

'''simple docstring'''

from __future__ import annotations

from sys import maxsize
from typing import Generic, TypeVar

SCREAMING_SNAKE_CASE							:				Union[str, Any]     	=			TypeVar("T")




def 							_UpperCamelCase				(   lowerCAmelCase__:					int   )      -> int:
							return (position - 1) // 2




def 							_UpperCamelCase				(   lowerCAmelCase__:					int   )      -> int:
							return (2 * position) + 1




def 							_UpperCamelCase				(   lowerCAmelCase__:					int   )      -> int:
							return (2 * position) + 2






class    snake_case     (      Generic[T]		):






				"""simple docstring"""



				def __init__(    self       )     ->							None:
											SCREAMING_SNAKE_CASE_				=				[]
											SCREAMING_SNAKE_CASE_				=				{}
											SCREAMING_SNAKE_CASE_				=				0



				def __len__(    self       )     ->							int:
											return self.elements



				def __repr__(    self       )     ->							str:
											return str(self.heap       )



				def   a__					(    self       )     ->							bool:
											# Check if the priority queue is empty
											return self.elements == 0



				def   a__					(    self,     _lowercase,     _lowercase       )     ->							None:
											# Add an element with given priority to the queue
											self.heap.append((elem, weight)       )
											SCREAMING_SNAKE_CASE_				=				self.elements
											self.elements += 1
											self._bubble_up(snake_case_       )



				def   a__					(    self       )     ->							T:
											# Remove and return the element with lowest weight (highest priority)
											if self.elements > 1:
																		self._swap_nodes(0,     self.elements - 1       )
											SCREAMING_SNAKE_CASE_				,    SCREAMING_SNAKE_CASE_				=				self.heap.pop()
											del self.position_map[elem]
											self.elements -= 1
											if self.elements > 0:
																		SCREAMING_SNAKE_CASE_				,    SCREAMING_SNAKE_CASE_				=				self.heap[0]
																		self._bubble_down(snake_case_       )
											return elem



				def   a__					(    self,     _lowercase,     _lowercase       )     ->							None:
											# Update the weight of the given key
											SCREAMING_SNAKE_CASE_				=				self.position_map[elem]
											SCREAMING_SNAKE_CASE_				=				(elem, weight)
											if position > 0:
																		SCREAMING_SNAKE_CASE_				=				get_parent_position(snake_case_       )
																		SCREAMING_SNAKE_CASE_				,    SCREAMING_SNAKE_CASE_				=				self.heap[parent_position]
																		if parent_weight > weight:
																									self._bubble_up(snake_case_       )
																		else:
																									self._bubble_down(snake_case_       )
											else:
																		self._bubble_down(snake_case_       )



				def   a__					(    self,     _lowercase       )     ->							None:
											# Place a node at the proper position (upward movement) [to be used internally
											# only]
											SCREAMING_SNAKE_CASE_				=				self.position_map[elem]
											if curr_pos == 0:
																		return None
											SCREAMING_SNAKE_CASE_				=				get_parent_position(snake_case_       )
											SCREAMING_SNAKE_CASE_				,    SCREAMING_SNAKE_CASE_				=				self.heap[curr_pos]
											SCREAMING_SNAKE_CASE_				,    SCREAMING_SNAKE_CASE_				=				self.heap[parent_position]
											if parent_weight > weight:
																		self._swap_nodes(snake_case_,     snake_case_       )
																		return self._bubble_up(snake_case_       )
											return None



				def   a__					(    self,     _lowercase       )     ->							None:
											# Place a node at the proper position (downward movement) [to be used
											# internally only]
											SCREAMING_SNAKE_CASE_				=				self.position_map[elem]
											SCREAMING_SNAKE_CASE_				,    SCREAMING_SNAKE_CASE_				=				self.heap[curr_pos]
											SCREAMING_SNAKE_CASE_				=				get_child_left_position(snake_case_       )
											SCREAMING_SNAKE_CASE_				=				get_child_right_position(snake_case_       )
											if child_left_position < self.elements and child_right_position < self.elements:
																		SCREAMING_SNAKE_CASE_				,    SCREAMING_SNAKE_CASE_				=				self.heap[child_left_position]
																		SCREAMING_SNAKE_CASE_				,    SCREAMING_SNAKE_CASE_				=				self.heap[child_right_position]
																		if child_right_weight < child_left_weight and child_right_weight < weight:
																									self._swap_nodes(snake_case_,     snake_case_       )
																									return self._bubble_down(snake_case_       )
											if child_left_position < self.elements:
																		SCREAMING_SNAKE_CASE_				,    SCREAMING_SNAKE_CASE_				=				self.heap[child_left_position]
																		if child_left_weight < weight:
																									self._swap_nodes(snake_case_,     snake_case_       )
																									return self._bubble_down(snake_case_       )
											else:
																		return None
											if child_right_position < self.elements:
																		SCREAMING_SNAKE_CASE_				,    SCREAMING_SNAKE_CASE_				=				self.heap[child_right_position]
																		if child_right_weight < weight:
																									self._swap_nodes(snake_case_,     snake_case_       )
																									return self._bubble_down(snake_case_       )
											return None





				def   a__					(    self,     _lowercase,     _lowercase       )     ->							None:
											# Swap the nodes at the given positions
											SCREAMING_SNAKE_CASE_				=				self.heap[nodea_pos][0]
											SCREAMING_SNAKE_CASE_				=				self.heap[nodea_pos][0]
											SCREAMING_SNAKE_CASE_				,    SCREAMING_SNAKE_CASE_				=				(
											    self.heap[nodea_pos],
											    self.heap[nodea_pos],
											)
											SCREAMING_SNAKE_CASE_				=				nodea_pos
											SCREAMING_SNAKE_CASE_				=				nodea_pos






class    snake_case     (      Generic[T]		):






