



import math
import sys





class       __lowerCAmelCase				:




				def __init__(							self	):



									"""simple docstring"""





									_lowerCAmelCase      			=					0
									_lowerCAmelCase      			=					[]
									_lowerCAmelCase      			=					{}  # To store the pos of node in array




				def 							snake_case     (							self	):



									"""simple docstring"""





									return self.cur_size == 0




				def 							snake_case     (							self		,       _snake_case	):



									"""simple docstring"""





									_lowerCAmelCase      			=					self.left(_snake_case	)
									_lowerCAmelCase      			=					self.right(_snake_case	)
									if lc < self.cur_size and self.array(_snake_case	)[0] < self.array(_snake_case	)[0]:
														_lowerCAmelCase      			=					lc
									else:
														_lowerCAmelCase      			=					idx
									if rc < self.cur_size and self.array(_snake_case	)[0] < self.array(_snake_case	)[0]:
														_lowerCAmelCase      			=					rc
									if smallest != idx:
														self.swap(_snake_case		,       _snake_case	)
														self.min_heapify(_snake_case	)




				def 							snake_case     (							self		,       _snake_case	):



									"""simple docstring"""





									_lowerCAmelCase      			=					self.cur_size
									self.cur_size += 1
									self.array.append((sys.maxsize, tup[1])	)
									self.decrease_key((sys.maxsize, tup[1])		,       tup[0]	)




				def 							snake_case     (							self	):



									"""simple docstring"""





									_lowerCAmelCase      			=					self.array[0][1]
									_lowerCAmelCase      			=					self.array[self.cur_size - 1]
									self.cur_size -= 1
									self.min_heapify(1	)
									del self.pos[min_node]
									return min_node




				def 							snake_case     (							self		,       _snake_case	):



									"""simple docstring"""





									return 2 * i + 1




				def 							snake_case     (							self		,       _snake_case	):



									"""simple docstring"""





									return 2 * i + 2




				def 							snake_case     (							self		,       _snake_case	):



									"""simple docstring"""





									return math.floor(i / 2	)




				def 							snake_case     (							self		,       _snake_case		,       _snake_case	):



									"""simple docstring"""





									_lowerCAmelCase      			=					j
									_lowerCAmelCase      			=					i
									_lowerCAmelCase      			=					self.array[i]
									_lowerCAmelCase      			=					self.array[j]
									_lowerCAmelCase      			=					temp




				def 							snake_case     (							self		,       _snake_case		,       _snake_case	):



									"""simple docstring"""





									_lowerCAmelCase      			=					self.pos[tup[1]]
									# assuming the new_d is atmost old_d
									_lowerCAmelCase      			=					(new_d, tup[1])
									while idx > 0 and self.array[self.par(_snake_case	)][0] > self.array[idx][0]:
														self.swap(_snake_case		,       self.par(_snake_case	)	)
														_lowerCAmelCase      			=					self.par(_snake_case	)





class       __lowerCAmelCase				:




				def __init__(							self		,       _snake_case	):



									"""simple docstring"""





									_lowerCAmelCase      			=					{}  # To store graph: u -> (v,w)
									_lowerCAmelCase      			=					num  # Number of nodes in graph
									# To store the distance from source vertex
									_lowerCAmelCase      			=					[0] * self.num_nodes
									_lowerCAmelCase      			=					[-1] * self.num_nodes  # To store the path




				def 							snake_case     (							self		,       _snake_case		,       _snake_case		,       _snake_case	):



									"""simple docstring"""





									if u in self.adjList:
														self.adjList[u].append((v, w)	)
									else:
														_lowerCAmelCase      			=					[(v, w)]

									# Assuming undirected graph
									if v in self.adjList:
														self.adjList[v].append((u, w)	)
									else:
														_lowerCAmelCase      			=					[(u, w)]




				def 							snake_case     (							self	):



									"""simple docstring"""





									for u in self.adjList:
														print(_snake_case		,       """->"""		,       """ -> """.join(str(F'{v}({w})'	) for v, w in self.adjList[u]	)	)




				def 							snake_case     (							self		,       _snake_case	):



									"""simple docstring"""





