使用Python的字典建立无向图并找到最短路径

先决条件：

• 图的BFS
• Python的字典

在本文中，我们将研究如何构建无向图，然后使用Python语言中的字典轻松地找到该图的两个节点/顶点之间的最短路径。

使用字典建立图

方法：想法是将邻接表存储到字典中，这有助于以任意格式存储图，而不仅是整数形式。在这里，我们将字符用作所有自定义对象也可以使用的地方的参考。
下面是上述方法的实现：

Python3

# Python3 implementation to build a
# graph using Dictonaries
 
from collections import defaultdict
 
# Function to build the graph
def build_graph():
    edges = [
        ["A", "B"], ["A", "E"],
        ["A", "C"], ["B", "D"],
        ["B", "E"], ["C", "F"],
        ["C", "G"], ["D", "E"]
    ]
    graph = defaultdict(list)
     
    # Loop to iterate over every
    # edge of the graph
    for edge in edges:
        a, b = edge[0], edge[1]
         
        # Creating the graph
        # as adjacency list
        graph[a].append(b)
        graph[b].append(a)
    return graph
 
if __name__ == "__main__":
    graph = build_graph()
     
    print(graph)

输出：

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

图的两个节点之间的最短路径

方法：想法是使用队列并以“广度优先搜索”方式访问遍历图形的起始节点的每个相邻节点，以找到图形的两个节点之间的最短路径。
下面是上述方法的实现：

Python3

# Python implementation to find the
# shortest path in the graph using
# dictionaries
 
# Function to find the shortest
# path between two nodes of a graph
def BFS_SP(graph, start, goal):
    explored = []
     
    # Queue for traversing the
    # graph in the BFS
    queue = [[start]]
     
    # If the desired node is
    # reached
    if start == goal:
        print("Same Node")
        return
     
    # Loop to traverse the graph
    # with the help of the queue
    while queue:
        path = queue.pop(0)
        node = path[-1]
         
        # Condition to check if the
        # current node is not visited
        if node not in explored:
            neighbours = graph[node]
             
            # Loop to iterate over the
            # neighbours of the node
            for neighbour in neighbours:
                new_path = list(path)
                new_path.append(neighbour)
                queue.append(new_path)
                 
                # Condition to check if the
                # neighbour node is the goal
                if neighbour == goal:
                    print("Shortest path = ", *new_path)
                    return
            explored.append(node)
 
    # Condition when the nodes
    # are not connected
    print("So sorry, but a connecting"\
                "path doesn't exist :(")
    return
 
# Driver Code
if __name__ == "__main__":
     
    # Graph using dictionaries
    graph = {'A': ['B', 'E', 'C'],
            'B': ['A', 'D', 'E'],
            'C': ['A', 'F', 'G'],
            'D': ['B', 'E'],
            'E': ['A', 'B', 'D'],
            'F': ['C'],
            'G': ['C']}
     
    # Function Call
    BFS_SP(graph, 'A', 'D')

输出：

Shortest path =  A B D