Dijkstra's Algorithm - Shortest Paths

Introduction

Dijkstra's Algorithm is used to find the shortest paths from a starting node to all other nodes in a graph. It is particularly efficient for graphs with non-negative edge weights.

Key Concepts

Visual Explanation of Dijkstra's Algorithm

Title

This is the introduction to the concept of Shortest Paths using Dijkstra's Algorithm.

Definition

This image explains the basics of Dijkstra's Algorithm, including its purpose and the type of graphs it works with. It highlights that Dijkstra finds the shortest path from a start node to all other nodes, efficiently using non-negative edge weights.

Code

The pseudocode provides an overview of how Dijkstra's Algorithm works. It shows the use of a priority queue to select the next node, and how the predecessor and cost are updated as we traverse the graph.

Example 1

This example illustrates how Dijkstra's Algorithm proceeds through a graph step-by-step, starting from the initial node and updating the shortest path as it visits each node.

Example 2

This image shows how to reconstruct the shortest paths from the starting node to the other nodes. The arrows indicate the paths found by the algorithm and the corresponding costs.

Complexity

This image explains the time complexity of Dijkstra's Algorithm, detailing the number of nodes (V) and edges (E), and the operations performed on the priority queue during the algorithm's execution.

More Information

For more details, visit Dijkstra's Algorithm on Wikipedia.