




import math
import sys
class 							lowerCamelCase		:







   def __init__(							self ):
       UpperCamelCase				:   Tuple          =							0
       UpperCamelCase				:   Optional[int]          =							[]
       UpperCamelCase				:   Optional[int]          =							{}  # To store the pos of node in array







   def       a_							(							self ):
       return self.cur_size == 0







   def       a_							(							self    ,      SCREAMING_SNAKE_CASE_ ):
       UpperCamelCase				:   List[str]          =							self.left(SCREAMING_SNAKE_CASE_ )
       UpperCamelCase				:   Optional[int]          =							self.right(SCREAMING_SNAKE_CASE_ )
       if lc < self.cur_size and self.array(SCREAMING_SNAKE_CASE_ )[0] < self.array(SCREAMING_SNAKE_CASE_ )[0]:
           UpperCamelCase				:   str          =							lc
       else:
           UpperCamelCase				:   Union[str, Any]          =							idx
       if rc < self.cur_size and self.array(SCREAMING_SNAKE_CASE_ )[0] < self.array(SCREAMING_SNAKE_CASE_ )[0]:
           UpperCamelCase				:   Optional[Any]          =							rc
       if smallest != idx:
           self.swap(SCREAMING_SNAKE_CASE_    ,      SCREAMING_SNAKE_CASE_ )
           self.min_heapify(SCREAMING_SNAKE_CASE_ )







   def       a_							(							self    ,      SCREAMING_SNAKE_CASE_ ):
       # Inserts a node into the Priority Queue
       UpperCamelCase				:   List[Any]          =							self.cur_size
       self.cur_size += 1
       self.array.append((sys.maxsize, tup[1]) )
       self.decrease_key((sys.maxsize, tup[1])    ,      tup[0] )







   def       a_							(							self ):
       # Removes and returns the min element at top of priority queue
       UpperCamelCase				:   str          =							self.array[0][1]
       UpperCamelCase				:   Optional[int]          =							self.array[self.cur_size - 1]
       self.cur_size -= 1
       self.min_heapify(1 )
       del self.pos[min_node]
       return min_node







   def       a_							(							self    ,      SCREAMING_SNAKE_CASE_ ):
       # returns the index of left child
       return 2 * i + 1







   def       a_							(							self    ,      SCREAMING_SNAKE_CASE_ ):
       # returns the index of right child
       return 2 * i + 2







   def       a_							(							self    ,      SCREAMING_SNAKE_CASE_ ):
       # returns the index of parent
       return math.floor(i / 2 )







   def       a_							(							self    ,      SCREAMING_SNAKE_CASE_    ,      SCREAMING_SNAKE_CASE_ ):
       # swaps array elements at indices i and j
       # update the pos{}
       UpperCamelCase				:   Dict          =							j
       UpperCamelCase				:   List[str]          =							i
       UpperCamelCase				:   Optional[int]          =							self.array[i]
       UpperCamelCase				:   Union[str, Any]          =							self.array[j]
       UpperCamelCase				:   Optional[int]          =							temp







   def       a_							(							self    ,      SCREAMING_SNAKE_CASE_    ,      SCREAMING_SNAKE_CASE_ ):
       UpperCamelCase				:   Tuple          =							self.pos[tup[1]]
       # assuming the new_d is atmost old_d
       UpperCamelCase				:   Union[str, Any]          =							(new_d, tup[1])
       while idx > 0 and self.array[self.par(SCREAMING_SNAKE_CASE_ )][0] > self.array[idx][0]:
           self.swap(SCREAMING_SNAKE_CASE_    ,      self.par(SCREAMING_SNAKE_CASE_ ) )
           UpperCamelCase				:   Union[str, Any]          =							self.par(SCREAMING_SNAKE_CASE_ )







class 							lowerCamelCase		:







   def __init__(							self    ,      SCREAMING_SNAKE_CASE_ ):
       UpperCamelCase				:   Any          =							{}  # To store graph: u -> (v,w)
       UpperCamelCase				:   int          =							num  # Number of nodes in graph
       # To store the distance from source vertex
       UpperCamelCase				:   Any          =							[0] * self.num_nodes
       UpperCamelCase				:   Union[str, Any]          =							[-1] * self.num_nodes  # To store the path







   def       a_							(							self    ,      SCREAMING_SNAKE_CASE_    ,      SCREAMING_SNAKE_CASE_    ,      SCREAMING_SNAKE_CASE_ ):
       #  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:
           UpperCamelCase				:   Optional[int]          =							[(v, w)]

