Python数据结构与算法之图的广度优先与深度优先搜索算法示例

Z时代
2024-01-10
分类：综合

本文实例讲述了Python数据结构与算法之图的广度优先与深度优先搜索算法。分享给大家供大家参考，具体如下：

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)