图及算法----广度优先搜索

1. 图结构的广度优先遍历的迭代算法

# Python3 Program to print BFS traversal from a given source vertex.
# BFS(int s) traverses vertices reachable from s. 
from collections import defaultdict, namedtuple
from typing import List, Dict


class Node(object):
    def __init__(self, name=None, pi=None, dis=None, color='white'):
        self.name = name
        self.pi = pi
        self.dis = dis
        self.color = color


class Graph: 
    def __init__(self): 
        # This class represents a directed graph using adjacency list representation
        self.graph: Dict[str, List[str]] = defaultdict(list)
        self.nodes: Dict[str, Node] = dict()
    
    def addEdge(self, u, v): 
        self.graph[str(u)].append(str(v))
        self.nodes.update({str(it): Node(name=str(it)) for it in [u, v] if str(it) not in self.nodes})
        
    def BFS(self, u): 
        queue = []  
        # 维护前驱节点队列, 节点第一次被访问是作为后继节点访问的，第二次是作为加入队列的目的是为了作为前驱节点再次访问
        # Mark the source node as visited and enqueue it 
        queue.append(str(u)) 
        self.nodes[str(u)].color = 'gray'
        while queue: 
            u = queue.pop(0)  # 弹出前驱节点
            print(u, end=">>>>
 ") 
            # 获取弹出节点u的邻居节点. 若其未被访问, 标记为访问并将其入队列，都是相邻节点入列，正好满足层层迭代
            for v in self.graph[u]: 
                if self.nodes[v].color == 'white': 
                    print(v, self.nodes[v].color)
                    self.nodes[v].color = 'gray'
                    queue.append(v) 
            self.nodes[str(u)].color = 'black'
            
                 
# Create a graph given in the above diagram 
g = Graph() 
g.addEdge(0, 1) 
g.addEdge(0, 2) 
g.addEdge(1, 2) 
g.addEdge(2, 0) 
g.addEdge(2, 3) 
g.addEdge(3, 3) 

print("Following is Breadth First Traversal (starting from vertex 2)") 
g.BFS(2)