Python數據結構與算法之圖的廣度優先與深度優先搜索算法示例

本文實例講述了Python數據結構與算法之圖的廣度優先與深度優先搜索算法。分享給大家供大家參考，具體如下：

廣度優先BFS：

使用隊列，集合

標記初始結點已被發現，放入隊列

每次循環從隊列彈出一個結點

將該節點的所有相連結點放入隊列，並標記已被發現

通過隊列，將迷宮路口所有的門打開，從一個門進去繼續打開裡面的門，然後返回前一個門處

<code>"""
 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):
  """ 廣度優先搜索 """
  q, s = [], set()
  q.extend(v0)
  s.add(v0)
  while q:  # 當隊列q非空
    v = q.pop(0)
    procedure(v)
    for w in G[v]:   # 對圖G中頂點v的所有鄰近點w 

      if w not in s: # 如果頂點 w 沒被發現
        q.extend(w)
        s.add(w)  # 記錄w已被發現
/<code>

深度優先DFS

使用 棧，集合

初始結點入棧

每輪循環從棧中彈出一個結點，並標記已被發現

對每個彈出的結點，將其連接的所有結點放到隊列中

通過棧的結構，一步步深入挖掘

<code>""""
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)
/<code>

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