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"""

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

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) -> set[str]:

"""

>>> ''.join(sorted(breadth_first_search(G, 'A')))

'ABCDEF'

"""

explored = {start}

queue = [start]

while queue:

v = queue.pop(0) # queue.popleft()

for w in graph[v]:

if w not in explored:

explored.add(w)

queue.append(w)

return explored

if __name__ == "__main__":

print(breadth_first_search(G, "A"))

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