Update breadth_first_search_2.py (TheAlgorithms#7765)

* Cleanup the BFS

* Add both functions and timeit

* [pre-commit.ci] auto fixes from pre-commit.com hooks

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* Add performace results as comment

* Update breadth_first_search_2.py

Co-authored-by: pre-commit-ci[bot] <66853113+pre-commit-ci[bot]@users.noreply.github.com>
Co-authored-by: Christian Clauss <[email protected]>

graphs/breadth_first_search_2.py

@@ -14,7 +14,9 @@
 """
 from __future__ import annotations
 
+from collections import deque
 from queue import Queue
+from timeit import timeit
 
 G = {
     "A": ["B", "C"],
@@ -26,25 +28,60 @@
 }
 
 
-def breadth_first_search(graph: dict, start: str) -> set[str]:
+def breadth_first_search(graph: dict, start: str) -> list[str]:
     """
-    >>> ''.join(sorted(breadth_first_search(G, 'A')))
+    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 explored
+    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()
-    print(breadth_first_search(G, "A"))
+
+    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