Introduction

Dijkstra’s algorithm is a famous graph algorithm that is used to find the shortest path between two nodes in a graph. It is named after its inventor, Edsger Dijkstra, and has numerous applications in various fields like transportation networks, computer networks, and route optimization.

How does it work?

Dijkstra’s algorithm is a versatile and efficient algorithm that solves the single-source shortest path problem. Here, the goal is to find the shortest path from a given source node to all other nodes in the graph.

The algorithm works by maintaining a priority queue of nodes, called the “unvisited” set, and keeping track of the current shortest distance from the source node to each node using a distance array. It then iteratively selects the node with the smallest current distance, updates the distances of its neighboring nodes if a shorter path is found, and marks the selected node as “visited”.

The algorithm continues this process until all nodes have been visited or until the destination node is reached, resulting in the shortest path from the source to the destination.

Example Code (Python)

Below is an example implementation of Dijkstra’s algorithm in Python:

import heapq

def dijkstra(graph, source):
    # Initialize distance array and set all distances to infinity except for the source node
    distance = {node: float('inf') for node in graph}
    distance[source] = 0

    # Initialize the priority queue with the source node and its initial distance
    queue = [(0, source)]

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

        # Skip processing if the distance is greater than the current shortest distance
        if current_distance > distance[current_node]:
            continue

        # Iterate through the neighbors of the current node
        for neighbor, weight in graph[current_node].items():
            distance_to_neighbor = current_distance + weight

            # If a shorter path is found, update the distance and enqueue the neighbor
            if distance_to_neighbor < distance[neighbor]:
                distance[neighbor] = distance_to_neighbor
                heapq.heappush(queue, (distance_to_neighbor, neighbor))

    return distance

Conclusion

Dijkstra’s algorithm is a powerful and widely-used algorithm for finding the shortest path in a graph. It offers an efficient way to solve the single-source shortest path problem and has numerous real-world applications.

Understanding the principles behind Dijkstra’s algorithm and being able to implement it in code can greatly enhance your problem-solving skills in various domains. Happy coding and exploring new paths with Dijkstra’s algorithm!

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