






'''simple docstring'''
from __future__ import annotations

from math import pi

# Define the Reduced Planck Constant ℏ (H bar), speed of light C, value of
# Pi and the function
UpperCamelCase__ =			1.054571817e-34  # unit of ℏ : J * s

UpperCamelCase__ =			3e8  # unit of c : m * s^-1




def 		__SCREAMING_SNAKE_CASE					(  _UpperCamelCase						,		_UpperCamelCase						,		_UpperCamelCase							):


   """simple docstring"""




   if (force, area, distance).count(0							) != 1:
      raise ValueError("One and only one argument must be 0"							)
   if force < 0:
      raise ValueError("Magnitude of force can not be negative"							)
   if distance < 0:
      raise ValueError("Distance can not be negative"							)
   if area < 0:
      raise ValueError("Area can not be negative"							)
   if force == 0:
      lowercase_	:    Union[str, Any]           =     (REDUCED_PLANCK_CONSTANT * SPEED_OF_LIGHT * pi**2 * area) / (
          240 * (distance) ** 4
      )
      return {"force": force}
   elif area == 0:
      lowercase_	:    Optional[int]           =     (240 * force * (distance) ** 4) / (
          REDUCED_PLANCK_CONSTANT * SPEED_OF_LIGHT * pi**2
      )
      return {"area": area}
   elif distance == 0:
      lowercase_	:    str           =     (
          (REDUCED_PLANCK_CONSTANT * SPEED_OF_LIGHT * pi**2 * area) / (240 * force)
      ) ** (1 / 4)
      return {"distance": distance}
   raise ValueError("One and only one argument must be 0"							)


# Run doctest
if __name__ == "__main__":
 import doctest

 doctest.testmod()












'''simple docstring'''
import heapq




def 		__SCREAMING_SNAKE_CASE					(  _UpperCamelCase							):


   """simple docstring"""




   lowercase_	:    list[list]           =     []

   # for each node and his adjacency list add them and the rank of the node to queue
   # using heapq module the queue will be filled like a Priority Queue
   # heapq works with a min priority queue, so I used -1*len(v) to build it
   for key, value in graph.items():
      # O(log(n))
      heapq.heappush(_UpperCamelCase						,		[-1 * len(_UpperCamelCase							), (key, value)]							)

   # chosen_vertices = set of chosen vertices
   lowercase_	:    Optional[Any]           =     set()

   # while queue isn't empty and there are still edges
   #   (queue[0][0] is the rank of the node with max rank)
   while queue and queue[0][0] != 0:
      # extract vertex with max rank from queue and add it to chosen_vertices
      lowercase_	:    Any           =     heapq.heappop(_UpperCamelCase							)[1][0]
      chosen_vertices.add(_UpperCamelCase							)

      # Remove all arcs adjacent to argmax
      for elem in queue:
         # if v haven't adjacent node, skip
         if elem[0] == 0:
            continue
         # if argmax is reachable from elem
         # remove argmax from elem's adjacent list and update his rank
         if argmax in elem[1][1]:
            lowercase_	:    str           =     elem[1][1].index(_UpperCamelCase							)
            del elem[1][1][index]
            elem[0] += 1
        # re-order the queue
      heapq.heapify(_UpperCamelCase							)
   return chosen_vertices


if __name__ == "__main__":
 import doctest

 doctest.testmod()

 UpperCamelCase__ =			{0: [1, 3], 1: [0, 3], 2: [0, 3, 4], 3: [0, 1, 2], 4: [2, 3]}
 print(f"""Minimum vertex cover:\n{greedy_min_vertex_cover(graph)}""")




