
from __future__ import annotations

import math
from collections import Counter
from string import ascii_lowercase


def 						UpperCAmelCase      (     a_						)		->     None:







				"""simple docstring"""



				__A      ,							__A             =			analyze_text(a_						)
				__A             =			list(" " + ascii_lowercase						)
				# what is our total sum of probabilities.
				__A             =			sum(single_char_strings.values()						)

				# one length string
				__A             =			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:
												__A             =			single_char_strings[ch]
												__A             =			my_str / all_sum
												my_fir_sum += prob * math.loga(a_						)  # entropy formula.

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

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

    # 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 						UpperCAmelCase      (     a_						)		->     tuple[dict, dict]:







				"""simple docstring"""



				__A             =			Counter()  # type: ignore
				__A             =			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(a_						) - 1						):
								single_char_strings[text[i]] += 1
								two_char_strings[text[i : i + 2]] += 1
				return single_char_strings, two_char_strings


def 						UpperCAmelCase      (     )		->     Optional[Any]:







				"""simple docstring"""



				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()


def 						UpperCAmelCase      (     )		->     list[list[int]]:







				"""simple docstring"""



				return [list(range(1_0_0_0 - i		,       -1_0_0_0 - i		,       -1						)						) for i in range(1_0_0_0						)]


SCREAMING_SNAKE_CASE							:List[str]										=    generate_large_matrix()
SCREAMING_SNAKE_CASE							:str										=    (
    [[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 						UpperCAmelCase      (     a_						)		->     None:







				"""simple docstring"""



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


def 						UpperCAmelCase      (     a_						)		->     int:







				"""simple docstring"""



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


def 						UpperCAmelCase      (     a_						)		->     int:







				"""simple docstring"""



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

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


def 						UpperCAmelCase      (     a_						)		->     int:







				"""simple docstring"""



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


def 						UpperCAmelCase      (     a_						)		->     int:







				"""simple docstring"""



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


def 						UpperCAmelCase      (     )		->     None:







				"""simple docstring"""



				from timeit import timeit

				print("Running benchmarks"						)
				__A             =			(
				    "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
				):
								__A             =			timeit(F'''{func}(grid=grid)'''		,       setup=a_		,       number=5_0_0						)
								print(F'''{func}() took {time:0.4f} seconds'''						)


if __name__ == "__main__":
					import doctest

					doctest.testmod()
					benchmark()
