Graph Algorithms and Data Structures Project

This project demonstrates my skills in software engineering by implementing efficient algorithms and custom data structures for solving graph-related problems. It includes the creation of a directed graph, a priority queue (min-heap), and a topological sort algorithm. These components highlight my abilities to write clean, efficient, and modular code while solving complex problems.

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Project Objective

The goal of this project is to represent and manipulate directed graphs with edge priorities using a custom implementation. It solves problems like finding the order of tasks (topological sort), managing priorities efficiently (min-heap), and working with graph relationships.

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Files Overview

1. Destination.java

• Purpose: Represents edges in the graph, including the destination node and its priority (e.g., cost or weight).
• Problem Solved: Helps in sorting edges by priority, making it useful for algorithms like shortest paths or topological sort.
• Key Skills: Object-oriented programming, custom comparators, encapsulation.

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2. Display.java

• Purpose: Provides an easy-to-read display of graph structures for debugging and testing.
• Problem Solved: Simplifies understanding and debugging complex graph relationships.
• Key Skills: User interface design for debugging, attention to detail.

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3. MinHeap.java

• Purpose: Implements a priority queue using a binary heap structure.
• Problem Solved: Efficiently manages tasks or edges based on priority, ensuring optimal performance for operations like poll and offer.
• Key Methods: offer, poll, peek, siftUp, siftDown.
• Key Skills: Algorithm design, data structure implementation, performance optimization.

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4. ThreeTenGraph.java

• Purpose: Implements a directed graph with adjacency lists and edge priorities using the MinHeap.
• Problem Solved: Manages graph operations such as adding/removing nodes and edges, finding neighbors, and handling directed connections.
• Key Methods:
  • addVertex and addEdge: Build the graph dynamically.
  • getSuccessors and getPredecessors: Retrieve related nodes.
  • findEdge, getEndpoints: Analyze edge relationships.
• Key Skills: Graph theory, dynamic data structures, problem-solving.

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5. TopologicalSort.java

• Purpose: Implements a topological sort algorithm for directed acyclic graphs (DAGs) with edge priorities.
• Problem Solved: Determines the order of tasks while respecting priorities and ensures the graph has no cycles.
• Key Methods:
  • getGraph: Reads graph data from a file and constructs a graph.
  • topologicalSort: Sorts nodes in a valid order while detecting cycles.
  • visit: Uses depth-first search to traverse the graph.
• Key Skills: Algorithm design, recursion, file handling, cycle detection.