In the world of data structures, the choice between arrays and linked lists often depends on a program's specific needs. Understanding the performance characteristics of these data structures is crucial to making an informed decision. In this assignment, we will delve into the efficiency of arrays and linked lists for various operations, including reading, searching, inserting, and deleting. By comparing their time complexities, we can gain insights into when to favor one over the other.
While arrays enable direct access to any element in constant time O(1), reading from a linked list involves a distinct process. Imagine we want to retrieve the value of the fourth item in a linked list. Unlike arrays, where elements reside consecutively in memory, the nodes of a linked list can be scattered throughout memory. Initially, our program only possesses knowledge of the memory address of the first node, lacking immediate awareness of other node locations.
To access the fourth node, the computer undertakes a step-by-step journey. It starts by accessing the first node and then follows the link within that node to reach the second node. Subsequently, it traverses the link in the second node, then the third, to finally arrive at the fourth node. Thus, reaching any desired node within a linked list requires starting with the head node and following the chain of nodes until reaching the intended node.
In the worst-case scenario, when reading from the last node, the process requires N steps, where N denotes the total number of nodes in the list. This insight unveils a notable drawback of linked lists: their read efficiency becomes O(N), a substantial contrast to arrays that provide constant-time access to any element O(1). However, it is crucial to recognize that linked lists possess distinctive advantages, which we will soon discover, rendering them valuable despite this limitation.
Both arrays and linked lists have a linear time complexity O(N) for searching elements. In a linked list, we must follow the links from the first node until we find the desired value. Similar to reading, the worst-case scenario for searching in a linked list occurs when we have to traverse all the nodes. Likewise, searching an array requires examining each element in turn until we find the desired element.
Unlike arrays, where inserting at index 0 requires shifting all subsequent elements, linked lists can effortlessly insert data at the front of the list in just one step, resulting in a constant time complexity of O(1). Regardless of the size of the linked list, inserting at the beginning always takes the same amount of time.
While the best-case scenario of inserting at the beginning of a linked list is O(1), it's also essential to consider the worst-case scenario. In the worst-case scenario, inserting at the end of the linked list requires traversing the entire list to reach the last node, resulting in a time complexity of O(N), where N represents the number of nodes in the list. It is also worth noting that the worst-case scenario for linked lists, appending elements, is the best-case scenario for arrays, and vice versa.
At a glance, the difference between inserting into an array and a linked list seems negligible. In the next lesson, however, we'll find out that in certain scenarios, the difference in how we insert elements can lead to incredible savings in time complexity.
Similar to insertion, linked lists outperform arrays in deletion operations when removing elements from the beginning of the list. Deleting the first node in a linked list only involves updating the reference to the first node, resulting in constant time complexity O(1).
In contrast, deleting the first element of an array requires shifting all remaining elements one cell to the left, resulting in a time complexity of O(N).
When it comes to deleting the final node of a linked list, the deletion itself requires only one step. We can accomplish this by modifying the link of the second-to-last node, making it null. However, accessing the second-to-last node requires traversing N steps since we must start at the beginning of the list and follow the links until we reach the end, resulting in a worst-case time complexity of O(N).
The result is similar to inserting elements, where the best-case scenario for linked lists is the worst-case scenario for arrays, and vice versa.
In the next assignment, we will explore why one might choose to use linked lists over arrays.