



'''simple docstring'''

from __future__ import annotations

from collections.abc import Callable
from typing import Any, Generic, TypeVar

__lowerCAmelCase						      =       TypeVar('''T''')

class      __magic_name__						(   Generic[T]       ):







       def __init__(							self :	Any     ,_UpperCAmelCase :	list[T]     ,_UpperCAmelCase :	Callable[[T, T], T]		):
         _a					:				Any | T				=							None

         _a					:				int				=							len(_UpperCAmelCase		)
         _a					:				list[T]				=							[any_type for _ in range(self.N		)] + arr
         _a					:				List[str]				=							fnc
         self.build()







       def 							__lowercase      (							self :	List[Any]		):
         for p in range(self.N - 1     ,0     ,-1		):
           _a					:				Optional[Any]				=							self.fn(self.st[p * 2]     ,self.st[p * 2 + 1]		)







       def 							__lowercase      (							self :	List[str]     ,_UpperCAmelCase :	int     ,_UpperCAmelCase :	T		):
         p += self.N
         _a					:				List[Any]				=							v
         while p > 1:
           _a					:				Any				=							p // 2
           _a					:				Union[str, Any]				=							self.fn(self.st[p * 2]     ,self.st[p * 2 + 1]		)







       def 							__lowercase      (							self :	str     ,_UpperCAmelCase :	int     ,_UpperCAmelCase :	int		):  # noqa: E741
         _a					:				Union[str, Any]				=							l + self.N, r + self.N

         _a					:				T | None				=							None
         while l <= r:
           if l % 2 == 1:
             _a					:				List[Any]				=							self.st[l] if res is None else self.fn(_UpperCAmelCase     ,self.st[l]		)
           if r % 2 == 0:
             _a					:				Optional[int]				=							self.st[r] if res is None else self.fn(_UpperCAmelCase     ,self.st[r]		)
           _a					:				int				=							(l + 1) // 2, (r - 1) // 2
         return res


if __name__ == "__main__":
       from functools import reduce

       __lowerCAmelCase						      =       [1, 10, -2, 9, -3, 8, 4, -7, 5, 6, 11, -12]

       __lowerCAmelCase						      =       {
           0: 7,
           1: 2,
           2: 6,
           3: -14,
           4: 5,
           5: 4,
           6: 7,
           7: -10,
           8: 9,
           9: 10,
           10: 12,
           11: 1,
       }

       __lowerCAmelCase						      =       SegmentTree(test_array, min)
       __lowerCAmelCase						      =       SegmentTree(test_array, max)
       __lowerCAmelCase						      =       SegmentTree(test_array, lambda a, b: a + b)



       def 					__lowerCamelCase					(				)      ->				None:
         for i in range(len(lowerCAmelCase_  )  ):
           for j in range(lowerCAmelCase_						,      len(lowerCAmelCase_  )  ):
             _a					:				Tuple				=							reduce(lowerCAmelCase_						,      test_array[i : j + 1]  )
             _a					:				List[Any]				=							reduce(lowerCAmelCase_						,      test_array[i : j + 1]  )
             _a					:				Optional[int]				=							reduce(lambda lowerCAmelCase_						,      lowerCAmelCase_  : a + b						,      test_array[i : j + 1]  )
             assert min_range == min_segment_tree.query(lowerCAmelCase_						,      lowerCAmelCase_  )
             assert max_range == max_segment_tree.query(lowerCAmelCase_						,      lowerCAmelCase_  )
             assert sum_range == sum_segment_tree.query(lowerCAmelCase_						,      lowerCAmelCase_  )

       test_all_segments()

       for index, value in test_updates.items():
              __lowerCAmelCase						      =       value
              min_segment_tree.update(index, value)
              max_segment_tree.update(index, value)
              sum_segment_tree.update(index, value)
              test_all_segments()









'''simple docstring'''

import heapq



def 					__lowerCamelCase					(				lowerCAmelCase_  )      ->				set[int]:
		_a					:				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(lowerCAmelCase_						,      [-1 * len(lowerCAmelCase_  ), (key, value)]  )

		# chosen_vertices = set of chosen vertices
		_a					:				str				=							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
				_a					:				Optional[int]				=							heapq.heappop(lowerCAmelCase_  )[1][0]
				chosen_vertices.add(lowerCAmelCase_  )

				# 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]:
								_a					:				Dict				=							elem[1][1].index(lowerCAmelCase_  )
								del elem[1][1][index]
								elem[0] += 1
        # re-order the queue
				heapq.heapify(lowerCAmelCase_  )
		return chosen_vertices


if __name__ == "__main__":
							import doctest

							doctest.testmod()

							__lowerCAmelCase						      =       {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)}""")




