



'''simple docstring'''


from __future__ import annotations

import math
from collections import Counter
from string import ascii_lowercase







def      SCREAMING_SNAKE_CASE				(				lowercase_    :      List[str]						):
						lowercase     ,   lowercase        =							analyze_text(_snake_case						)
						lowercase        =							list(""" """ + ascii_lowercase						)
						# what is our total sum of probabilities.
						lowercase        =							sum(single_char_strings.values()						)

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

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

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

    # 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				(				lowercase_    :      Tuple						):
						lowercase        =							Counter()  # type: ignore
						lowercase        =							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(_snake_case						) - 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      SCREAMING_SNAKE_CASE				(				lowercase_    :      int ,  lowercase_    :      int ,  lowercase_    :      list[list[int]]						):

						def update_area_of_max_square(lowercase_    :      int ,  lowercase_    :      int						) -> int:
												# BASE CASE
												if row >= rows or col >= cols:
																		return 0

												lowercase        =							update_area_of_max_square(lowercase_ ,  col + 1						)
												lowercase        =							update_area_of_max_square(row + 1 ,  col + 1						)
												lowercase        =							update_area_of_max_square(row + 1 ,  lowercase_						)

												if mat[row][col]:
																		lowercase        =							1 + min([right, diagonal, down]						)
																		lowercase        =							max(largest_square_area[0] ,  lowercase_						)
																		return sub_problem_sol
												else:
																		return 0

						lowercase        =							[0]
						update_area_of_max_square(0 ,  0						)
						return largest_square_area[0]







def      SCREAMING_SNAKE_CASE				(				lowercase_    :      int ,  lowercase_    :      int ,  lowercase_    :      list[list[int]]						):

						def update_area_of_max_square_using_dp_array(
						    lowercase_    :      int ,  lowercase_    :      int ,  lowercase_    :      list[list[int]]						) -> int:
												if row >= rows or col >= cols:
																		return 0
												if dp_array[row][col] != -1:
																		return dp_array[row][col]

												lowercase        =							update_area_of_max_square_using_dp_array(lowercase_ ,  col + 1 ,  lowercase_						)
												lowercase        =							update_area_of_max_square_using_dp_array(row + 1 ,  col + 1 ,  lowercase_						)
												lowercase        =							update_area_of_max_square_using_dp_array(row + 1 ,  lowercase_ ,  lowercase_						)

												if mat[row][col]:
																		lowercase        =							1 + min([right, diagonal, down]						)
																		lowercase        =							max(largest_square_area[0] ,  lowercase_						)
																		lowercase        =							sub_problem_sol
																		return sub_problem_sol
												else:
																		return 0

						lowercase        =							[0]
						lowercase        =							[[-1] * cols for _ in range(lowercase_						)]
						update_area_of_max_square_using_dp_array(0 ,  0 ,  lowercase_						)

						return largest_square_area[0]







def      SCREAMING_SNAKE_CASE				(				lowercase_    :      int ,  lowercase_    :      int ,  lowercase_    :      list[list[int]]						):
						lowercase        =							[[0] * (cols + 1) for _ in range(rows + 1						)]
						lowercase        =							0
						for row in range(rows - 1 ,  -1 ,  -1						):
												for col in range(cols - 1 ,  -1 ,  -1						):
																		lowercase        =							dp_array[row][col + 1]
																		lowercase        =							dp_array[row + 1][col + 1]
																		lowercase        =							dp_array[row + 1][col]

																		if mat[row][col] == 1:
																								lowercase        =							1 + min(lowercase_ ,  lowercase_ ,  lowercase_						)
																								lowercase        =							max(dp_array[row][col] ,  lowercase_						)
																		else:
																								lowercase        =							0

						return largest_square_area







def      SCREAMING_SNAKE_CASE				(				lowercase_    :      int ,  lowercase_    :      int ,  lowercase_    :      list[list[int]]						):
						lowercase        =							[0] * (cols + 1)
						lowercase        =							[0] * (cols + 1)
						lowercase        =							0
						for row in range(rows - 1 ,  -1 ,  -1						):
												for col in range(cols - 1 ,  -1 ,  -1						):
																		lowercase        =							current_row[col + 1]
																		lowercase        =							next_row[col + 1]
																		lowercase        =							next_row[col]

																		if mat[row][col] == 1:
																								lowercase        =							1 + min(lowercase_ ,  lowercase_ ,  lowercase_						)
																								lowercase        =							max(current_row[col] ,  lowercase_						)
																		else:
																								lowercase        =							0
												lowercase        =							current_row

						return largest_square_area


if __name__ == "__main__":
						import doctest

						doctest.testmod()
						print(largest_square_area_in_matrix_bottom_up(2, 2, [[1, 1], [1, 1]]))


