code: 
  
  
  
  
  
  
  '''simple docstring'''
  
  
  
  
  
  import math
  import sys
  class 	a__				:
  
  
  
  
  
  			'''simple docstring'''
  
  			def __init__(     self       : List[str]  )			->		Dict:
  						__A=  0
  						__A=  []
  						__A=  {}  # To store the pos of node in array
  			def 				lowerCAmelCase    (     self       : Tuple  )			->		Any:
  						return self.cur_size == 0
  			def 				lowerCAmelCase    (     self       : List[Any] ,						lowerCAmelCase_       : Optional[Any]  )			->		Dict:
  						__A=  self.left(lowerCAmelCase_  )
  						__A=  self.right(lowerCAmelCase_  )
  						if lc < self.cur_size and self.array(lowerCAmelCase_  )[0] < self.array(lowerCAmelCase_  )[0]:
  									__A=  lc
  						else:
  									__A=  idx
  						if rc < self.cur_size and self.array(lowerCAmelCase_  )[0] < self.array(lowerCAmelCase_  )[0]:
  									__A=  rc
  						if smallest != idx:
  									self.swap(lowerCAmelCase_ ,						lowerCAmelCase_  )
  									self.min_heapify(lowerCAmelCase_  )
  			def 				lowerCAmelCase    (     self       : Union[str, Any] ,						lowerCAmelCase_       : Union[str, Any]  )			->		Tuple:
  						# Inserts a node into the Priority Queue
  						__A=  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       : Optional[Any]  )			->		int:
  						# Removes and returns the min element at top of priority queue
  						__A=  self.array[0][1]
  						__A=  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       : str ,						lowerCAmelCase_       : Optional[Any]  )			->		List[str]:
  						# returns the index of left child
  						return 2 * i + 1
  			def 				lowerCAmelCase    (     self       : Union[str, Any] ,						lowerCAmelCase_       : Optional[int]  )			->		int:
  						# returns the index of right child
  						return 2 * i + 2
  			def 				lowerCAmelCase    (     self       : List[Any] ,						lowerCAmelCase_       : List[Any]  )			->		List[str]:
  						# returns the index of parent
  						return math.floor(i / 2  )
  			def 				lowerCAmelCase    (     self       : Dict ,						lowerCAmelCase_       : Any ,						lowerCAmelCase_       : str  )			->		Any:
  						# swaps array elements at indices i and j
  						# update the pos{}
  						__A=  j
  						__A=  i
  						__A=  self.array[i]
  						__A=  self.array[j]
  						__A=  temp
  
  			def 				lowerCAmelCase    (     self       : Union[str, Any] ,						lowerCAmelCase_       : Dict ,						lowerCAmelCase_       : Optional[Any]  )			->		int:
  						__A=  self.pos[tup[1]]
  						# assuming the new_d is atmost old_d
  						__A=  (new_d, tup[1])
  						while idx > 0 and self.array[self.par(lowerCAmelCase_  )][0] > self.array[idx][0]:
  									self.swap(lowerCAmelCase_ ,						self.par(lowerCAmelCase_  )  )
  									__A=  self.par(lowerCAmelCase_  )
  
  
  class 	a__				:
  
  
  
  
  
  			'''simple docstring'''
  
  			def __init__(     self       : List[Any] ,						lowerCAmelCase_       : str  )			->		str:
  						__A=  {}  # To store graph: u -> (v,w)
  						__A=  num  # Number of nodes in graph
  						# To store the distance from source vertex
  						__A=  [0] * self.num_nodes
  						__A=  [-1] * self.num_nodes  # To store the path
  			def 				lowerCAmelCase    (     self       : Any ,						lowerCAmelCase_       : Any ,						lowerCAmelCase_       : Tuple ,						lowerCAmelCase_       : Any  )			->		Tuple:
  						#  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:
  									__A=  [(v, w)]
  
  						# Assuming undirected graph
  						if v in self.adjList:
  									self.adjList[v].append((u, w)  )
  						else:
  									__A=  [(u, w)]
  			def 				lowerCAmelCase    (     self       : str  )			->		str:
  						# u -> v(w)
  						for u in self.adjList:
  									print(lowerCAmelCase_ ,						'->' ,						' -> '.join(str(F"""{v}({w})"""  ) for v, w in self.adjList[u]  )  )
  			def 				lowerCAmelCase    (     self       : Any ,						lowerCAmelCase_       : str  )			->		Optional[Any]:
  						# Flush old junk values in par[]
  						__A=  [-1] * self.num_nodes
  						# src is the source node
  						__A=  0
  						__A=  PriorityQueue()
  						q.insert((0, src)  )  # (dist from src, node)
  						for u in self.adjList:
  									if u != src:
  												__A=  sys.maxsize  # Infinity
  												__A=  -1
  
  						while not q.is_empty():
  									__A=  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]:
  												__A=  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) ,						lowerCAmelCase_  )
  															__A=  new_dist
  															__A=  u
  
