Heap Sort and Heap Construction Analysis

This repository contains Python code for analyzing and comparing the performance of heap construction methods, both in the average and worst-case scenarios, using the Heap Sort algorithm.

Table of Contents

• Introduction
• Usage
• Functions
• Average Case Analysis
• Worst Case Analysis
• License

Introduction

Heap Sort is a comparison-based sorting algorithm that makes use of a binary heap data structure. This repository includes Python code for performing an analysis of the heap construction methods in two scenarios: average-case and worst-case.

The heap construction methods analyzed include:

• Bottom-Up Build Heap
• Top-Down Build Heap

Usage

To run the code and perform the analysis, follow these steps:

1. Clone this repository to your local machine:

   git clone https://github.com/yourusername/heap-sort-analysis.git
   

2. Ensure you have Python installed on your system.

3. Install the required libraries using pip:

   pip install matplotlib
   

4. Run the analysis by executing the analysis.py script:

   python analysis.py
   

5. The analysis results will be displayed in the form of plots for both average and worst-case scenarios.

Functions

The code includes several functions, each serving a specific purpose:

• heapify: Maintains the heap property in a max-heap.
• build_heap_bottom_up: Creates a max-heap using the bottom-up approach.
• insert_top_down: Inserts an element into a max-heap using the top-down approach.
• build_heap_top_down: Creates a max-heap using the top-down approach.
• heap_sort: Sorts a list using the heap sort algorithm.
• generate_random_data: Generates a list of random data.
• average_case_analysis: Analyzes the average case performance of the heap construction methods and plots the results.
• worst_case_analysis: Analyzes the worst case performance of the heap construction methods and plots the results.

Average Case Analysis

The average_case_analysis function generates random data and measures the average case performance of both heap construction methods. It produces plots illustrating comparisons, assignments, and total operations.

Worst Case Analysis

The worst_case_analysis function analyzes the worst case performance of the heap construction methods. It generates data that represents the worst-case scenario and produces plots for comparisons and assignments in the worst case.

You should replace "https://github.com/yourusername/heap-sort-analysis.git" with the actual URL of your repository. Make sure to provide a detailed explanation of how to use the code and describe the functions used in your analysis. Additionally, include a section about the license to make it clear how others can use your code.