What are some applications of Dijkstra's algorithm in Python?

What are some applications of Dijkstra's algorithm in Python?

Dijkstra's algorithm is commonly used in pathfinding and graph traversal. Some applications include routing in GPS systems, network routing protocols, and game development for AI movement.

Can you give me a code example of Dijkstra's algorithm in Python?

Sure! Here's a simple implementation:

import heapq

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

    def add_edge(self, u, v, weight):
        if u not in self.graph:
            self.graph[u] = []
        self.graph[u].append((v, weight))

    def dijkstra(self, start):
        queue = [(0, start)]
        distances = {node: float('infinity') for node in self.graph}
        distances[start] = 0

        while queue:
            current_distance, current_node = heapq.heappop(queue)

            if current_distance > distances[current_node]:
                continue

            for neighbor, weight in self.graph[current_node]:
                distance = current_distance + weight

                if distance < distances[neighbor]:
                    distances[neighbor] = distance
                    heapq.heappush(queue, (distance, neighbor))

        return distances

This code defines a graph and implements Dijkstra's algorithm to find the shortest path from a starting node.

What are the time complexity and space complexity of Dijkstra's algorithm?

The time complexity of Dijkstra's algorithm is O((V + E) log V) when using a priority queue, where V is the number of vertices and E is the number of edges. The space complexity is O(V) due to the storage of distances and the priority queue.