Theory & Background

BFS (Breadth-First Search): use queue, explore level by level. Track visited set. Animation: color nodes by discovery time (gradient). Shows shortest path in unweighted graphs. DFS (Depth-First Search): use stack (or recursion). Track discovery and finish times. Animation: show backtracking with different color. Applications: cycle detection, topological sort (reverse finish order), connected components, bipartite checking.

Components & Requirements

10 components required for this project.

#	Component	Purpose	Qty
1	JavaScript (ES6+)	All algorithm and visualization logic	x1
2	HTML5 Canvas	Graph drawing and animation	x1
3	CSS3 Animations	Node and edge highlight effects	x1
4	React (optional)	UI component management	x1
5	D3.js (optional)	Force-directed graph layout	x1
6	Vite	Fast development build tool	x1
7	Jest	Algorithm unit testing	x1
8	P5.js (alternative)	Simpler canvas drawing API	x1
9	Cytoscape.js	Production graph rendering	x1
10	GitHub Pages	Free hosting	x1

Step-by-Step Implementation

Follow these 4 steps carefully.

1

BFS and DFS Implementation

BFS (Breadth-First Search): use queue, explore level by level. Track visited set. Animation: color nodes by discovery time (gradient). Shows shortest path in unweighted graphs. DFS (Depth-First Search): use stack (or recursion). Track discovery and finish times. Animation: show backtracking with different color. Applications: cycle detection, topological sort (reverse finish order), connected components, bipartite checking.

2

Dijkstra

Priority queue (min-heap) implementation: extract vertex with minimum tentative distance. Relaxation: for each neighbor, if dist[u] + weight(u,v) < dist[v], update dist[v] and prev[v]. Animation: show priority queue state, highlight relaxed edges, display distance labels. Build path: backtrack from target to source using prev array. Visualize final shortest path highlighted in distinct color.

3

A* Pathfinding with Heuristic

A* improves Dijkstra by using a heuristic: f(n) = g(n) + h(n), where g(n) = actual distance from start, h(n) = estimated distance to goal (e.g., Euclidean or Manhattan distance). Only explores nodes where f(n) is promising — far fewer nodes than Dijkstra for grid pathfinding. Animation: show open and closed sets with different colors, display f/g/h values on nodes. Demonstrate how different heuristics (admissible vs inadmissible) affect correctness and speed.

4

Minimum Spanning Tree (Kruskal/Prim)

Kruskal: sort all edges by weight, add edge if it doesn

Code & Implementation

Core code for graph_algorithms.js:

graph_algorithms.js
  JAVASCRIPT

Testing & Troubleshooting

Test Graph Algorithm Visualizer by verifying each subsystem individually before full integration.

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Troubleshooting Tips

Verify power voltages, check ground connections, use serial monitor for debug.

Real-World Applications

*Social network connection analysis

*GPS navigation route planning

*Network routing protocol education

*Game AI pathfinding

*Dependency graph visualization

*Circuit layout optimization

*Transportation network analysis

*Knowledge graph exploration tool

Extensions & Next Steps

Add Ford-Fulkerson max-flow algorithm visualization
Build a maze generator + solver combining DFS maze generation with A* solving
Add NP-complete problem visualizers (Traveling Salesman approximations)
Implement real map data loading from OpenStreetMap API
Add algorithm comparison mode running two algorithms side by side

Interactive Playground

Coming Soon

An interactive simulator will be available here — simulate circuits and run code in-browser without hardware.

Frequently Asked Questions

What is the time complexity of Dijkstra

Dijkstra with binary heap: O((V+E) log V). With Fibonacci heap: O(E + V log V) — optimal but complex to implement. Appropriate when: non-negative edge weights, dense graphs. Not appropriate when: negative edge weights (use Bellman-Ford: O(VE)), need all-pairs shortest paths (use Floyd-Warshall: O(V³)), or unweighted graphs (use BFS: O(V+E)). A* is faster than Dijkstra for single-pair shortest path when a good heuristic is available (like Euclidean distance for geographic routing).

Introduction