          # Show the shortest distances from src
  						self.show_distances(lowerCAmelCase_  )
  			def 				lowerCAmelCase    (     self       : Tuple ,						lowerCAmelCase_       : Any  )			->		Optional[Any]:
  						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       : str ,						lowerCAmelCase_       : Optional[int] ,						lowerCAmelCase_       : List[str]  )			->		int:
  						# To show the shortest path from src to dest
  						# WARNING: Use it *after* calling dijkstra
  						__A=  []
  						__A=  0
  						__A=  dest
  						# Backtracking from dest to src
  						while self.par[temp] != -1:
  									path.append(lowerCAmelCase_  )
  									if temp != src:
  												for v, w in self.adjList[temp]:
  															if v == self.par[temp]:
  																		cost += w
  																		break
  									__A=  self.par[temp]
  						path.append(lowerCAmelCase_  )
  						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: ' ,						lowerCAmelCase_  )
  
  
  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, 1_1)
  					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, 1_4)
  					graph.add_edge(4, 5, 1_0)
  					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
  
  
  
  
style_context: 
  
  
  '''simple docstring'''
  
  
  
  
  
  import numpy as np
  from cva import destroyAllWindows, imread, imshow, waitKey
  class 	a__				:
  
  
  
  
  
  			'''simple docstring'''
  
  			def __init__(     self       : Dict ,						lowerCAmelCase_       : Optional[Any] ,						lowerCAmelCase_       : int  )			->		Optional[int]:
  						__A=  0
  						# max greyscale value for #FFFFFF
  						__A=  int(self.get_greyscale(255 ,						255 ,						255  )  )
  
  						if not self.min_threshold < threshold < self.max_threshold:
  									__A=  F"""Factor value should be from 0 to {self.max_threshold}"""
  									raise ValueError(lowerCAmelCase_  )
  
  						__A=  input_img
  						__A=  threshold
  						__A,  __A=  self.input_img.shape[1], self.input_img.shape[0]
  
  						# error table size (+4 columns and +1 row) greater than input image because of
  						# lack of if statements
  						__A=  [
  						    [0 for _ in range(self.height + 4  )] for __ in range(self.width + 1  )
  						]
  						__A=  np.ones((self.width, self.height, 3) ,						np.uinta  ) * 255
  			@classmethod
  			def 				lowerCAmelCase    (     cls       : Tuple ,						lowerCAmelCase_       : int ,						lowerCAmelCase_       : int ,						lowerCAmelCase_       : int  )			->		float:
  						return 0.1_14 * blue + 0.5_87 * green + 0.21_26 * red
  
  			def 				lowerCAmelCase    (     self       : str  )			->		None:
  						for y in range(self.height  ):
  									for x in range(self.width  ):
  												__A=  int(self.get_greyscale(*self.input_img[y][x]  )  )
  												if self.threshold > greyscale + self.error_table[y][x]:
  															__A=  (0, 0, 0)
  															__A=  greyscale + self.error_table[x][y]
  												else:
  															__A=  (255, 255, 255)
  															__A=  greyscale + self.error_table[x][y] - 255
  												self.error_table[y][x + 1] += int(8 / 32 * current_error  )
  												self.error_table[y][x + 2] += int(4 / 32 * current_error  )
  												self.error_table[y + 1][x] += int(8 / 32 * current_error  )
  												self.error_table[y + 1][x + 1] += int(4 / 32 * current_error  )
  												self.error_table[y + 1][x + 2] += int(2 / 32 * current_error  )
  												self.error_table[y + 1][x - 1] += int(4 / 32 * current_error  )
  												self.error_table[y + 1][x - 2] += int(2 / 32 * current_error  )
  
  
  if __name__ == "__main__":
  					# create Burke's instances with original images in greyscale
  					UpperCAmelCase__      =							[
  					    Burkes(imread('''image_data/lena.jpg''', 1), threshold)
  					    for threshold in (1, 1_2_6, 1_3_0, 1_4_0)
  					]
  
  					for burkes in burkes_instances:
  										burkes.process()
  
  					for burkes in burkes_instances:
  										imshow(
  										    F"""Original image with dithering threshold: {burkes.threshold}""",
  										    burkes.output_img,
  										)
  
  					waitKey(0)
  					destroyAllWindows()
  
  
  
  