Dijkstra's Shortest Path Calculator

What is Dijkstra's Algorithm?

Dijkstra's algorithm, invented by Dutch computer scientist Edsger W. Dijkstra in 1956, is a graph search algorithm that solves the single-source shortest path problem for a weighted graph with non-negative edge weights. Given a source node, it finds the shortest path from that node to every other node in the graph.

The algorithm works by maintaining a set of unvisited nodes and repeatedly selecting the unvisited node with the smallest tentative distance (a greedy strategy). Once a node is "visited," its shortest distance is guaranteed to be final.

How to Use the Calculator

• Define edges: Enter edges in the format source, destination, weight, one per line. Each line represents a connection between two nodes with a non-negative weight.
• Choose graph type: Select "Undirected" for two-way edges (like roads) or "Directed" for one-way edges (like flight routes).
• Set source node: Enter the starting node for all shortest path calculations.
• Review results: View the shortest distance to each node, the complete path, and a step-by-step execution trace.

Time Complexity

The efficiency of Dijkstra's algorithm depends on the data structure used for the priority queue. With a binary heap implementation, the time complexity is $O((V + E) \log V)$ where $V$ is the number of vertices and $E$ is the number of edges.

Real-World Applications

• GPS Navigation: Mapping services use Dijkstra's algorithm to find the fastest route between locations.
• Network Routing: Internet routing protocols like OSPF and IS-IS use Dijkstra's algorithm for packet forwarding.
• Game Development: NPC pathfinding uses Dijkstra's algorithm or A* for navigation.
• Social Network Analysis: Finding shortest connection paths between users.
• Supply Chain: Optimizing delivery routes and logistics networks.

Also check: Graph Distance Calculator, Path Finding Calculator, Connected Graph Checker.