p
```"""
pseudo-code:
// 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.

'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:
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.

'ABCDEF'
"""
visited = {start}
result = [start]
queue = deque([start])
while queue:
v = queue.popleft()
for child in graph[v]:
if child not in visited:
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()  