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







   def       a_							(							self ):
       # u -> v(w)
       for u in self.adjList:
           print(SCREAMING_SNAKE_CASE_    ,      """->"""    ,      """ -> """.join(str(f'{v}({w})' ) for v, w in self.adjList[u] ) )







   def       a_							(							self    ,      SCREAMING_SNAKE_CASE_ ):
       # Flush old junk values in par[]
       UpperCamelCase				:   Tuple          =							[-1] * self.num_nodes
       # src is the source node
       UpperCamelCase				:   Dict          =							0
       UpperCamelCase				:   int          =							PriorityQueue()
       q.insert((0, src) )  # (dist from src, node)
       for u in self.adjList:
           if u != src:
               UpperCamelCase				:   Any          =							sys.maxsize  # Infinity
               UpperCamelCase				:   int          =							-1

       while not q.is_empty():
           UpperCamelCase				:   int          =							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]:
               UpperCamelCase				:   List[Any]          =							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)    ,      SCREAMING_SNAKE_CASE_ )
                   UpperCamelCase				:   Any          =							new_dist
                   UpperCamelCase				:   Tuple          =							u

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







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







   def       a_							(							self    ,      SCREAMING_SNAKE_CASE_    ,      SCREAMING_SNAKE_CASE_ ):
       # To show the shortest path from src to dest
       # WARNING: Use it *after* calling dijkstra
       UpperCamelCase				:   Tuple          =							[]
       UpperCamelCase				:   Optional[Any]          =							0
       UpperCamelCase				:   int          =							dest
       # Backtracking from dest to src
       while self.par[temp] != -1:
           path.append(SCREAMING_SNAKE_CASE_ )
           if temp != src:
               for v, w in self.adjList[temp]:
                   if v == self.par[temp]:
                       cost += w
                       break
           UpperCamelCase				:   int          =							self.par[temp]
       path.append(SCREAMING_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: """    ,      SCREAMING_SNAKE_CASE_ )


if __name__ == "__main__":
  __A :		int      							=    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










"""simple docstring"""




import numpy as np
import PIL
import torch
import torchvision.transforms as T
import torchvision.transforms.functional as TF
from PIL import Image
def 					A_			(		snake_case_     :       List[str]						,snake_case_     :       Union[str, Any]=2_5_6    ):







    '''simple docstring'''
    UpperCamelCase				:   Optional[int]          =							min(img.size    )

    if s < target_image_size:
        raise ValueError(f'min dim for image {s} < {target_image_size}'    )

    UpperCamelCase				:   Dict          =							target_image_size / s
    UpperCamelCase				:   Any          =							(round(r * img.size[1]    ), round(r * img.size[0]    ))
    UpperCamelCase				:   Union[str, Any]          =							TF.resize(snake_case_						,snake_case_						,interpolation=PIL.Image.LANCZOS    )
    UpperCamelCase				:   Optional[int]          =							TF.center_crop(snake_case_						,output_size=2 * [target_image_size]    )
    UpperCamelCase				:   Optional[Any]          =							torch.unsqueeze(T.ToTensor()(snake_case_    )						,0    )
    return img
def 					A_			(		snake_case_     :       List[Any]    ):







    '''simple docstring'''
    UpperCamelCase				:   Any          =							2.0 * x - 1.0
    return x
def 					A_			(		snake_case_     :       Tuple						,snake_case_     :       Optional[Any]=True						,snake_case_     :       Dict="RGB"    ):







    '''simple docstring'''
    UpperCamelCase				:   Dict          =							x.detach().cpu()
    if process:
        UpperCamelCase				:   str          =							post_process_tensor(snake_case_    )
    UpperCamelCase				:   List[Any]          =							x.numpy()
    if process:
        UpperCamelCase				:   Optional[int]          =							(2_5_5 * x).astype(np.uinta    )
    UpperCamelCase				:   List[Any]          =							Image.fromarray(snake_case_    )
    if not x.mode == mode:
        UpperCamelCase				:   Any          =							x.convert(snake_case_    )
    return x
def 					A_			(		snake_case_     :       int    ):







    '''simple docstring'''
    UpperCamelCase				:   int          =							torch.clamp(snake_case_						,-1.0						,1.0    )
    UpperCamelCase				:   Optional[Any]          =							(x + 1.0) / 2.0
    UpperCamelCase				:   Dict          =							x.permute(1						,2						,0    )
    return x


def 					A_			(		snake_case_     :       int    ):







    '''simple docstring'''
    UpperCamelCase				:   Optional[Any]          =							post_process_tensor(x.squeeze()    )
    return x.permute(2						,0						,1    ).unsqueeze(0    )




