
'''simple docstring'''







class 			lowerCAmelCase__       :






     def __init__(       self    ,							__SCREAMING_SNAKE_CASE    ,							__SCREAMING_SNAKE_CASE    ,							__SCREAMING_SNAKE_CASE		):


           """simple docstring"""





           lowercase_     :					str													=	None
           lowercase_     :					Union[str, Any]													=	None
           lowercase_     :					Any													=	graph

           self._normalize_graph(lowercase__    ,							lowercase__		)
           lowercase_     :					str													=	len(lowercase__		)
           lowercase_     :					Optional[Any]													=	None






     def      _snake_case   (       self    ,							__SCREAMING_SNAKE_CASE    ,							__SCREAMING_SNAKE_CASE		):


           """simple docstring"""





           if sources is int:
                 lowercase_     :					Union[str, Any]													=	[sources]
           if sinks is int:
                 lowercase_     :					Dict													=	[sinks]

           if len(lowercase__		) == 0 or len(lowercase__		) == 0:
                 return

           lowercase_     :					Union[str, Any]													=	sources[0]
           lowercase_     :					Dict													=	sinks[0]

           # make fake vertex if there are more
           # than one source or sink
           if len(lowercase__		) > 1 or len(lowercase__		) > 1:
                 lowercase_     :					Union[str, Any]													=	0
                 for i in sources:
                       max_input_flow += sum(self.graph[i]		)

                 lowercase_     :					List[str]													=	len(self.graph		) + 1
                 for room in self.graph:
                       room.insert(0    ,							0		)
                 self.graph.insert(0    ,							[0] * size		)
                 for i in sources:
                       lowercase_     :					Optional[int]													=	max_input_flow
                 lowercase_     :					Optional[Any]													=	0

                 lowercase_     :					Union[str, Any]													=	len(self.graph		) + 1
                 for room in self.graph:
                       room.append(0		)
                 self.graph.append([0] * size		)
                 for i in sinks:
                       lowercase_     :					List[Any]													=	max_input_flow
                 lowercase_     :					Union[str, Any]													=	size - 1






     def      _snake_case   (       self		):


           """simple docstring"""





           if self.maximum_flow_algorithm is None:
                 raise Exception('''You need to set maximum flow algorithm before.'''		)
           if self.source_index is None or self.sink_index is None:
                 return 0

           self.maximum_flow_algorithm.execute()
           return self.maximum_flow_algorithm.getMaximumFlow()






     def      _snake_case   (       self    ,							__SCREAMING_SNAKE_CASE		):


           """simple docstring"""





           lowercase_     :					Optional[int]													=	algorithm(self		)







class 			lowerCAmelCase__       :






     def __init__(       self    ,							__SCREAMING_SNAKE_CASE		):


           """simple docstring"""





           lowercase_     :					Dict													=	flow_network
           lowercase_     :					List[str]													=	flow_network.verticesCount
           lowercase_     :					Any													=	flow_network.sourceIndex
           lowercase_     :					str													=	flow_network.sinkIndex
           # it's just a reference, so you shouldn't change
           # it in your algorithms, use deep copy before doing that
           lowercase_     :					Any													=	flow_network.graph
           lowercase_     :					List[str]													=	False






     def      _snake_case   (       self		):


           """simple docstring"""





           if not self.executed:
                 self._algorithm()
                 lowercase_     :					Dict													=	True






     def      _snake_case   (       self		):


           """simple docstring"""





           pass







class 			lowerCAmelCase__       (  lowerCamelCase__					):






     def __init__(       self    ,							__SCREAMING_SNAKE_CASE		):


           """simple docstring"""





           super().__init__(lowercase__		)
           # use this to save your result
           lowercase_     :					List[str]													=	-1






     def      _snake_case   (       self		):


           """simple docstring"""





           if not self.executed:
                 raise Exception('''You should execute algorithm before using its result!'''		)

           return self.maximum_flow







class 			lowerCAmelCase__       (  lowerCamelCase__					):






     def __init__(       self    ,							__SCREAMING_SNAKE_CASE		):


