This project is not just an academic exercise, but a significant step in your understanding

of data structures. It aims to implement a multiway search tree $($M$-$Tree$),$ a data structure designed to

store and efficiently manage sorted data while maintaining balanced tree properties. The M$-$Tree

provides efficient insertion, deletion, and search operations by splitting a sorted array recursively and

using the split values for tree navigation. The M$-$Tree uses recursive splitting of arrays and places the

split values in internal $($non$-$leaf$)$ nodes, while the leaf nodes store actual values in sorted order.

Additionally, you will implement a rebuild operation to maintain balance in the tree after deletions.

This project is a key part of your learning journey in data structures and will equip you with practical

skills for your future career.

Search trees, particularly the M$-$Tree, are not just theoretical constructs. They enable efficient data

retrieval and modification in many real$-$world applications, such as database indexing, file systems,

and memory management. The M$-$Tree enhances traditional binary search trees by allowing each

node to hold multiple values and up to M child pointers, resulting in more compact trees with fewer

levels. This project will give you a hands$-$on understanding of how these structures are used in

practical scenarios.

Through this project, students will gain practical experience in:

$$ Implementing and working with multiway search trees.

$$ Understanding how recursive node splitting is used to balance a tree dynamically.

$$ Managing a sorted array within tree nodes and determining split points for navigation.

$$ Exploring dynamic tree balancing techniques through a rebuild operation that reconstructs

the tree when necessary.

$$ Gaining proficiency in memory management and pointer$-$based tree structures in C$++.$

The M$-$tree is structured around splitting values into M parts. The values used for splitting are not

stored in the nodes themselves but are instead used to navigate to the correct child nodes. The left

parts of the array are stored in the corresponding child nodes, and the tree expands dynamically as

new values are inserted.

This project will give students hands$-$on experience with:

$$ Templated data structures in C$++.$

$$ Recursive algorithms for insertion and deletion in tree structures.

$$ Implementing a rebuild operation to maintain tree balance and efficiency.

$$ Optimizing search operations within the context of multiway trees.

By designing and implementing the M$-$Tree, students will explore how tree$-$based data structures can

efficiently manage and search large datasets and how maintaining balance in a search tree directly

impacts performance. This project reinforces core data structure concepts and helps understand

how these structures are applied in systems like databases and memory hierarchies.