from __future__ import annotations

from abc import abstractmethod
from collections.abc import Iterable
from typing import Generic, Protocol, TypeVar





class   lowerCAmelCase    (       _a      ):



     @abstractmethod
     def __lt__(       self					,   lowerCAmelCase__							):
            pass



     @abstractmethod
     def __gt__(       self					,   lowerCAmelCase__							):
            pass





     @abstractmethod
     def __eq__(       self					,   lowerCAmelCase__							):
            pass


UpperCAmelCase_    		=				TypeVar('''T''', bound=Comparable)





class   lowerCAmelCase    (       Generic[T]      ):



     def __init__(       self							):
            _A=						[]
            _A=						0



     def __repr__(       self							):
            return str(self.h							)



     def       a__	(       self					,   lowerCAmelCase__							):
            if child_idx > 0:
                   return (child_idx - 1) // 2
            return None



     def       a__	(       self					,   lowerCAmelCase__							):
            _A=						2 * parent_idx + 1
            if left_child_index < self.heap_size:
                   return left_child_index
            return None



     def       a__	(       self					,   lowerCAmelCase__							):
            _A=						2 * parent_idx + 2
            if right_child_index < self.heap_size:
                   return right_child_index
            return None



     def       a__	(       self					,   lowerCAmelCase__							):
            if index < self.heap_size:
                   _A=						index
                   _A=						self.left_child_idx(lowerCAmelCase__							)
                   _A=						self.right_child_idx(lowerCAmelCase__							)
                   # check which child is larger than its parent
                   if left_child is not None and self.h[left_child] > self.h[violation]:
                          _A=						left_child
                   if right_child is not None and self.h[right_child] > self.h[violation]:
                          _A=						right_child
                   # if violation indeed exists
                   if violation != index:
                          # swap to fix the violation
                          _A,      _A=						self.h[index], self.h[violation]
                          # fix the subsequent violation recursively if any
                          self.max_heapify(lowerCAmelCase__							)



     def       a__	(       self					,   lowerCAmelCase__							):
            _A=						list(lowerCAmelCase__							)
            _A=						len(self.h							)
            if self.heap_size > 1:
                   # max_heapify from right to left but exclude leaves (last level)
                   for i in range(self.heap_size // 2 - 1					,   -1					,   -1							):
                          self.max_heapify(lowerCAmelCase__							)



     def       a__	(       self							):
            if self.heap_size >= 2:
                   _A=						self.h[0]
                   _A=						self.h.pop(-1							)
                   self.heap_size -= 1
                   self.max_heapify(0							)
                   return me
            elif self.heap_size == 1:
                   self.heap_size -= 1
                   return self.h.pop(-1							)
            else:
                   raise Exception('Empty heap'							)



     def       a__	(       self					,   lowerCAmelCase__							):
            self.h.append(lowerCAmelCase__							)
            _A=						(self.heap_size - 1) // 2
            self.heap_size += 1
            while idx >= 0:
                   self.max_heapify(lowerCAmelCase__							)
                   _A=						(idx - 1) // 2





     def       a__	(       self							):
            _A=						self.heap_size
            for j in range(size - 1					,   0					,   -1							):
                   _A,      _A=						self.h[j], self.h[0]
                   self.heap_size -= 1
                   self.max_heapify(0							)
            _A=						size


if __name__ == "__main__":
      import doctest

      # run doc test
      doctest.testmod()

      # demo
      for unsorted in [
          [0],
          [2],
          [3, 5],
          [5, 3],
          [5, 5],
          [0, 0, 0, 0],
          [1, 1, 1, 1],
          [2, 2, 3, 5],
          [0, 2, 2, 3, 5],
          [2, 5, 3, 0, 2, 3, 0, 3],
          [6, 1, 2, 7, 9, 3, 4, 5, 10, 8],
          [103, 9, 1, 7, 11, 15, 25, 201, 209, 107, 5],
          [-45, -2, -5],
      ]:
            print(F"unsorted array: {unsorted}")

            UpperCAmelCase_    		=				Heap()
            heap.build_max_heap(unsorted)
            print(F"after build heap: {heap}")

            print(F"max value: {heap.extract_max()}")
            print(F"after max value removed: {heap}")

            heap.insert(100)
            print(F"after new value 100 inserted: {heap}")

            heap.heap_sort()
            print(F"heap-sorted array: {heap}\n")
import heapq

def 				UpperCamelCase					(     lowerCAmelCase_							,       lowerCAmelCase_							,       lowerCAmelCase_ )		->    Dict:




       '''simple docstring'''






       _A=						[(0, start)]  # cost from start node,end node
       _A=						set()
       while heap:
              ((_A),      (_A))=						heapq.heappop(lowerCAmelCase_ )
              if u in visited:
                     continue
              visited.add(lowerCAmelCase_ )
              if u == end:
                     return cost
              for v, c in graph[u]:
                     if v in visited:
                            continue
                     _A=						cost + c
                     heapq.heappush(lowerCAmelCase_							,       (next_item, v) )
       return -1


UpperCAmelCase_    		=				{
    '''A''': [['''B''', 2], ['''C''', 5]],
    '''B''': [['''A''', 2], ['''D''', 3], ['''E''', 1], ['''F''', 1]],
    '''C''': [['''A''', 5], ['''F''', 3]],
    '''D''': [['''B''', 3]],
    '''E''': [['''B''', 4], ['''F''', 3]],
    '''F''': [['''C''', 3], ['''E''', 3]],
}
UpperCAmelCase_    		=				{
    '''B''': [['''C''', 1]],
    '''C''': [['''D''', 1]],
    '''D''': [['''F''', 1]],
    '''E''': [['''B''', 1], ['''F''', 3]],
    '''F''': [],
}
UpperCAmelCase_    		=				{
    '''B''': [['''C''', 1]],
    '''C''': [['''D''', 1]],
    '''D''': [['''F''', 1]],
    '''E''': [['''B''', 1], ['''G''', 2]],
    '''F''': [],
    '''G''': [['''F''', 1]],
}

UpperCAmelCase_    		=				dijkstra(G, '''E''', '''C''')
print(short_distance)  # E -- 3 --> F -- 3 --> C == 6

UpperCAmelCase_    		=				dijkstra(Ga, '''E''', '''F''')
print(short_distance)  # E -- 3 --> F == 3

UpperCAmelCase_    		=				dijkstra(Ga, '''E''', '''F''')
print(short_distance)  # E -- 2 --> G -- 1 --> F == 3

if __name__ == "__main__":
      import doctest

      doctest.testmod()