Can I get help with the worst case time and space complexity of the following code please. In big$-$O notation preferably

from collections import deque

class TreeMap:

def $\_\_$init$\_\_($self$,$ roads, solulus$)$:

self.graph $=\{\}$ # Initialize an empty graph

self.solulus $=\{\}$ # Initialize an empty dictionary for Solulu trees

# Add roads to the graph

for road in roads:

u$,$ v$,$ w $=$ road

if u not in self.graph:

self.graph$[$u$]=[]$

self.graph$[$u$].$append$(($v$,$ w$))$

# Add solulus to the dictionary

for solulu in solulus:

x$,$ y$,$ z $=$ solulu

self.solulus$[$x$]=($y$,$ z$)$

def escape$($self$,$ start, exits$)$:

# Initialize queue with paths containing only the start node

queue $=$ deque$([($start$,[$start$],0,$ False$)])$ # $($node$,$ path, time, solulu$\_$broken$)$

# While there are paths to explore

while queue:

node, path, time, solulu$\_$broken $=$ queue.popleft$()$

# If the current node is an exit and a Solulu tree has been broken, return the path

if node in exits and solulu$\_$broken:

return time, path

# Explore all neighbors

for neighbor, travel$\_$time in self.graph.get$($node$,[])$:

# If the neighbor is a Solulu tree

if neighbor in self.solulus:

solulu$\_$destroy$\_$time, teleport$\_$destination $=$ self.solulus$[$neighbor$]$

if not solulu$\_$broken:

# Break the Solulu tree and continue

queue.append$(($teleport$\_$destination, path $+[$teleport$\_$destination$],$ time $+$ travel$\_$time $+$ solulu$\_$destroy$\_$time, True$))$

# Continue without breaking the Solulu tree

queue.append$(($teleport$\_$destination, path $+[$teleport$\_$destination$],$ time $+$ travel$\_$time, solulu$\_$broken$))$

else:

# Regular node traversal

queue.append$(($neighbor$,$ path $+[$neighbor$],$ time $+$ travel$\_$time, solulu$\_$broken$))$

# If no valid path is found

return None

# Example $1$

# The roads represented as a list of tuples

roads $=[(0,1,4),(1,2,2),(2,3,3),(3,4,1),(1,5,2),$

$(5,6,5),(6,3,2),(6,4,3),(1,7,4),(7,8,2),$

$(8,7,2),(7,3,2),(8,0,11),(4,3,1),(4,8,10)]$

# The solulus represented as a list of tuples

solulus $=[(5,10,0),(6,1,6),(7,5,7),(0,5,2),(8,4,8)]$

# Creating a TreeMap object based on the given roads

myforest $=$ TreeMap$($roads$,$ solulus$)$

# Example $1\mathrm{.}1$

start $=3$

exits $=[4]$

print$($myforest$.$escape$($start$,$ exits$))$