




import math
import sys





class        lowerCamelCase__:
      def __init__(							self:					Optional[Any]  ):
             __lowerCamelCase  =		0
             __lowerCamelCase  =		[]
             __lowerCamelCase  =		{}  # To store the pos of node in array
      def      lowerCAmelCase__		(							self:					str  ):
             return self.cur_size == 0
      def      lowerCAmelCase__		(							self:					str       ,			UpperCamelCase_:					List[str]  ):
             __lowerCamelCase  =		self.left(UpperCamelCase_  )
             __lowerCamelCase  =		self.right(UpperCamelCase_  )
             if lc < self.cur_size and self.array(UpperCamelCase_  )[0] < self.array(UpperCamelCase_  )[0]:
                    __lowerCamelCase  =		lc
             else:
                    __lowerCamelCase  =		idx
             if rc < self.cur_size and self.array(UpperCamelCase_  )[0] < self.array(UpperCamelCase_  )[0]:
                    __lowerCamelCase  =		rc
             if smallest != idx:
                    self.swap(UpperCamelCase_       ,			UpperCamelCase_  )
                    self.min_heapify(UpperCamelCase_  )
      def      lowerCAmelCase__		(							self:					Union[str, Any]       ,			UpperCamelCase_:					Optional[int]  ):
             # Inserts a node into the Priority Queue
             __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      lowerCAmelCase__		(							self:					List[Any]  ):
             # Removes and returns the min element at top of priority queue
             __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      lowerCAmelCase__		(							self:					List[Any]       ,			UpperCamelCase_:					int  ):
             # returns the index of left child
             return 2 * i + 1
      def      lowerCAmelCase__		(							self:					Tuple       ,			UpperCamelCase_:					int  ):
             # returns the index of right child
             return 2 * i + 2
      def      lowerCAmelCase__		(							self:					List[Any]       ,			UpperCamelCase_:					int  ):
             # returns the index of parent
             return math.floor(i / 2  )
      def      lowerCAmelCase__		(							self:					Union[str, Any]       ,			UpperCamelCase_:					Tuple       ,			UpperCamelCase_:					Tuple  ):
             # swaps array elements at indices i and j
             # update the pos{}
             __lowerCamelCase  =		j
             __lowerCamelCase  =		i
             __lowerCamelCase  =		self.array[i]
             __lowerCamelCase  =		self.array[j]
             __lowerCamelCase  =		temp




      def      lowerCAmelCase__		(							self:					Tuple       ,			UpperCamelCase_:					Union[str, Any]       ,			UpperCamelCase_:					Optional[int]  ):
             __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(UpperCamelCase_  )][0] > self.array[idx][0]:
                    self.swap(UpperCamelCase_       ,			self.par(UpperCamelCase_  )  )
                    __lowerCamelCase  =		self.par(UpperCamelCase_  )





class        lowerCamelCase__:
      def __init__(							self:					List[Any]       ,			UpperCamelCase_:					Dict  ):
             __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      lowerCAmelCase__		(							self:					Optional[Any]       ,			UpperCamelCase_:					str       ,			UpperCamelCase_:					Optional[int]       ,			UpperCamelCase_:					Union[str, Any]  ):
             #  Edge going from node u to v and v to u with weight w
             # u (w)-> v, v (w) -> u
             # Check if u already in graph
             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      lowerCAmelCase__		(							self:					Union[str, Any]  ):
             # u -> v(w)
             for u in self.adjList:
                    print(UpperCamelCase_       ,			"""->"""       ,			""" -> """.join(str(F'{v}({w})'  ) for v, w in self.adjList[u]  )  )
      def      lowerCAmelCase__		(							self:					Tuple       ,			UpperCamelCase_:					Optional[Any]  ):
             # Flush old junk values in par[]
             __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)       ,			UpperCamelCase_  )
                                  __lowerCamelCase  =		new_dist
                                  __lowerCamelCase  =		u

        # Show the shortest distances from src
             self.show_distances(UpperCamelCase_  )
      def      lowerCAmelCase__		(							self:					List[Any]       ,			UpperCamelCase_:					Tuple  ):
             print(F'Distance from node: {src}'  )
             for u in range(self.num_nodes  ):
                    print(F'Node {u} has distance: {self.dist[u]}'  )




      def      lowerCAmelCase__		(							self:					List[str]       ,			UpperCamelCase_:					str       ,			UpperCamelCase_:					List[Any]  ):
             # To show the shortest path from src to dest
             # WARNING: Use it *after* calling dijkstra
             __lowerCamelCase  =		[]
             __lowerCamelCase  =		0
             __lowerCamelCase  =		dest
             # Backtracking from dest to src
             while self.par[temp] != -1:
                    path.append(UpperCamelCase_  )
                    if temp != src:
                           for v, w in self.adjList[temp]:
                                  if v == self.par[temp]:
                                         cost += w
                                         break
                    __lowerCamelCase  =		self.par[temp]
             path.append(UpperCamelCase_  )
             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: """       ,			UpperCamelCase_  )


if __name__ == "__main__":
       UpperCAmelCase_   							=      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 typing import TYPE_CHECKING

from ...utils import OptionalDependencyNotAvailable, _LazyModule, is_torch_available


UpperCAmelCase_   							=      {'configuration_dinat': ['DINAT_PRETRAINED_CONFIG_ARCHIVE_MAP', 'DinatConfig']}


try:
       if not is_torch_available():
              raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
       pass
else:
       UpperCAmelCase_   							=      [
           'DINAT_PRETRAINED_MODEL_ARCHIVE_LIST',
           'DinatForImageClassification',
           'DinatModel',
           'DinatPreTrainedModel',
           'DinatBackbone',
       ]

if TYPE_CHECKING:
       from .configuration_dinat import DINAT_PRETRAINED_CONFIG_ARCHIVE_MAP, DinatConfig

       try:
              if not is_torch_available():
                     raise OptionalDependencyNotAvailable()
       except OptionalDependencyNotAvailable:
              pass
       else:
              from .modeling_dinat import (
                  DINAT_PRETRAINED_MODEL_ARCHIVE_LIST,
                  DinatBackbone,
                  DinatForImageClassification,
                  DinatModel,
                  DinatPreTrainedModel,
              )

else:
       import sys

       UpperCAmelCase_   							=      _LazyModule(__name__, globals()['__file__'], _import_structure, module_spec=__spec__)

