		__magic_name__:	int							=       a[index]
																		__magic_name__:	Union[str, Any]							=       temp

						__magic_name__:	List[Any]							=       a[new_pivot_index + 1]
						__magic_name__:	Union[str, Any]							=       a[end]
						__magic_name__:	Dict							=       temp
						return new_pivot_index + 1, count


__lowerCamelCase							=  TemporaryFile()
__lowerCamelCase							=  1_00  # 1000 elements are to be sorted


__lowerCamelCase		,					__lowerCamelCase							=  0, 1  # mean and standard deviation
__lowerCamelCase							=  np.random.normal(mu, sigma, p)
np.save(outfile, X)
print('The array is')
print(X)


outfile.seek(0)  # using the same array
__lowerCamelCase							=  np.load(outfile)
__lowerCamelCase							=  len(M) - 1
__lowerCamelCase							=  _in_place_quick_sort(M, 0, r)

print(
    'No of Comparisons for 100 elements selected from a standard normal distribution'
    'is :'
)

print(z)