				"""simple docstring"""



				def __init__(    self       )     ->							None:
											SCREAMING_SNAKE_CASE_				=				{}
											SCREAMING_SNAKE_CASE_				=				0



				def __repr__(    self       )     ->							str:
											return str(self.connections       )



				def __len__(    self       )     ->							int:
											return self.nodes



				def   a__					(    self,     _lowercase       )     ->							None:
											# Add a node in the graph if it is not in the graph
											if node not in self.connections:
																		SCREAMING_SNAKE_CASE_				=				{}
																		self.nodes += 1





				def   a__					(    self,     _lowercase,     _lowercase,     _lowercase       )     ->							None:
											# Add an edge between 2 nodes in the graph
											self.add_node(snake_case_       )
											self.add_node(snake_case_       )
											SCREAMING_SNAKE_CASE_				=				weight
											SCREAMING_SNAKE_CASE_				=				weight




def 							_UpperCamelCase				(   lowerCAmelCase__:					GraphUndirectedWeighted[T]		,)      -> tuple[dict[T, int], dict[T, T | None]]:
							SCREAMING_SNAKE_CASE_				=				{node: maxsize for node in graph.connections}
							SCREAMING_SNAKE_CASE_				=				{node: None for node in graph.connections}

							SCREAMING_SNAKE_CASE_				=				MinPriorityQueue()
							for node, weight in dist.items():
														priority_queue.push(__lowerCamelCase		,__lowerCamelCase   )

							if priority_queue.is_empty():
														return dist, parent

							# initialization
							SCREAMING_SNAKE_CASE_				=				priority_queue.extract_min()
							SCREAMING_SNAKE_CASE_				=				0
							for neighbour in graph.connections[node]:
														if dist[neighbour] > dist[node] + graph.connections[node][neighbour]:
																					SCREAMING_SNAKE_CASE_				=				dist[node] + graph.connections[node][neighbour]
																					priority_queue.update_key(__lowerCamelCase		,dist[neighbour]   )
																					SCREAMING_SNAKE_CASE_				=				node

    # running prim's algorithm
							while not priority_queue.is_empty():
														SCREAMING_SNAKE_CASE_				=				priority_queue.extract_min()
														for neighbour in graph.connections[node]:
																					if dist[neighbour] > dist[node] + graph.connections[node][neighbour]:
																												SCREAMING_SNAKE_CASE_				=				dist[node] + graph.connections[node][neighbour]
																												priority_queue.update_key(__lowerCamelCase		,dist[neighbour]   )
																												SCREAMING_SNAKE_CASE_				=				node
							return dist, parent










from __future__ import annotations






class     __a			:



	def __init__(    self				:     List[Any]					,						snake_case_				:     str					,						snake_case_				:     str)->				Optional[int]:
						__lowerCAmelCase ,						__lowerCAmelCase						 =text, pattern
						__lowerCAmelCase ,						__lowerCAmelCase						 =len(snake_case_), len(snake_case_)



	def 		UpperCamelCase				(    self				:     List[Any]					,						snake_case_				:     str)->				int:

						for i in range(self.patLen - 1					,						-1					,						-1):
											if char == self.pattern[i]:
																return i
						return -1



	def 		UpperCamelCase				(    self				:     List[str]					,						snake_case_				:     int)->				int:

						for i in range(self.patLen - 1					,						-1					,						-1):
											if self.pattern[i] != self.text[current_pos + i]:
																return current_pos + i
						return -1



	def 		UpperCamelCase				(    self				:     Dict)->				list[int]:
						# searches pattern in text and returns index positions
						__lowerCAmelCase						 =[]
						for i in range(self.textLen - self.patLen + 1):
											__lowerCAmelCase						 =self.mismatch_in_text(snake_case_)
											if mismatch_index == -1:
																positions.append(snake_case_)
											else:
																__lowerCAmelCase						 =self.match_in_pattern(self.text[mismatch_index])
																__lowerCAmelCase						 =(
																    mismatch_index - match_index
																)  # shifting index lgtm [py/multiple-definition]
						return positions


lowercase_													=      '''ABAABA'''
lowercase_													=      '''AB'''
lowercase_													=      BoyerMooreSearch(text, pattern)
lowercase_													=      bms.bad_character_heuristic()

if len(positions) == 0:
				print('''No match found''')
else:
				print('''Pattern found in following positions: ''')
				print(positions)




