





"""simple docstring"""
from __future__ import annotations

import math
from collections import Counter
from string import ascii_lowercase

def 		_SCREAMING_SNAKE_CASE			(_UpperCAmelCase					:    str			):
 lowerCAmelCase				,lowerCAmelCase    				= analyze_text(_UpperCAmelCase			)
 lowerCAmelCase    				= list(' ' + ascii_lowercase			)
 # what is our total sum of probabilities.
 lowerCAmelCase    				= sum(single_char_strings.values()			)

 # one length string
 lowerCAmelCase    				= 0
 # for each alpha we go in our dict and if it is in it we calculate entropy
 for ch in my_alphas:
  if ch in single_char_strings:
   lowerCAmelCase    				= single_char_strings[ch]
   lowerCAmelCase    				= my_str / all_sum
   my_fir_sum += prob * math.loga(_UpperCAmelCase			)  # entropy formula.

    # print entropy
 print(F'{round(-1 * my_fir_sum			):.1f}'			)

 # two len string
 lowerCAmelCase    				= sum(two_char_strings.values()			)
 lowerCAmelCase    				= 0
 # for each alpha (two in size) calculate entropy.
 for cha in my_alphas:
  for cha in my_alphas:
   lowerCAmelCase    				= cha + cha
   if sequence in two_char_strings:
    lowerCAmelCase    				= two_char_strings[sequence]
    lowerCAmelCase    				= int(_UpperCAmelCase			) / all_sum
    my_sec_sum += prob * math.loga(_UpperCAmelCase			)

    # print second entropy
 print(F'{round(-1 * my_sec_sum			):.1f}'			)

 # print the difference between them
 print(F'{round((-1 * my_sec_sum) - (-1 * my_fir_sum)			):.1f}'			)

def 		_SCREAMING_SNAKE_CASE			(_UpperCAmelCase					:    str			):
 lowerCAmelCase    				= Counter()  # type: ignore
 lowerCAmelCase    				= Counter()  # type: ignore
 single_char_strings[text[-1]] += 1

 # first case when we have space at start.
 two_char_strings[" " + text[0]] += 1
 for i in range(0  ,     len(_UpperCAmelCase			) - 1			):
  single_char_strings[text[i]] += 1
  two_char_strings[text[i : i + 2]] += 1
 return single_char_strings, two_char_strings

def 		_SCREAMING_SNAKE_CASE			():
 import doctest

 doctest.testmod()
 # text = (
 #     "Had repulsive dashwoods suspicion sincerity but advantage now him. Remark "
 #     "easily garret nor nay. Civil those mrs enjoy shy fat merry. You greatest "
 #     "jointure saw horrible. He private he on be imagine suppose. Fertile "
 #     "beloved evident through no service elderly is. Blind there if every no so "
 #     "at. Own neglected you preferred way sincerity delivered his attempted. To "
 #     "of message cottage windows do besides against uncivil.  Delightful "
 #     "unreserved impossible few estimating men favourable see entreaties. She "
 #     "propriety immediate was improving. He or entrance humoured likewise "
 #     "moderate. Much nor game son say feel. Fat make met can must form into "
 #     "gate. Me we offending prevailed discovery. "
 # )

 # calculate_prob(text)


if __name__ == "__main__":
       main()










'''simple docstring'''





def 							lowerCamelCase	(					):





    '''simple docstring'''


    return [list(range(1_000 - i  ,-1_000 - i  ,-1							)							) for i in range(1_000							)]


SCREAMING_SNAKE_CASE__          =  generate_large_matrix()
SCREAMING_SNAKE_CASE__          =  (
    [[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	(					_snake_case	:    list[list[int]]							):





    '''simple docstring'''


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




def 							lowerCamelCase	(					_snake_case	:    list[int]							):





    '''simple docstring'''


    lowercase__									=    0
    lowercase__									=    len(_snake_case							) - 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:
        lowercase__									=    (left + right) // 2
        lowercase__									=    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:
            lowercase__									=    mid + 1
        else:
            lowercase__									=    mid - 1
    # No negative numbers so return the last index of the array + 1 which is the length.
    return len(_snake_case							)




def 							lowerCamelCase	(					_snake_case	:    list[list[int]]							):





    '''simple docstring'''


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

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




def 							lowerCamelCase	(					_snake_case	:    list[list[int]]							):





    '''simple docstring'''


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




def 							lowerCamelCase	(					_snake_case	:    list[list[int]]							):





    '''simple docstring'''


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




def 							lowerCamelCase	(					):





    '''simple docstring'''


    from timeit import timeit

    print("Running benchmarks"							)
    lowercase__									=    (
        "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
    ):
        lowercase__									=    timeit(f'''{func}(grid=grid)'''  ,setup=_snake_case  ,number=500							)
        print(f'''{func}() took {time:0.4f} seconds'''							)


if __name__ == "__main__":
 import doctest

 doctest.testmod()
 benchmark()




