# What is a Multi-level linked List in Data Structure?

A multi-level linked list is a type of data structure that consists of a series of linked lists, where each node in the main linked list points to another linked list. This allows for the creation of a hierarchical structure, where each node in the main linked list represents a level, and the linked list it points to represents the next level in the hierarchy. Multi-level linked lists are commonly used to represent tree-like structures, such as the file system on a computer.

## How Multi-level Linked List Works in Data Structure?

A multi-level linked list works by having each node in the main linked list contain a reference (or "pointer") to another linked list. This reference is used to connect the main linked list to the next level in the hierarchy. Each node in the main linked list is also typically designed to hold some data, such as a name or identifier, which is used to identify the corresponding level in the hierarchy.

The linked list that a node in the main linked list points to is known as a child linked list, and the nodes in that child linked list are known as child nodes. Each child node may also have a reference to yet another linked list, creating a recursive relationship between the main linked list and its child linked lists.

In this way, a multi-level linked list can represent a hierarchical structure, where the main linked list represents the top level, the child linked lists represent the next level, and so on. This allows for efficient traversal and manipulation of hierarchical data, such as the file system on a computer.

You can traverse the multi-level linked list by starting at the head of the main linked list, then following the reference to the child linked list, then following the reference of the child node to the next child linked list, and so on.

## Types of Multi-level Linked List

There are several different types of multi-level linked lists, including:

**Singly linked list:**In this type of multi-level linked list, each node only contains a reference to the next node in the same linked list and the child linked list.**Doubly linked list:**In this type of multi-level linked list, each node contains references to both the next and previous nodes in the same linked list, and the child linked list.**Multilevel circular linked list:**Each linked list in the multi-level linked list is circular, meaning the last node points to the first node, creating a loop.**Multilevel doubly circular linked list:**This type is a combination of doubly linked list and multilevel circular linked list.**Multilevel singly circular linked list:**This type is a combination of singly linked list and multilevel circular linked list.

## Example of Multi-level Linked List

```
class Node:
def __init__(self, data):
self.data = data
self.child = None
self.next = None
class MultiLevelLinkedList:
def __init__(self):
self.head = None
def add_node(self, data):
new_node = Node(data)
new_node.next = self.head
self.head = new_node
def add_child(self, parent, data):
new_child = Node(data)
new_child.next = parent.child
parent.child = new_child
def traverse(self):
current = self.head
while current:
print(current.data)
if current.child:
current_child = current.child
while current_child:
print(f"\t{current_child.data}")
current_child = current_child.next
current = current.next
# Create a new MultiLevelLinkedList
mlist = MultiLevelLinkedList()
# Add some nodes to the list
mlist.add_node(1)
mlist.add_node(2)
mlist.add_node(3)
# Add some child nodes
mlist.add_child(mlist.head, 4)
mlist.add_child(mlist.head, 5)
mlist.add_child(mlist.head.next, 6)
mlist.add_child(mlist.head.next.next, 7)
# Traverse the list
mlist.traverse()
```

In this example, I defined a Node class with properties data, child, and next. I also defined a MultiLevelLinkedList class which have a head property to keep track of the first node in the list. The class has three methods, add_node, add_child and traverse. The add_node method creates a new node with data and adds it to the head of the list. The add_child method creates a new child node for a parent node. The traverse method prints out the data of each node in the list, starting from the head. It also checks if the current node has a child and if it does, it traverses that child linked list as well. In the main function, it creates a new instance of MultiLevelLinkedList and adds some nodes to it. Then it adds some child nodes to some of the parent nodes. And finally, it calls the traverse method to print out the data of each node in the list. The output will look like this:

```
3
7
2
6
1
5
4
```

The choice of which type of multi-level linked list to use will depend on the specific requirements of the application. Some types of multi-level linked lists may be more efficient for certain operations, while others may be more suitable for certain types of data.

## Applications of Multi-level Linked List

Multi-level linked lists can be used in a variety of applications, such as:

**Hierarchical data representation:**Multi-level linked lists can be used to represent hierarchical data structures, such as a file system where files and folders are organized in a tree-like structure.**Document parsing and formatting:**Multi-level linked lists can be used to store the structure of a document, such as the headings, paragraphs, and lists in a word processing document.**Graphs and networks:**Multi-level linked lists can be used to represent graphs and networks, where each node in the list represents a vertex in the graph, and the child nodes represent edges to adjacent vertices.**Artificial intelligence and machine learning:**Multi-level linked lists can be used to represent decision trees and other hierarchical structures used in AI and machine learning algorithms.**Web development:**Multi-level linked lists can be used to represent the structure of a web page, such as the headings, paragraphs, and lists, which can be used to generate the HTML code for the page.**Database management:**Multi-level linked lists can be used to represent the relationships between tables in a relational database, where each node in the list represents a table and the child nodes represent the relations between the tables.**Game development:**Multi-level linked lists can be used to represent the game objects and their relationships in a game, such as the players, enemies, and objects in a game level.

## Time and Space Complexity of Multi-level Linked List

The time and space complexity of a multi-level linked list will depend on the specific operations that are performed on the list. Here are some examples of the time and space complexity of some common operations:

**Adding a node:**Adding a new node to a multi-level linked list typically has a time complexity of O(1) and a space complexity of O(1), as it only involves creating a new node and updating the pointers.**Adding a child:**Adding a child to a node in a multi-level linked list typically has a time complexity of O(1) and a space complexity of O(1), as it only involves creating a new node and updating the pointers.**Traversing the list:**Traversing a multi-level linked list can be done recursively or iteratively. Recursive traversal has a time complexity of O(n) where n is the number of nodes in the list, and a space complexity of O(n) due to the recursion stack. Iterative traversal has a time complexity of O(n) where n is the number of nodes in the list, and a space complexity of O(1)**Searching for a node:**Searching for a specific node in a multi-level linked list typically has a time complexity of O(n) where n is the number of nodes in the list. The space complexity is O(1) as we only need to store the current node during the search.**Removing a node:**Removing a node from a multi-level linked list typically has a time complexity of O(n) where n is the number of nodes in the list, as it may require traversing the list to find the node. The space complexity is O(1) as we only need to update the pointers to remove the node.

Please note that these are general time and space complexities and can vary depending on the specific implementation of the multi-level linked list.

## Advantages and Disadvantages of Multi-level Linked List

**Advantages of using a multi-level linked list:**

**Flexibility:**Multi-level linked lists can be used to represent a wide range of hierarchical data structures, making them a versatile data structure.**Low memory usage:**Multi-level linked lists only store the data and pointers to the next and child nodes, which makes them a space-efficient data structure compared to other data structures, such as arrays and matrices.**Dynamic size:**Multi-level linked lists can grow or shrink as needed, making them well-suited for applications that require dynamic memory management.**Easy to implement:**Multi-level linked lists are relatively simple to implement, making them a good choice for small-scale projects or educational purposes.

**Disadvantages of using a multi-level linked list:**

**Slow random access:**Since the elements of a multi-level linked list are not stored in contiguous memory, it can be slow to access elements at a specific index.**Higher overhead:**Multi-level linked lists require additional memory to store the pointers to the next and child nodes, which can increase memory usage compared to other data structures.**More complex algorithms:**Some operations, such as searching and sorting, can be more complex to implement with a multi-level linked list compared to other data structures such as arrays and binary trees.**Limited scalability:**Multi-level linked lists may not be well-suited for large-scale projects or applications that require high-performance data structures.

Overall, multi-level linked lists are a simple, flexible and space-efficient data structure that is well-suited for small-scale projects or educational purposes, but may not be the best choice for large-scale projects or applications that require high-performance data structures.