           """simple docstring"""





           super().__init__(lowercase__		)

           lowercase_     :					str													=	[[0] * self.verticies_count for i in range(self.verticies_count		)]

           lowercase_     :					Dict													=	[0] * self.verticies_count
           lowercase_     :					str													=	[0] * self.verticies_count






     def      _snake_case   (       self		):


           """simple docstring"""





           lowercase_     :					str													=	self.verticies_count

           # push some substance to graph
           for nextvertex_index, bandwidth in enumerate(self.graph[self.source_index]		):
                 self.preflow[self.source_index][nextvertex_index] += bandwidth
                 self.preflow[nextvertex_index][self.source_index] -= bandwidth
                 self.excesses[nextvertex_index] += bandwidth

           # Relabel-to-front selection rule
           lowercase_     :					Union[str, Any]													=	[
               i
               for i in range(self.verticies_count		)
               if i != self.source_index and i != self.sink_index
           ]

           # move through list
           lowercase_     :					List[Any]													=	0
           while i < len(lowercase__		):
                 lowercase_     :					Tuple													=	vertices_list[i]
                 lowercase_     :					Dict													=	self.heights[vertex_index]
                 self.process_vertex(lowercase__		)
                 if self.heights[vertex_index] > previous_height:
                       # if it was relabeled, swap elements
                       # and start from 0 index
                       vertices_list.insert(0    ,							vertices_list.pop(lowercase__		)		)
                       lowercase_     :					Any													=	0
                 else:
                       i += 1

           lowercase_     :					str													=	sum(self.preflow[self.source_index]		)






     def      _snake_case   (       self    ,							__SCREAMING_SNAKE_CASE		):


           """simple docstring"""





           while self.excesses[vertex_index] > 0:
                 for neighbour_index in range(self.verticies_count		):
                       # if it's neighbour and current vertex is higher
                       if (
                           self.graph[vertex_index][neighbour_index]
                           - self.preflow[vertex_index][neighbour_index]
                           > 0
                           and self.heights[vertex_index] > self.heights[neighbour_index]
                       ):
                             self.push(lowercase__    ,							lowercase__		)

                 self.relabel(lowercase__		)






     def      _snake_case   (       self    ,							__SCREAMING_SNAKE_CASE    ,							__SCREAMING_SNAKE_CASE		):


           """simple docstring"""





           lowercase_     :					List[Any]													=	min(
               self.excesses[from_index]    ,							self.graph[from_index][to_index] - self.preflow[from_index][to_index]    ,							)
           self.preflow[from_index][to_index] += preflow_delta
           self.preflow[to_index][from_index] -= preflow_delta
           self.excesses[from_index] -= preflow_delta
           self.excesses[to_index] += preflow_delta






     def      _snake_case   (       self    ,							__SCREAMING_SNAKE_CASE		):


           """simple docstring"""





           lowercase_     :					Union[str, Any]													=	None
           for to_index in range(self.verticies_count		):
                 if (
                     self.graph[vertex_index][to_index]
                     - self.preflow[vertex_index][to_index]
                     > 0
                 ) and (min_height is None or self.heights[to_index] < min_height):
                       lowercase_     :					List[Any]													=	self.heights[to_index]

           if min_height is not None:
                 lowercase_     :					List[str]													=	min_height + 1


if __name__ == "__main__":
       _lowercase			:  Optional[int]   							=	[0]
       _lowercase			:  List[str]   							=	[3]
       # graph = [
       #     [0, 0, 4, 6, 0, 0],
       #     [0, 0, 5, 2, 0, 0],
       #     [0, 0, 0, 0, 4, 4],
       #     [0, 0, 0, 0, 6, 6],
       #     [0, 0, 0, 0, 0, 0],
       #     [0, 0, 0, 0, 0, 0],
       # ]
       _lowercase			:  Optional[int]   							=	[[0, 7, 0, 0], [0, 0, 6, 0], [0, 0, 0, 8], [9, 0, 0, 0]]

