- A multiway search tree is a type of tree data structure where each node can have more than two children.
- This is in contrast to binary trees, where each node can have at most two children.
- Multiway search trees are used to organize and store data in a hierarchical manner, allowing for efficient searching, insertion, deletion, and traversal operations.

## Types of Multiway Search Trees:

1.) **B-tree: **

A B-tree is a balanced multiway search tree that is commonly used in databases and file systems for indexing. It maintains balance by allowing a variable number of keys and children per node within a specified range.

**2.) B+-tree: **

Similar to a B-tree, but only keys are stored in internal nodes. Data records are stored in leaf nodes, linked together to form a sorted linked list, facilitating range queries.

3.) **B-tree*: **

A variation of the B-tree that aims to reduce the number of nodes accessed during operations, thereby improving performance.

4.) **Trie (Prefix tree):**

A multiway search tree used for storing a dynamic set of strings or associative arrays where the keys are usually sequences, such as words in a dictionary.

## Applications of Multiway Search Trees:

**Databases:**

Multiway search trees like B-trees are widely used for indexing in databases, allowing for efficient retrieval, insertion, and deletion of records.

**File Systems:**

Multiway search trees are used in file systems for organizing directory structures and facilitating fast file access.

**Routing Tables:**

Trie data structures are used in networking for IP routing and prefix matching.

**Spell Checkers and Auto-completion:**

Trie data structures are used in spell checkers and auto-completion systems for fast word lookup and suggestion generation.

## Advantages of Multiway Search Trees:

**Balanced Structure:**

Many types of multiway search trees, such as B-trees, maintain balance, ensuring that operations remain efficient even as the tree grows.

**Efficient Operations:**

Multiway search trees provide efficient operations for searching, insertion, deletion, and traversal, especially in large datasets.

**Flexible Design:**

Multiway search trees can be adapted to various applications and scenarios by adjusting parameters such as the maximum number of children per node.

## Disadvantages of Multiway Search Trees:

**Complexity:**

Implementing and understanding multiway search trees can be more complex compared to binary trees due to the varying number of children per node.

**Overhead:**

Some types of multiway search trees may have additional overhead in terms of memory usage and node management compared to simpler data structures.

**Specific Use Cases:**

While multiway search trees have broad applications, they may not be the best choice for all scenarios. Choosing the appropriate type of tree depends on factors such as the nature of the data and the expected operations.

## Note:

In an m-Way tree of order **m**, each node contains a maximum of **m â€“ 1** elements and m children.

The goal of m-Way search tree of height h calls for O(h) no. of accesses for an insert/delete/retrieval operation. Hence, it ensures that the height **h** is close to **log_m(n + 1)**.

The number of elements in an m-Way search tree of height **h** ranges from a minimum of **h** to a maximum of m^h-1.

An m-Way search tree of n elements ranges from a minimum height of **log_m(n+1)** to a maximum of **n**

An example of a 5-Way search tree is shown in the figure below. Observe how each node has at most 5 child nodes & therefore has at most 4 keys contained in it.