python数据结构与算法——图的广度优先和深度优先的算法

根据维基百科的伪代码实现：

广度优先BFS：

使用队列，集合

标记初始结点已被发现，放入队列

每次循环从队列弹出一个结点

将该节点的所有相连结点放入队列，并标记已被发现

通过队列，将迷宫路口所有的门打开，从一个门进去继续打开里面的门，然后返回前一个门处

 """
  procedure BFS(G,v) is
      let Q be a queue
      Q.enqueue(v)
      label v as discovered
      while Q is not empty
         v ← Q.dequeue()
         procedure(v)
         for all edges from v to w in G.adjacentEdges(v) do
             if w is not labeled as discovered
                 Q.enqueue(w)
                 label w as discovered
 """
 def procedure(v):
     pass

 def BFS(G,v0):
     """ 广度优先搜索 """
     q, s = [], set()
     q.extend(v0)
     s.add(v0)
     while q:    # 当队列q非空
         v = q.pop(0)
         procedure(v)
         for w in G[v]:     # 对图G中顶点v的所有邻近点w
             if w not in s: # 如果顶点 w 没被发现
                 q.extend(w)
                 s.add(w)    # 记录w已被发现

深度优先DFS

使用 栈，集合

初始结点入栈

每轮循环从栈中弹出一个结点，并标记已被发现

对每个弹出的结点，将其连接的所有结点放到队列中

通过栈的结构，一步步深入挖掘

 """"
 Pseudocode[edit]
 Input: A graph G and a vertex v of G

 Output: All vertices reachable from v labeled as discovered

 A recursive implementation of DFS:[5]

 1  procedure DFS(G,v):
 2      label v as discovered
 3      for all edges from v to w in G.adjacentEdges(v) do
 4          if vertex w is not labeled as discovered then
 5              recursively call DFS(G,w)
 A non-recursive implementation of DFS:[6]

 1  procedure DFS-iterative(G,v):
 2      let S be a stack
 3      S.push(v)
 4      while S is not empty
 5            v = S.pop()
 6            if v is not labeled as discovered:
 7                label v as discovered
 8                for all edges from v to w in G.adjacentEdges(v) do
 9                    S.push(w)
 """

 def DFS(G,v0):
     S = []
     S.append(v0)
     label = set()
     while S:
         v = S.pop()
         if v not in label:
             label.add(v)
             procedure(v)
             for w in G[v]:
                 S.append(w)