       # prepare our network
       _lowercase			:  Dict   							=	FlowNetwork(graph, entrances, exits)
       # set algorithm
       flow_network.set_maximum_flow_algorithm(PushRelabelExecutor)
       # and calculate
       _lowercase			:  Dict   							=	flow_network.find_maximum_flow()

       print(f"""maximum flow is {maximum_flow}""")





'''simple docstring'''







from __future__ import annotations

from typing import Any






class 			lowerCAmelCase__       :






					def __init__(       self    ,							__SCREAMING_SNAKE_CASE		):


											"""simple docstring"""





											lowercase_     :					str													=	num_of_nodes
											lowercase_     :					list[list[int]]													=	[]
											lowercase_     :					dict[int, int]													=	{}






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


											"""simple docstring"""





											self.m_edges.append([u_node, v_node, weight]		)






					def      _snake_case   (       self    ,							__SCREAMING_SNAKE_CASE		):


											"""simple docstring"""





											if self.m_component[u_node] == u_node:
																	return u_node
											return self.find_component(self.m_component[u_node]		)






					def      _snake_case   (       self    ,							__SCREAMING_SNAKE_CASE		):


											"""simple docstring"""





											if self.m_component[u_node] != u_node:
																	for k in self.m_component:
																							lowercase_     :					Optional[int]													=	self.find_component(__SCREAMING_SNAKE_CASE		)






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


											"""simple docstring"""





											if component_size[u_node] <= component_size[v_node]:
																	lowercase_     :					Any													=	v_node
																	component_size[v_node] += component_size[u_node]
																	self.set_component(__SCREAMING_SNAKE_CASE		)

											elif component_size[u_node] >= component_size[v_node]:
																	lowercase_     :					int													=	self.find_component(__SCREAMING_SNAKE_CASE		)
																	component_size[u_node] += component_size[v_node]
																	self.set_component(__SCREAMING_SNAKE_CASE		)






					def      _snake_case   (       self		):


											"""simple docstring"""





											lowercase_     :					Dict													=	[]
											lowercase_     :					Optional[Any]													=	0

											lowercase_     :					list[Any]													=	[-1] * self.m_num_of_nodes

											# A list of components (initialized to all of the nodes)
											for node in range(self.m_num_of_nodes		):
																	self.m_component.update({node: node}		)
																	component_size.append(1		)

											lowercase_     :					Union[str, Any]													=	self.m_num_of_nodes

											while num_of_components > 1:
																	for edge in self.m_edges:
																							lowercase_						,			lowercase_						,			lowercase_     :					List[Any]													=	edge

																							lowercase_     :					Dict													=	self.m_component[u]
																							lowercase_     :					Any													=	self.m_component[v]

																							if u_component != v_component:

																													for component in (u_component, v_component):
																																			if (
																																			    minimum_weight_edge[component] == -1
																																			    or minimum_weight_edge[component][2] > w
																																			):
																																									lowercase_     :					Union[str, Any]													=	[u, v, w]

																	for edge in minimum_weight_edge:
																							if isinstance(__SCREAMING_SNAKE_CASE    ,							__SCREAMING_SNAKE_CASE		):
																													lowercase_						,			lowercase_						,			lowercase_     :					str													=	edge

																													lowercase_     :					Tuple													=	self.m_component[u]
																													lowercase_     :					Union[str, Any]													=	self.m_component[v]

																													if u_component != v_component:
																																			mst_weight += w
																																			self.union(__SCREAMING_SNAKE_CASE    ,							__SCREAMING_SNAKE_CASE    ,							__SCREAMING_SNAKE_CASE		)
																																			print(F'''Added edge [{u} - {v}]\nAdded weight: {w}\n'''		)
																																			num_of_components -= 1

																	lowercase_     :					str													=	[-1] * self.m_num_of_nodes
											print(F'''The total weight of the minimal spanning tree is: {mst_weight}'''		)







def  snake_case_		(    ):



						"""simple docstring"""







if __name__ == "__main__":
							import doctest

							doctest.testmod()



