Algorithm Complexity Analyzer (Web-Based)

Project Title

Web-Based Algorithm Complexity Analyzer Using JavaScript and PHP for Dr. Yanga's College Inc. Algorithm Education

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Project Overview

This project is a web-based system designed to compute and analyze the time and space complexity of selected algorithms. It is intended to support college-level instruction in algorithm analysis by providing both theoretical and empirical insights.

The system allows users to select algorithms, input problem sizes, execute implementations in JavaScript, and observe measured runtime alongside theoretical complexity classifications. Results are stored and can be visualized through graphs for comparative analysis.

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Objectives

• Apply theoretical complexity analysis (Big-O, Big-Theta, Big-Omega)
• Implement algorithms using JavaScript
• Measure empirical runtime behavior
• Compare empirical and theoretical results
• Store and retrieve execution data using a database
• Visualize algorithm efficiency through graphs

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Scope of the System

Supported Algorithms

• Bubble Sort — Time: O(n²), Space: O(1)
• Merge Sort — Time: O(n log n), Space: O(n)
• Binary Search — Time: O(log n), Space: O(1)
• Linear Search — Time: O(n), Space: O(1)
• Fibonacci (Recursive) — Time: O(2ⁿ), Space: O(n)
• Fibonacci (Dynamic Programming) — Time: O(n), Space: O(n)

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System Architecture

Frontend

• HTML, CSS, JavaScript
• Handles user interaction, input configuration, and visualization

Backend

• PHP
• Processes requests and manages data storage

Database

• MySQL
• Stores execution results and input configurations

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Key Features

• Algorithm selection interface
• Input size configuration
• Runtime measurement using high-resolution timing
• Complexity classification (time and space)
• Graph-based visualization of results
• Persistent data storage

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Development Roadmap

Phase 1: Planning

• Define system scope and requirements
• Assign roles and responsibilities

Phase 2: System Design

• Design user interface
• Plan database schema
• Define API endpoints

Phase 3: Core Development

• Implement frontend components
• Develop backend services
• Implement algorithms and runtime measurement

Phase 4: Integration

• Connect frontend and backend systems
• Ensure proper data flow

Phase 5: Testing

• Validate algorithm correctness
• Verify runtime measurements
• Handle edge cases

Phase 6: Visualization

• Implement graphing features
• Improve usability and clarity

Phase 7: Documentation and Presentation

• Prepare written documentation
• Develop presentation materials

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Team Roles and Responsibilities

Project Manager

• Oversees project timeline and coordination
• Ensures milestones are met

System Analyst

• Defines system requirements and architecture
• Ensures alignment with theoretical concepts

Frontend Developer

• Develops user interface
• Implements visualization features

Backend Developer

• Builds API endpoints
• Handles server-side logic and database interaction

Database Manager

• Designs and maintains database schema
• Ensures data integrity

Quality Assurance Tester

• Tests system functionality
• Identifies bugs and inconsistencies

Documentation Lead

• Prepares technical documentation
• Ensures clarity and completeness

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Presentation Guidelines

Duration: 10–15 minutes

Sections:

1. Introduction
2. Problem Statement
3. System Architecture
4. Algorithm Demonstration
5. Complexity Analysis
6. Live Demonstration
7. Conclusion

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Evaluation Criteria

Category	Points
Functionality	30
System Design	20
Complexity Analysis	25
Code Quality	15
Presentation	10
Total	100

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Notes and Limitations

• Runtime results may vary depending on hardware and browser environment
• Complexity classification is based on predefined mappings
• Large input sizes may affect responsiveness

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Future Improvements

• Additional algorithm support
• Step-by-step execution visualization
• Multi-language implementation support
• Advanced static analysis capabilities