code: 
  
  
  
  
  
  
  import math
  import sys
  
  
  
  
  
  
  
  class 							UpperCAmelCase_     :
  
  
  
  
       def __init__(							self		):
            UpperCAmelCase__			:     Union[str, Any]										= 0
            UpperCAmelCase__			:     Tuple										= []
            UpperCAmelCase__			:     Optional[Any]										= {}  # To store the pos of node in array
  
  
  
  
       def      __UpperCAmelCase     (							self		):
            return self.cur_size == 0
  
  
  
  
       def      __UpperCAmelCase     (							self  ,	_lowerCAmelCase		):
            UpperCAmelCase__			:     str										= self.left(_lowerCAmelCase		)
            UpperCAmelCase__			:     int										= self.right(_lowerCAmelCase		)
            if lc < self.cur_size and self.array(_lowerCAmelCase		)[0] < self.array(_lowerCAmelCase		)[0]:
                 UpperCAmelCase__			:     List[str]										= lc
            else:
                 UpperCAmelCase__			:     Optional[int]										= idx
            if rc < self.cur_size and self.array(_lowerCAmelCase		)[0] < self.array(_lowerCAmelCase		)[0]:
                 UpperCAmelCase__			:     Tuple										= rc
            if smallest != idx:
                 self.swap(_lowerCAmelCase  ,	_lowerCAmelCase		)
                 self.min_heapify(_lowerCAmelCase		)
  
  
  
  
       def      __UpperCAmelCase     (							self  ,	_lowerCAmelCase		):
            # 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      __UpperCAmelCase     (							self		):
            # Removes and returns the min element at top of priority queue
            UpperCAmelCase__			:     Tuple										= self.array[0][1]
            UpperCAmelCase__			:     Dict										= self.array[self.cur_size - 1]
            self.cur_size -= 1
            self.min_heapify(1		)
            del self.pos[min_node]
            return min_node
  
  
  
  
       def      __UpperCAmelCase     (							self  ,	_lowerCAmelCase		):
            # returns the index of left child
            return 2 * i + 1
  
  
  
  
       def      __UpperCAmelCase     (							self  ,	_lowerCAmelCase		):
            # returns the index of right child
            return 2 * i + 2
  
  
  
  
       def      __UpperCAmelCase     (							self  ,	_lowerCAmelCase		):
            # returns the index of parent
            return math.floor(i / 2		)
  
  
  
  
       def      __UpperCAmelCase     (							self  ,	_lowerCAmelCase  ,	_lowerCAmelCase		):
            # swaps array elements at indices i and j
            # update the pos{}
            UpperCAmelCase__			:     Any										= j
            UpperCAmelCase__			:     Any										= i
            UpperCAmelCase__			:     Dict										= self.array[i]
            UpperCAmelCase__			:     Union[str, Any]										= self.array[j]
            UpperCAmelCase__			:     List[str]										= temp
  
  
  
  
       def      __UpperCAmelCase     (							self  ,	_lowerCAmelCase  ,	_lowerCAmelCase		):
            UpperCAmelCase__			:     Optional[Any]										= self.pos[tup[1]]
            # assuming the new_d is atmost old_d
            UpperCAmelCase__			:     str										= (new_d, tup[1])
            while idx > 0 and self.array[self.par(_lowerCAmelCase		)][0] > self.array[idx][0]:
                 self.swap(_lowerCAmelCase  ,	self.par(_lowerCAmelCase		)		)
                 UpperCAmelCase__			:     List[Any]										= self.par(_lowerCAmelCase		)
  
  
  
  
  
  
  
  class 							UpperCAmelCase_     :
  
  
  
  
       def __init__(							self  ,	_lowerCAmelCase		):
            UpperCAmelCase__			:     Optional[Any]										= {}  # To store graph: u -> (v,w)
            UpperCAmelCase__			:     Union[str, Any]										= num  # Number of nodes in graph
            # To store the distance from source vertex
            UpperCAmelCase__			:     List[str]										= [0] * self.num_nodes
            UpperCAmelCase__			:     Dict										= [-1] * self.num_nodes  # To store the path
  
  
  
  
       def      __UpperCAmelCase     (							self  ,	_lowerCAmelCase  ,	_lowerCAmelCase  ,	_lowerCAmelCase		):
            #  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      __UpperCAmelCase     (							self		):
            # u -> v(w)
            for u in self.adjList:
                 print(_lowerCAmelCase  ,	"""->"""  ,	""" -> """.join(str(f"{v}({w})"		) for v, w in self.adjList[u]		)		)
  
  
  
  
       def      __UpperCAmelCase     (							self  ,	_lowerCAmelCase		):
            # Flush old junk values in par[]
            UpperCAmelCase__			:     Dict										= [-1] * self.num_nodes
            # src is the source node
            UpperCAmelCase__			:     Any										= 0
            UpperCAmelCase__			:     Optional[Any]										= PriorityQueue()
            q.insert((0, src)		)  # (dist from src, node)
            for u in self.adjList:
                 if u != src:
                      UpperCAmelCase__			:     List[Any]										= sys.maxsize  # Infinity
                      UpperCAmelCase__			:     Tuple										= -1
  
            while not q.is_empty():
                 UpperCAmelCase__			:     List[Any]										= 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__			:     Optional[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)  ,	_lowerCAmelCase		)
                           UpperCAmelCase__			:     Dict										= new_dist
                           UpperCAmelCase__			:     List[Any]										= u
  
          # Show the shortest distances from src
            self.show_distances(_lowerCAmelCase		)
  
  
  
  
       def      __UpperCAmelCase     (							self  ,	_lowerCAmelCase		):
            print(f"Distance from node: {src}"		)
            for u in range(self.num_nodes		):
                 print(f"Node {u} has distance: {self.dist[u]}"		)
  
  
  
  
       def      __UpperCAmelCase     (							self  ,	_lowerCAmelCase  ,	_lowerCAmelCase		):
            # To show the shortest path from src to dest
            # WARNING: Use it *after* calling dijkstra
            UpperCAmelCase__			:     str										= []
            UpperCAmelCase__			:     List[str]										= 0
            UpperCAmelCase__			:     int										= 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
                 UpperCAmelCase__			:     str										= 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__":
        SCREAMING_SNAKE_CASE__		:       Any   							=							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
  
  
  
  
  
  
  
style_context: 
  
  
  
  
  
  
  from .stack import Stack
  
  
  
  
  
  def    _lowerCamelCase	(	__lowerCamelCase					)   -> bool:
  
       '''simple docstring'''
       UpperCAmelCase__			:     Stack[str]										= Stack()
       UpperCAmelCase__			:     str										= {"""(""": """)""", """[""": """]""", """{""": """}"""}
       for bracket in parentheses:
            if bracket in bracket_pairs:
                 stack.push(__lowerCamelCase					)
            elif bracket in (")", "]", "}"):
                 if stack.is_empty() or bracket_pairs[stack.pop()] != bracket:
                      return False
       return stack.is_empty()
  
  
  if __name__ == "__main__":
        from doctest import testmod
  
        testmod()
  
        SCREAMING_SNAKE_CASE__		:       Any   							=							["""((()))""", """((())""", """(()))"""]
        print("""Balanced parentheses demonstration:\n""")
        for example in examples:
              SCREAMING_SNAKE_CASE__		:       List[str]   							=							"""""" if balanced_parentheses(example) else """not """
              print(f'''{example} is {not_str}balanced''')
  
  
  
  
  
  
  