									_lowerCAmelCase      			=					[-1] * self.num_nodes
									# src is the source node
									_lowerCAmelCase      			=					0
									_lowerCAmelCase      			=					PriorityQueue()
									q.insert((0, src)	)  # (dist from src, node)
									for u in self.adjList:
														if u != src:
																			_lowerCAmelCase      			=					sys.maxsize  # Infinity
																			_lowerCAmelCase      			=					-1

									while not q.is_empty():
														_lowerCAmelCase      			=					q.extract_min()  # Returns node with the min dist from source
														# Update the distance of all the neighbours of u and
														# if their prev dist was INFINITY then push them in Q
														for v, w in self.adjList[u]:
																			_lowerCAmelCase      			=					self.dist[u] + w
																			if self.dist[v] > new_dist:
																								if self.dist[v] == sys.maxsize:
																													q.insert((new_dist, v)	)
																								else:
																													q.decrease_key((self.dist[v], v)		,       _snake_case	)
																								_lowerCAmelCase      			=					new_dist
																								_lowerCAmelCase      			=					u

        # Show the shortest distances from src
									self.show_distances(_snake_case	)




				def 							snake_case     (							self		,       _snake_case	):



									"""simple docstring"""





									print(F'Distance from node: {src}'	)
									for u in range(self.num_nodes	):
														print(F'Node {u} has distance: {self.dist[u]}'	)




				def 							snake_case     (							self		,       _snake_case		,       _snake_case	):



									"""simple docstring"""





									_lowerCAmelCase      			=					[]
									_lowerCAmelCase      			=					0
									_lowerCAmelCase      			=					dest
									# Backtracking from dest to src
									while self.par[temp] != -1:
														path.append(_snake_case	)
														if temp != src:
																			for v, w in self.adjList[temp]:
																								if v == self.par[temp]:
																													cost += w
																													break
														_lowerCAmelCase      			=					self.par[temp]
									path.append(_snake_case	)
									path.reverse()

									print(F'----Path to reach {dest} from {src}----'	)
									for u in path:
														print(F'{u}'		,       end=""" """	)
														if u != dest:
																			print("""-> """		,       end=""""""	)

									print("""\nTotal cost of path: """		,       _snake_case	)


if __name__ == "__main__":
	A__			   = Graph(9)
	graph.add_edge(0, 1, 4)
	graph.add_edge(0, 7, 8)
	graph.add_edge(1, 2, 8)
	graph.add_edge(1, 7, 11)
	graph.add_edge(2, 3, 7)
	graph.add_edge(2, 8, 2)
	graph.add_edge(2, 5, 4)
	graph.add_edge(3, 4, 9)
	graph.add_edge(3, 5, 14)
	graph.add_edge(4, 5, 10)
	graph.add_edge(5, 6, 2)
	graph.add_edge(6, 7, 1)
	graph.add_edge(6, 8, 6)
	graph.add_edge(7, 8, 7)
	graph.show_graph()
	graph.dijkstra(0)
	graph.show_path(0, 4)

# OUTPUT
# 0 -> 1(4) -> 7(8)
# 1 -> 0(4) -> 2(8) -> 7(11)
# 7 -> 0(8) -> 1(11) -> 6(1) -> 8(7)
# 2 -> 1(8) -> 3(7) -> 8(2) -> 5(4)
# 3 -> 2(7) -> 4(9) -> 5(14)
# 8 -> 2(2) -> 6(6) -> 7(7)
# 5 -> 2(4) -> 3(14) -> 4(10) -> 6(2)
# 4 -> 3(9) -> 5(10)
# 6 -> 5(2) -> 7(1) -> 8(6)
# Distance from node: 0
# Node 0 has distance: 0
# Node 1 has distance: 4
# Node 2 has distance: 12
# Node 3 has distance: 19
# Node 4 has distance: 21
# Node 5 has distance: 11
# Node 6 has distance: 9
# Node 7 has distance: 8
# Node 8 has distance: 14
# ----Path to reach 4 from 0----
# 0 -> 7 -> 6 -> 5 -> 4
# Total cost of path:  21








from __future__ import annotations


def 	_UpperCAmelCase       (   snake_case    ):





					"""simple docstring"""

					_lowerCAmelCase      			=					sorted(snake_case    )
					_lowerCAmelCase      			=					len(snake_case    )
					_lowerCAmelCase      			=					length >> 1
					return (
					    (sorted_list[mid_index] + sorted_list[mid_index - 1]) / 2
					    if length % 2 == 0
					    else sorted_list[mid_index]
					)


def 	_UpperCAmelCase       (   ):





					"""simple docstring"""

					import doctest

					doctest.testmod()


if __name__ == "__main__":
	main()



