




_snake_case            = [
    [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        lowerCAmelCase_			(  snake_case_,snake_case_,snake_case_,snake_case_  ):
      # Return True if there is node that has not iterated.
      _A							:  str    =		[False] * len(snake_case_  )
      _A							:  Optional[int]    =		[s]
      _A							:  str    =		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							:  Tuple    =		True
                        _A							:  Tuple    =		u

      return visited[t]







def        lowerCAmelCase_			(  snake_case_,snake_case_,snake_case_  ):
      _A							:  List[str]    =		[-1] * (len(snake_case_  ))
      _A							:  List[Any]    =		0
      _A							:  Dict    =		[]
      _A							:  Any    =		[i[:] for i in graph]  # Record original cut, copy.
      while bfs(snake_case_,snake_case_,snake_case_,snake_case_  ):
            _A							:  Optional[int]    =		float("""Inf"""  )
            _A							:  Dict    =		sink

            while s != source:
                  # Find the minimum value in select path
                  _A							:  Any    =		min(snake_case_,graph[parent[s]][s]  )
                  _A							:  Tuple    =		parent[s]

            max_flow += path_flow
            _A							:  Tuple    =		sink

            while v != source:
                  _A							:  Optional[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))







from collections.abc import Callable
from math import pi, sqrt
from random import uniform
from statistics import mean







def        lowerCAmelCase_			(  snake_case_  ):

      # A local function to see if a dot lands in the circle.
      def is_in_circle(snake_case_,snake_case_  ) -> bool:
            _A							:  List[str]    =		sqrt((x**2) + (y**2)  )
            # Our circle has a radius of 1, so a distance
            # greater than 1 would land outside the circle.
            return distance_from_centre <= 1

      # The proportion of guesses that landed in the circle
      _A							:  Optional[int]    =		mean(
          int(is_in_circle(uniform(-1.0,1.0  ),uniform(-1.0,1.0  )  )  )
          for _ in range(snake_case_  )  )
      # The ratio of the area for circle to square is pi/4.
      _A							:  List[str]    =		proportion * 4
      print(f'''The estimated value of pi is {pi_estimate}'''  )
      print(f'''The numpy value of pi is {pi}'''  )
      print(f'''The total error is {abs(pi - pi_estimate  )}'''  )







def        lowerCAmelCase_			(  snake_case_,snake_case_,snake_case_ = 0.0,snake_case_ = 1.0,):
      return mean(
          function_to_integrate(uniform(snake_case_,snake_case_  )  ) for _ in range(snake_case_  )  ) * (max_value - min_value)







def        lowerCAmelCase_			(  snake_case_,snake_case_ = 0.0,snake_case_ = 1.0  ):

      def identity_function(snake_case_  ) -> float:
            return x

      _A							:  Any    =		area_under_curve_estimator(
          snake_case_,snake_case_,snake_case_,snake_case_  )
      _A							:  Tuple    =		(max_value * max_value - min_value * min_value) / 2

      print("""******************"""  )
      print(f'''Estimating area under y=x where x varies from {min_value} to {max_value}'''  )
      print(f'''Estimated value is {estimated_value}'''  )
      print(f'''Expected value is {expected_value}'''  )
      print(f'''Total error is {abs(estimated_value - expected_value  )}'''  )
      print("""******************"""  )







def        lowerCAmelCase_			(  snake_case_  ):

      def function_to_integrate(snake_case_  ) -> float:
            return sqrt(4.0 - x * x  )

      _A							:  Optional[int]    =		area_under_curve_estimator(
          snake_case_,snake_case_,0.0,2.0  )

      print("""******************"""  )
      print("""Estimating pi using area_under_curve_estimator"""  )
      print(f'''Estimated value is {estimated_value}'''  )
      print(f'''Expected value is {pi}'''  )
      print(f'''Total error is {abs(estimated_value - pi  )}'''  )
      print("""******************"""  )


if __name__ == "__main__":
  import doctest

  doctest.testmod()

