Binomial Heaps Implementation 🔢

This project implements a Binomial Heap data structure in Java. Binomial heaps support efficient merging, insertion, deletion, and key decrease operations, with each operation having a logarithmic time complexity.
The implementation ensures that key operations maintain a time complexity of O(log n), thanks to the structure's properties and optimal algorithms.

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📌 About the Project

This project was developed as part of the Data Structures course at Tel Aviv University 🎓, in collaboration with a fellow student.

We focused on:

• Writing clean and efficient code
• Implementing well-documented algorithms
• Optimizing runtime performance across various methods 🚀🔍

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📖 Features

✅ Insertion (insert(int key, String info)) - Inserts a new key-value pair into the binomial heap.
✅ Delete Minimum (deleteMin()) - Removes the smallest element and restructures the heap.
✅ Search Minimum (findMin()) - Retrieves the minimum element in O(1).
✅ Decrease Key (decreaseKey(HeapItem item, int diff)) - Reduces the key value and ensures heap order.
✅ Delete Any Element (delete(HeapItem item)) - Deletes an arbitrary element efficiently.
✅ Merge (Meld) (meld(BinomialHeap heap2)) - Combines two binomial heaps in O(log n) time.
✅ Heap Size & Tree Count (size(), numTrees()) - Retrieves heap statistics.

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⏳ Time Complexity Analysis

Operation	Method Name	Time Complexity
Insertion	insert(int key, String info)	O(log n)
Find Minimum	findMin()	O(1)
Delete Minimum	deleteMin()	O(log n)
Decrease Key	decreaseKey(HeapItem item, int diff)	O(log n)
Delete Any Item	delete(HeapItem item)	O(log n)
Merge (Meld)	meld(BinomialHeap heap2)	O(log n)
Get Heap Size	size()	O(1)
Get Number of Trees	numTrees()	O(1)
Check if Empty	empty()	O(1)

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💻 Example Usage

public class Main {
    public static void main(String[] args) {
        BinomialHeap heap = new BinomialHeap();

        // Insert elements
        heap.insert(10, "Ten");
        heap.insert(20, "Twenty");
        heap.insert(5, "Five");

        // Find minimum element
        System.out.println("Min: " + heap.findMin().getKey());

        // Delete minimum element
        heap.deleteMin();
        System.out.println("New Min: " + heap.findMin().getKey());

        // Decrease key
        HeapItem item = heap.insert(15, "Fifteen");
        heap.decreaseKey(item, 5);
        System.out.println("Min after decrease key: " + heap.findMin().getKey());

        // Delete an item
        heap.delete(item);
    }
}