Linked List: The Basics

In computer science, a linked list is a data structure used for storing a collection of elements, like integers or strings. It consists of a sequence of nodes, where each node contains a data item and its address.

The address points to the next node in the sequence and so on until the end of the list is reached. The first node in the list is called the head, while the last node is called the tail.

The tail points to NULL, indicating the end of the list. Compared to an array, a linked list has several distinct characteristics that set it apart.

For instance, an array is a collection of elements stored in contiguous memory locations, while a linked list is a collection of elements stored in a non-contiguous manner. This means that a linked list allows for dynamic size, unlike an array, which has a fixed size.

Furthermore, a linked list does not allow random access, while an array does.

## Linked List over Array

One key advantage of using a linked list over an array is its dynamic size. In an array, the amount of memory allocated for it is fixed at compile-time.

This means that if we need to store more elements, we have to allocate a new chunk of memory and copy the contents of the old array to the new one. This can be time-consuming and inefficient, especially if the array is too large.

In a linked list, we can add or remove elements without worrying about the size limitations of a fixed memory block. Each node can be dynamically allocated as it is needed, and the system keeps track of its memory usage.

Another notable advantage is that linked lists do not require contiguous blocks of memory, making them more usable in systems where memory is fragmented.

## Linked List Traversal Algorithm

Traversing a linked list simply means visiting and accessing each node in the list. The traversal algorithm is an iterative process that involves visiting each node and performing an operation on its data.

The traversal algorithm starts with the first node (head) and continues through to the last node (tail), visiting each node in turn. At each node, the data item is accessed and used in some way.

Once all the nodes have been visited, the algorithm terminates. The following is a simple implementation of the traversal algorithm in pseudo-code:

“`

curr = head

## while (curr is not NULL)

print curr.data

curr = curr.next

“`

This algorithm initializes a temporary variable `curr` to point to the head of the linked list. It then enters a while-loop that continues as long as `curr` is not NULL.

At each iteration, the data item of the current node is printed, and the pointer `curr` is moved to the next node in the list.

## Linked List Traversal Illustration

To illustrate the concept of linked list traversal, let’s consider the following linked list:

“`

## head 1 2 3 NULL

“`

To traverse this list, we start at the head and move along each node until we reach NULL. “`

curr =

## head 1 2 3 NULL

Print curr.data (1)

curr = curr.next 2 3 NULL

Print curr.data (2)

curr = curr.next 3 NULL

Print curr.data (3)

curr = curr.next NULL

## Exit loop

“`

Note that the pointer `curr` starts at the head of the list, and each time we print the data of a node, we move the pointer to the next node until the end of the list is reached.

## Conclusion

In conclusion, linked lists are a powerful data structure with many advantages over arrays. They offer dynamic size, flexible memory allocation, and non-contiguous memory usage, making them ideal for many applications.

The traversal algorithm is a simple, yet powerful, technique used to access and manipulate the data in a linked list. Finally, the illustration of the traversal algorithm demonstrates how to access each node in the list and perform some operation on its data.

## 3) Linked List Traversal Implementation

Implementing a linked list traversal algorithm in code requires knowledge of the basic syntax and data structures used in the programming language. In this section, we will use the C++ programming language to create a simple implementation of a linked list traversal.

For this implementation, we assume that we have a linked list with an integer data item. Our task is to traverse the list and print the data items in each node.

We will implement the same traversal algorithm described above. “`

void printList(Node* head)

{

Node* curr = head;

while (curr != NULL)

{

cout << curr->data << " ";

curr = curr->next;

}

}

“`

This code implementation starts by defining the `printList()` function that takes a pointer to the head of the linked list as its parameter.

The function initializes a temporary variable `curr` to point to the head of the list. The while-loop is executed as long as the pointer `curr` is not NULL.

Each node’s data is printed, and the pointer `curr` is updated to point to the next node in the list. 4)

## Linked List Traversal Algorithm Complexity

Linked list traversal algorithms have a time complexity that depends on the size of the list.

In this section, we’ll discuss the average, best, and worst-case time complexity of the traversal algorithm.

## Time Complexity

The time complexity of the linked list traversal algorithm is directly proportional to the size of the list. On average, the algorithm will traverse half of the list (n/2) where n represents the number of elements in the list.

Therefore, the average case time complexity of the traversal algorithm is O(n/2). The best-case time complexity occurs when the list is empty (n=0).

Since there is no node to traverse, the algorithm terminates immediately. As such, the best-case time complexity of the traversal algorithm is O(1).

The worst-case time complexity occurs when the list is fully populated with n elements. In this case, the traversal algorithm must visit each node in the list (n).

Therefore, the worst-case time complexity of the traversal algorithm is O(n).

## Space Complexity

The space complexity of the linked list traversal algorithm is constant and is directly proportional to the number of temporary variables used. In the implementation above, we used a single temporary variable `curr` to traverse the list.

Therefore, the space complexity of the algorithm is O(1). However, it’s worth noting that many linked list algorithms require more space to traverse the list.

For example, algorithms that require looking back at previous nodes might store references to those nodes, increasing the space complexity.

## Conclusion

In conclusion, linked list traversal is a fundamental operation used in many linked list algorithms. The traversal algorithm involves moving through each node in the list and performing some operation on its data.

The implementation of the traversal algorithm will differ depending on the programming language and the underlying data structure. The time complexity of the traversal algorithm is directly proportional to the size of the list, while the space complexity is constant and typically small.

Understanding the complexity of the traversal algorithm is crucial to optimizing linked list algorithms and improving their performance. Linked lists are fundamental data structures that offer several advantages over arrays, including dynamic size, flexible memory allocation, and non-contiguous memory usage.

Traversing linked lists involves moving through each node in the list and performing some operation on its data, and the time complexity depends on the size of the list, while the space complexity is constant and typically small. Implementing linked list traversal requires knowledge of the basic syntax and data structures used in the programming language.

Understanding the complexity of the traversal algorithm is crucial to optimizing linked list algorithms and improving their performance. Overall, linked list traversal algorithms are powerful tools that form the basis of many sophisticated data structures and algorithms.