
'''simple docstring'''







def 					snake_case_		(				__SCREAMING_SNAKE_CASE					: str      ,      __SCREAMING_SNAKE_CASE					: str							):



						"""simple docstring"""





						lowercase_	:     Optional[int]													=       len(__SCREAMING_SNAKE_CASE							) + 1
						lowercase_	:     Tuple													=       len(__SCREAMING_SNAKE_CASE							) + 1

						# dp is a 2d matrix where dp[i][j] denotes whether prefix string of
						# length i of input_string matches with prefix string of length j of
						# given pattern.
						# "dp" stands for dynamic programming.
						lowercase_	:     List[Any]													=       [[0 for i in range(__SCREAMING_SNAKE_CASE							)] for j in range(__SCREAMING_SNAKE_CASE							)]

						# since string of zero length match pattern of zero length
						lowercase_	:     Optional[int]													=       1

						# since pattern of zero length will never match with string of non-zero length
						for i in range(1      ,      __SCREAMING_SNAKE_CASE							):
												lowercase_	:     Dict													=       0

						# since string of zero length will match with pattern where there
						# is at least one * alternatively
						for j in range(1      ,      __SCREAMING_SNAKE_CASE							):
												lowercase_	:     List[Any]													=       dp[0][j - 2] if pattern[j - 1] == '''*''' else 0

						# now using bottom-up approach to find for all remaining lengths
						for i in range(1      ,      __SCREAMING_SNAKE_CASE							):
												for j in range(1      ,      __SCREAMING_SNAKE_CASE							):
																		if input_string[i - 1] == pattern[j - 1] or pattern[j - 1] == ".":
																								lowercase_	:     str													=       dp[i - 1][j - 1]

																		elif pattern[j - 1] == "*":
																								if dp[i][j - 2] == 1:
																														lowercase_	:     int													=       1
																								elif pattern[j - 2] in (input_string[i - 1], "."):
																														lowercase_	:     Tuple													=       dp[i - 1][j]
																								else:
																														lowercase_	:     List[Any]													=       0
																		else:
																								lowercase_	:     Dict													=       0

						return bool(dp[-1][-1]							)


if __name__ == "__main__":
							import doctest

							doctest.testmod()
							# inputing the strings
							# input_string = input("input a string :")
							# pattern = input("input a pattern :")

							_lowercase :  Any    							=       "aab"
							_lowercase :  List[Any]    							=       "c*a*b"

							# using function to check whether given string matches the given pattern
							if match_pattern(input_string, pattern):
														print(f"""{input_string} matches the given pattern {pattern}""")
							else:
														print(f"""{input_string} does not match with the given pattern {pattern}""")





'''simple docstring'''







from __future__ import annotations

from collections import Counter
from random import random






class  lowerCAmelCase__   :






					def __init__(   self		):


											"""simple docstring"""





											lowercase_	:     int													=       {}






					def 	_snake_case    (   self				,							__SCREAMING_SNAKE_CASE		):


											"""simple docstring"""





											lowercase_	:     Dict													=       {}






					def 	_snake_case    (   self				,							__SCREAMING_SNAKE_CASE				,							__SCREAMING_SNAKE_CASE				,							__SCREAMING_SNAKE_CASE		):


											"""simple docstring"""





											if nodea not in self.connections:
																	self.add_node(__SCREAMING_SNAKE_CASE		)
											if nodea not in self.connections:
																	self.add_node(__SCREAMING_SNAKE_CASE		)
											lowercase_	:     Optional[Any]													=       probability






					def 	_snake_case    (   self		):


											"""simple docstring"""





											return list(self.connections		)






					def 	_snake_case    (   self				,							__SCREAMING_SNAKE_CASE		):


											"""simple docstring"""





											lowercase_	:     Any													=       0
											lowercase_	:     Tuple													=       random()

											for dest in self.connections[node]:
																	current_probability += self.connections[node][dest]
																	if current_probability > random_value:
																							return dest
											return ""







def 					snake_case_		(				__SCREAMING_SNAKE_CASE					: str      ,      __SCREAMING_SNAKE_CASE					: list[tuple[str, str, float]]      ,      __SCREAMING_SNAKE_CASE					: int							):



						"""simple docstring"""





						lowercase_	:     List[Any]													=       MarkovChainGraphUndirectedUnweighted()

						for nodea, nodea, probability in transitions:
												graph.add_transition_probability(__SCREAMING_SNAKE_CASE      ,      __SCREAMING_SNAKE_CASE      ,      __SCREAMING_SNAKE_CASE							)

						lowercase_	:     str													=       Counter(graph.get_nodes()							)
						lowercase_	:     Any													=       start

						for _ in range(__SCREAMING_SNAKE_CASE							):
												lowercase_	:     int													=       graph.transition(__SCREAMING_SNAKE_CASE							)
												visited[node] += 1

						return visited


if __name__ == "__main__":
							import doctest

							doctest.testmod()



