



"""simple docstring"""


def  _lowerCAmelCase      (   lowercase_		,	lowercase_		,	lowercase_		,	lowercase_						):
						UpperCAmelCase             = [False] * len(A_						)
						UpperCAmelCase             = []
						queue.append(A_						)
						UpperCAmelCase             = True

						while queue:
												UpperCAmelCase             = queue.pop(0						)
												for ind in range(len(graph[u]						)						):
																		if visited[ind] is False and graph[u][ind] > 0:
																								queue.append(A_						)
																								UpperCAmelCase             = True
																								UpperCAmelCase             = u

						return visited[t]

def  _lowerCAmelCase      (   lowercase_		,	lowercase_		,	lowercase_						):
						UpperCAmelCase             = [-1] * (len(A_						))
						UpperCAmelCase             = 0
						while bfs(A_		,	A_		,	A_		,	A_						):
												UpperCAmelCase             = float('Inf'						)
												UpperCAmelCase             = sink

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

												max_flow += path_flow
												UpperCAmelCase             = sink

												while v != source:
																		UpperCAmelCase             = parent[v]
																		graph[u][v] -= path_flow
																		graph[v][u] += path_flow
																		UpperCAmelCase             = parent[v]
						return max_flow


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],
]

snake_case_     ,   snake_case_				     =       0, 5






print(ford_fulkerson(graph, source, sink))









"""simple docstring"""







from __future__ import annotations

from numpy import array, cos, cross, floataa, radians, sin
from numpy.typing import NDArray


def      lowercase			(				A_  ,   A_  ,   A_ = False       )->      list[float]:
  '''simple docstring'''







  if radian_mode:
    return [magnitude * cos(A_       ), magnitude * sin(A_       )]
  return [magnitude * cos(radians(A_       )       ), magnitude * sin(radians(A_       )       )]


def      lowercase			(				A_  ,   A_  ,   A_ = 10**-1       )->      bool:
  '''simple docstring'''







  a						:		NDArray[floataa]      							=			cross(A_  ,   A_       )
  a						:		float      							=			sum(A_       )
  return abs(A_       ) < eps


if __name__ == "__main__":
 # Test to check if it works
 __lowercase    					=      array(
     [
         polar_force(7_18.4, 180 - 30),
         polar_force(8_79.54, 45),
         polar_force(100, -90),
     ]
 )

 __lowercase    					=      array([[0, 0], [0, 0], [0, 0]])

 assert in_static_equilibrium(forces, location)

 # Problem 1 in image_data/2D_problems.jpg
 __lowercase    					=      array(
     [
         polar_force(30 * 9.81, 15),
         polar_force(215, 180 - 45),
         polar_force(264, 90 - 30),
     ]
 )

 __lowercase    					=      array([[0, 0], [0, 0], [0, 0]])

 assert in_static_equilibrium(forces, location)

 # Problem in image_data/2D_problems_1.jpg
 __lowercase    					=      array([[0, -2000], [0, -1200], [0, 15600], [0, -12400]])

 __lowercase    					=      array([[0, 0], [6, 0], [10, 0], [12, 0]])

 assert in_static_equilibrium(forces, location)

 import doctest

 doctest.testmod()






