




_lowerCamelCase  :			List[str]        =       [
    [0, 16, 13, 0, 0, 0],
    [0, 0, 10, 12, 0, 0],
    [0, 4, 0, 0, 14, 0],
    [0, 0, 9, 0, 0, 20],
    [0, 0, 0, 7, 0, 4],
    [0, 0, 0, 0, 0, 0],
]

def 		lowercase_      (		_UpperCAmelCase  ,      _UpperCAmelCase  ,      _UpperCAmelCase  ,      _UpperCAmelCase	):




	"""simple docstring"""






	A_  :				List[str]	   =		[False] * len(snake_case__	)
	A_  :				str	   =		[s]
	A_  :				List[Any]	   =		True

	while queue:
		A_  :				Dict	   =		queue.pop(0	)
		for ind in range(len(graph[u]	)	):
			if visited[ind] is False and graph[u][ind] > 0:
				queue.append(snake_case__	)
				A_  :				List[Any]	   =		True
				A_  :				Union[str, Any]	   =		u

	return visited[t]

def 		lowercase_      (		_UpperCAmelCase  ,      _UpperCAmelCase  ,      _UpperCAmelCase	):




	"""simple docstring"""






	A_  :				Optional[Any]	   =		[-1] * (len(snake_case__	))
	A_  :				str	   =		0
	A_  :				Dict	   =		[]
	A_  :				Tuple	   =		[i[:] for i in graph]  # Record original cut, copy.
	while bfs(snake_case__  ,      snake_case__  ,      snake_case__  ,      snake_case__	):
		A_  :				List[Any]	   =		float('''Inf'''	)
		A_  :				int	   =		sink

		while s != source:
			# Find the minimum value in select path
			A_  :				int	   =		min(snake_case__  ,      graph[parent[s]][s]	)
			A_  :				List[str]	   =		parent[s]

		max_flow += path_flow
		A_  :				Optional[int]	   =		sink

		while v != source:
			A_  :				int	   =		parent[v]
			graph[u][v] -= path_flow
			graph[v][u] += path_flow
			A_  :				Union[str, Any]	   =		parent[v]

	for i in range(len(snake_case__	)	):
		for j in range(len(graph[0]	)	):
			if graph[i][j] == 0 and temp[i][j] > 0:
				res.append((i, j)	)

	return res


if __name__ == "__main__":
		print(mincut(test_graph, source=0, sink=5))











"""simple docstring"""

from queue import PriorityQueue
from typing import Any

import numpy as np

def 		lowercase_      (		_UpperCAmelCase  ,      _UpperCAmelCase  ,      _UpperCAmelCase  ,      _UpperCAmelCase  ,      _UpperCAmelCase  ,      _UpperCAmelCase  ,      _UpperCAmelCase  ,      _UpperCAmelCase  ,      _UpperCAmelCase  ,      ):




	"""simple docstring"""






	for nxt, d in graph[v]:
		if nxt in visited_forward:
			continue
		A_  :				Tuple	   =		cst_fwd.get(_UpperCAmelCase  ,      np.inf	)
		A_  :				Any	   =		cst_fwd[v] + d
		if new_cost_f < old_cost_f:
			queue.put((new_cost_f, nxt)	)
			A_  :				Tuple	   =		new_cost_f
			A_  :				Dict	   =		v
		if nxt in visited_backward:
			if cst_fwd[v] + d + cst_bwd[nxt] < shortest_distance:
				A_  :				Optional[Any]	   =		cst_fwd[v] + d + cst_bwd[nxt]
	return shortest_distance

def 		lowercase_      (		_UpperCAmelCase  ,      _UpperCAmelCase  ,      _UpperCAmelCase  ,      _UpperCAmelCase	):




	"""simple docstring"""






	A_  :				Tuple	   =		-1

	A_  :				Any	   =		set()
	A_  :				Tuple	   =		set()
	A_  :				Optional[int]	   =		{source: 0}
	A_  :				Dict	   =		{destination: 0}
	A_  :				Any	   =		{source: None}
	A_  :				Optional[Any]	   =		{destination: None}
	A_  :				PriorityQueue[Any]	   =		PriorityQueue()
	A_  :				PriorityQueue[Any]	   =		PriorityQueue()

	A_  :				Union[str, Any]	   =		np.inf

	queue_forward.put((0, source)	)
	queue_backward.put((0, destination)	)

	if source == destination:
		return 0

	while not queue_forward.empty() and not queue_backward.empty():
		A_   , A_  :				Union[str, Any]	   =		queue_forward.get()
		visited_forward.add(_UpperCAmelCase	)

		A_   , A_  :				Optional[int]	   =		queue_backward.get()
		visited_backward.add(_UpperCAmelCase	)

		A_  :				Any	   =		pass_and_relaxation(
		    _UpperCAmelCase  ,      _UpperCAmelCase  ,      _UpperCAmelCase  ,      _UpperCAmelCase  ,      _UpperCAmelCase  ,      _UpperCAmelCase  ,      _UpperCAmelCase  ,      _UpperCAmelCase  ,      _UpperCAmelCase  ,      )

		A_  :				Dict	   =		pass_and_relaxation(
		    _UpperCAmelCase  ,      _UpperCAmelCase  ,      _UpperCAmelCase  ,      _UpperCAmelCase  ,      _UpperCAmelCase  ,      _UpperCAmelCase  ,      _UpperCAmelCase  ,      _UpperCAmelCase  ,      _UpperCAmelCase  ,      )

		if cst_fwd[v_fwd] + cst_bwd[v_bwd] >= shortest_distance:
			break

	if shortest_distance != np.inf:
		A_  :				Optional[Any]	   =		shortest_distance
	return shortest_path_distance


_lowerCamelCase  :			Optional[Any]        =       {
    'B': [['C', 1]],
    'C': [['D', 1]],
    'D': [['F', 1]],
    'E': [['B', 1], ['G', 2]],
    'F': [],
    'G': [['F', 1]],
}
_lowerCamelCase  :			Any        =       {
    'B': [['E', 1]],
    'C': [['B', 1]],
    'D': [['C', 1]],
    'F': [['D', 1], ['G', 1]],
    'E': [[None, np.inf]],
    'G': [['E', 2]],
}

if __name__ == "__main__":
		import doctest

		doctest.testmod()





