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Introduction

Sorting algorithms are fundamental to computer science and play a critical role in organizing, processing, and retrieving data efficiently. They form the backbone of numerous applications, including databases, scheduling systems, analytics platforms, and search operations.

The efficiency of a system often depends on how effectively it can sort and structure its data. Understanding algorithmic behavior and performance characteristics is essential for building scalable and optimized solutions.

  • Background

    Sorting improves data accessibility and simplifies operations such as searching, merging, and filtering. Different algorithms offer distinct trade-offs in:

    • Time complexity
    • Space complexity
    • Implementation simplicity
    • Stability and scalability

    Algorithms such as Selection Sort, Insertion Sort, Merge Sort, and Quick Sort illustrate how design decisions affect runtime and memory.

  • Problem Statement

    This project compares the performance of four sorting algorithms through theoretical complexity analysis and empirical runtime measurement under a controlled environment.

    All methods are implemented using the same dataset to ensure a fair comparison. The dataset consists of student registration records, enabling a realistic academic use case such as identifying course demand trends.

    Key question: Which algorithm performs best as input size increases?

Scope of Work

  • Data Structure

    • Implement a custom Linked List to store registration records
    • Convert the list into an array for sorting

  • Demand Computation

    • Compute a demand score per record
    • Use multiple weighted factors for scoring

  • Sorting Algorithms

    Implement and apply:

    • Selection Sort
    • Insertion Sort
    • Merge Sort
    • Quick Sort

  • Performance Measurement

    • Measure runtime for each algorithm
    • Compare results under consistent conditions
    • Interpret performance differences at scale

Objective

  • Performance Understanding

    Explore the relationship between algorithmic design and runtime efficiency, especially under large-scale datasets.

  • Trade-off Analysis

    Evaluate practical trade-offs between simpler approaches and divide-and-conquer algorithms (time vs. space vs. implementation cost).

  • Empirical Validation

    Compare theoretical complexity expectations with measured runtimes to highlight real-world behavior.

Evaluation Focus

The comparison is performed using the same dataset and environment across all implementations to keep the results consistent and comparable.