Prerequisites:
In this article, we will be looking at how to build an undirected graph and then find the shortest path between two nodes/vertex of that graph easily using dictionaries in Python Language.
Building a Graph using Dictionaries
Approach: The idea is to store the adjacency list into the dictionaries, which helps to store the graph in any format not only in the form of the integers. Here we have used characters as a reference on those places any custom objects can also be used.
Below is the implementation of the above approach:
Python3
# Python3 implementation to build a # graph using Dictionariesfrom collections import defaultdict# Function to build the graphdef 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 graphif __name__ == "__main__": graph = build_graph() print(graph) |
{
'G': ['C'],
'F': ['C'],
'E': ['A', 'B', 'D'],
'A': ['B', 'E', 'C'],
'B': ['A', 'D', 'E'],
'D': ['B', 'E'],
'C': ['A', 'F', 'G']
}
Shortest Path between two nodes of graph
Approach: The idea is to use queue and visit every adjacent node of the starting nodes that traverses the graph in Breadth-First Search manner to find the shortest path between two nodes of the graph.
Below is the implementation of the above approach:
Python3
# Python implementation to find the # shortest path in the graph using # dictionaries # Function to find the shortest# path between two nodes of a graphdef 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 Codeif __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') |
Shortest path = A B D
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