How can I implement Dijkstra's algorithm in Python?

How can I implement Dijkstra's algorithm in Python?

You can implement Dijkstra's algorithm using a priority queue. Would you like a code example?

Yes, please provide a code example.

Here's a simple implementation:

import heapq

class Graph:
    def __init__(self):
        self.edges = {}

    def add_edge(self, from_node, to_node, weight):
        if from_node not in self.edges:
            self.edges[from_node] = []
        self.edges[from_node].append((to_node, weight))

    def dijkstra(self, start):
        queue = [(0, start)]
        distances = {start: 0}
        while queue:
            current_distance, current_node = heapq.heappop(queue)
            if current_distance > distances.get(current_node, float('inf')):
                continue
            for neighbor, weight in self.edges.get(current_node, []):
                distance = current_distance + weight
                if distance < distances.get(neighbor, float('inf')):
                    distances[neighbor] = distance
                    heapq.heappush(queue, (distance, neighbor))
        return distances

What are the time and space complexities of this implementation?

The time complexity is O((V + E) log V) and the space complexity is O(V), where V is the number of vertices and E is the number of edges.