I

```
"""
https://en.wikipedia.org/wiki/Breadth-first_search
pseudo-code:
breadth_first_search(graph G, start vertex s):
// all nodes initially unexplored
mark s as explored
let Q = queue data structure, initialized with s
while Q is non-empty:
remove the first node of Q, call it v
for each edge(v, w): // for w in graph[v]
if w unexplored:
mark w as explored
add w to Q (at the end)
"""
from __future__ import annotations
from collections import deque
from queue import Queue
from timeit import timeit
G = {
"A": ["B", "C"],
"B": ["A", "D", "E"],
"C": ["A", "F"],
"D": ["B"],
"E": ["B", "F"],
"F": ["C", "E"],
}
def breadth_first_search(graph: dict, start: str) -> list[str]:
"""
Implementation of breadth first search using queue.Queue.
>>> ''.join(breadth_first_search(G, 'A'))
'ABCDEF'
"""
explored = {start}
result = [start]
queue: Queue = Queue()
queue.put(start)
while not queue.empty():
v = queue.get()
for w in graph[v]:
if w not in explored:
explored.add(w)
result.append(w)
queue.put(w)
return result
def breadth_first_search_with_deque(graph: dict, start: str) -> list[str]:
"""
Implementation of breadth first search using collection.queue.
>>> ''.join(breadth_first_search_with_deque(G, 'A'))
'ABCDEF'
"""
visited = {start}
result = [start]
queue = deque([start])
while queue:
v = queue.popleft()
for child in graph[v]:
if child not in visited:
visited.add(child)
result.append(child)
queue.append(child)
return result
def benchmark_function(name: str) -> None:
setup = f"from __main__ import G, {name}"
number = 10000
res = timeit(f"{name}(G, 'A')", setup=setup, number=number)
print(f"{name:<35} finished {number} runs in {res:.5f} seconds")
if __name__ == "__main__":
import doctest
doctest.testmod()
benchmark_function("breadth_first_search")
benchmark_function("breadth_first_search_with_deque")
# breadth_first_search finished 10000 runs in 0.20999 seconds
# breadth_first_search_with_deque finished 10000 runs in 0.01421 seconds
```