bfs.py

"""
BFS.

pseudo-code:

BFS(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)

"""

G = {'A': ['B', 'C'],
     'B': ['A', 'D', 'E'],
     'C': ['A', 'F'],
     'D': ['B'],
     'E': ['B', 'F'],
     'F': ['C', 'E']}


def bfs(graph, start):
    """
    >>> ''.join(sorted(bfs(G, 'A')))
    'ABCDEF'
    """
    explored, queue = set(), [start]  # collections.deque([start])
    explored.add(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(bfs(G, 'A'))