



'''simple docstring'''

from __future__ import annotations

from typing import Generic, TypeVar

UpperCAmelCase     		=   TypeVar('T')

class __snake_case(				Generic[T] ):


						'''simple docstring'''



						def __init__( self     ,	A_				)     ->     None:
							lowerCAmelCase   =     data
							lowerCAmelCase   =     self
							lowerCAmelCase   =     0







class __snake_case(				Generic[T] ):


						'''simple docstring'''



						def __init__( self				)     ->     None:
							# map from node name to the node object
							lowerCAmelCase   =     {}


						def     __snake_case   ( self     ,	A_				)     ->     None:
							# create a new set with x as its member
							lowerCAmelCase   =     DisjointSetTreeNode(A_				)


						def     __snake_case   ( self     ,	A_				)     ->     DisjointSetTreeNode[T]:
							# find the set x belongs to (with path-compression)
							lowerCAmelCase   =     self.map[data]
							if elem_ref != elem_ref.parent:
								lowerCAmelCase   =     self.find_set(elem_ref.parent.data				)
							return elem_ref.parent


						def     __snake_case   ( self     ,	A_     ,	A_				)     ->     None:
							# helper function for union operation
							if nodea.rank > nodea.rank:
								lowerCAmelCase   =     nodea
							else:
								lowerCAmelCase   =     nodea
								if nodea.rank == nodea.rank:
									nodea.rank += 1




						def     __snake_case   ( self     ,	A_     ,	A_				)     ->     None:
							# merge 2 disjoint sets
							self.link(self.find_set(A_				)     ,	self.find_set(A_				)				)







class __snake_case(				Generic[T] ):


						'''simple docstring'''



						def __init__( self				)     ->     None:
							# connections: map from the node to the neighbouring nodes (with weights)
							lowerCAmelCase   =     {}


						def     __snake_case   ( self     ,	A_				)     ->     None:
							# add a node ONLY if its not present in the graph
							if node not in self.connections:
								lowerCAmelCase   =     {}


						def     __snake_case   ( self     ,	A_     ,	A_     ,	A_				)     ->     None:
							# add an edge with the given weight
							self.add_node(A_				)
							self.add_node(A_				)
							lowerCAmelCase   =     weight
							lowerCAmelCase   =     weight




						def     __snake_case   ( self				)     ->     GraphUndirectedWeighted[T]:
							lowerCAmelCase   =     []
							lowerCAmelCase   =     set()
							for start in self.connections:
								for end in self.connections[start]:
									if (start, end) not in seen:
										seen.add((end, start)				)
										edges.append((start, end, self.connections[start][end])				)
							edges.sort(key=lambda A_				: x[2]				)

							# creating the disjoint set
							lowerCAmelCase   =     DisjointSetTree[T]()
							for node in self.connections:
								disjoint_set.make_set(A_				)

							# MST generation
							lowerCAmelCase   =     0
							lowerCAmelCase   =     0
							lowerCAmelCase   =     GraphUndirectedWeighted[T]()
							while num_edges < len(self.connections				) - 1:
								lowerCAmelCase,       lowerCAmelCase,       lowerCAmelCase   =     edges[index]
								index += 1
								lowerCAmelCase   =     disjoint_set.find_set(A_				)
								lowerCAmelCase   =     disjoint_set.find_set(A_				)
								if parent_u != parent_v:
									num_edges += 1
									graph.add_edge(A_     ,	A_     ,	A_				)
									disjoint_set.union(A_     ,	A_				)
							return graph




'''simple docstring'''

class __snake_case(				_lowerCAmelCase ):


						'''simple docstring'''



						pass







class __snake_case(				_lowerCAmelCase ):


						'''simple docstring'''



						pass







class __snake_case:


						'''simple docstring'''



						def __init__( self				)     ->     int:
							lowerCAmelCase   =     [
							    [],
							    [],
							    [],
							]


						def     __snake_case   ( self     ,	A_     ,	A_				)     ->     None:
							try:
								if len(self.queues[priority]				) >= 100:
									raise OverflowError("""Maximum queue size is 100"""				)
								self.queues[priority].append(A_				)
							except IndexError:
								raise ValueError("""Valid priorities are 0, 1, and 2"""				)


						def     __snake_case   ( self				)     ->     int:
							for queue in self.queues:
								if queue:
									return queue.pop(0				)
							raise UnderFlowError("""All queues are empty"""				)




						def __str__( self				)     ->     str:
							return "\n".join(f'Priority {i}: {q}' for i, q in enumerate(self.queues				)				)







class __snake_case:


						'''simple docstring'''



						def __init__( self				)     ->     Dict:
							lowerCAmelCase   =     []


						def     __snake_case   ( self     ,	A_				)     ->     None:
							if len(self.queue				) == 100:
								raise OverFlowError("""Maximum queue size is 100"""				)
							self.queue.append(A_				)


						def     __snake_case   ( self				)     ->     int:
							if not self.queue:
								raise UnderFlowError("""The queue is empty"""				)
							else:
								lowerCAmelCase   =     min(self.queue				)
								self.queue.remove(A_				)
								return data




						def __str__( self				)     ->     str:
							return str(self.queue				)







def 		_snake_case		( )      ->						Tuple:







	"""simple docstring"""
	lowerCAmelCase   =     FixedPriorityQueue()
	fpq.enqueue(0							,		10							)
	fpq.enqueue(1							,		70							)
	fpq.enqueue(0							,		100							)
	fpq.enqueue(2							,		1							)
	fpq.enqueue(2							,		5							)
	fpq.enqueue(1							,		7							)
	fpq.enqueue(2							,		4							)
	fpq.enqueue(1							,		64							)
	fpq.enqueue(0							,		128							)
	print(_SCREAMING_SNAKE_CASE							)
	print(fpq.dequeue()							)
	print(fpq.dequeue()							)
	print(fpq.dequeue()							)
	print(fpq.dequeue()							)
	print(fpq.dequeue()							)
	print(_SCREAMING_SNAKE_CASE							)
	print(fpq.dequeue()							)
	print(fpq.dequeue()							)
	print(fpq.dequeue()							)
	print(fpq.dequeue()							)
	print(fpq.dequeue()							)






def 		_snake_case		( )      ->						Optional[Any]:







	"""simple docstring"""
	lowerCAmelCase   =     ElementPriorityQueue()
	epq.enqueue(10							)
	epq.enqueue(70							)
	epq.enqueue(100							)
	epq.enqueue(1							)
	epq.enqueue(5							)
	epq.enqueue(7							)
	epq.enqueue(4							)
	epq.enqueue(64							)
	epq.enqueue(128							)
	print(_SCREAMING_SNAKE_CASE							)
	print(epq.dequeue()							)
	print(epq.dequeue()							)
	print(epq.dequeue()							)
	print(epq.dequeue()							)
	print(epq.dequeue()							)
	print(_SCREAMING_SNAKE_CASE							)
	print(epq.dequeue()							)
	print(epq.dequeue()							)
	print(epq.dequeue()							)
	print(epq.dequeue()							)
	print(epq.dequeue()							)


if __name__ == "__main__":
				fixed_priority_queue()
				element_priority_queue()