Which time complexity is best for linked list?
Time Complexity of linked list storing 'N' elements. For insertion in the linked list, the time complexity is O(1) if done on the head, O(N) if done at any other location, as we need to reach that location by traversing the linked list.
This memory efficient Doubly Linked List is called XOR Linked List or Memory Efficient as the list uses bitwise XOR operation to save space for one address. In the XOR linked list, instead of storing actual memory addresses, every node stores the XOR of addresses of previous and next nodes.
In a singly linked list, the time complexity for inserting and deleting an element from the list is O(n). In a doubly-linked list, the time complexity for inserting and deleting an element is O(1).
If you want to delete a specific element, the time complexity is O(n) (where n is the number of elements) because you have to find the element first. If you want to delete an element at a specific index i , the time complexity is O(i) because you have to follow the links from the beginning.
LinkedList Implementation:
One enqueue () operation takes O(1) time. To insert N elements in the queue will take O(N) time. Time complexity = O(N) ( Drop the constant term).
| Data structure | Time complexity | |
|---|---|---|
| Avg: Indexing | Worst: Indexing | |
| Singly linked list | O(n) | O(n) |
| Doubly linked list | O(n) | O(n) |
| Skip list | O(log (n)) | O(n) |
If we need better performance while searching and memory is not a limitation in this case doubly linked list is more preferred. As singly linked list store pointer of only one node so consumes lesser memory. On other hand Doubly linked list uses more memory per node(two pointers).
Determining the Fastest Algorithm
If the linked list is relatively small or partially sorted, Insertion Sort can be a viable option due to its simplicity and constant-time insertion. However, for larger lists, Merge Sort and Quick Sort provide better performance with their time complexity of O(n log n).
A singly linked list consumes less memory as compared to the doubly linked list. The doubly linked list consumes more memory as compared to the singly linked list.
ArrayList has O(1) time complexity to access elements via the get and set methods. LinkedList has O(n/2) time complexity to access the elements. LinkedLinked class implements Deque interface also, so you can get the functionality of double ended queue in LinkedList.
What is the time complexity of linked list to array?
Array takes more time while performing any operation like insertion, deletion, etc. Linked list takes less time while performing any operation like insertion, deletion, etc. Accessing any element in an array is faster as the element in an array can be directly accessed through the index.
Time Complexity of linked list listiterator method in java: O(n), where n is the number of elements present starting from the given index, till the end of the list.
The insertion, addition, and removal operations are faster in a LinkedList because there is no resizing of an array done in the background. When a new item is added somewhere in the middle of the list, only references in surrounding elements need to change.
In Java LinkedList, get(int) operation is O(N), and size() operation is O(1) complexity. Since it is a linked list, to determine the size will be an O(N) operation, since you must traverse the whole list.
Worst Case Time Complexity of insertion sort on linked list is O(n^2). Average Case Time Complexity of insertion sort on linked list is O(n^2). Best Case Time Complexity of insertion sort on linked list is O(n). Space Complexity of insertion sort on linked list O(1).
What is the worst case time complexity of inserting a node in a doubly linked list? Explanation: In the worst case, the position to be inserted maybe at the end of the list, hence you have to traverse through the entire list to get to the correct position, hence O(n).
When the rate of addition or removal rate is more than the read scenarios, then go for the LinkedList. On the other hand, when the frequency of the read scenarios is more than the addition or removal rate, then ArrayList takes precedence over LinkedList.
Singly linked list is preferred when we have memory limitation(we can't use much memory) and searching is not required. Doubly linked list is preferred when we don't have memory limitation and searching is required(we need to perform search operation on the linked list).
Advantage of Circular linked list. We can go to any node from any node in the Circular linked list which was not possible in the singly linked list if we reached the last node. In a circular list, any node can be starting point means we can traverse each node from any point.
| Algorithm | Time Complexity | |
|---|---|---|
| Best | Worst | |
| Heap Sort | Ω(n log(n)) | O(n log(n)) |
| Quick Sort | Ω(n log(n)) | O(n^2) |
| Merge Sort | Ω(n log(n)) | O(n log(n)) |
Is Quicksort good for linked list?
Not stable, which means it may change the relative order of equal elements in the sorted array. Worst-case time complexity is O(n^2), which occurs when the pivot is not chosen properly and the partitioning process doesn't divide the array evenly. Not suitable for linked lists, as it requires random access to elements.
Efficiency : Merge sort is more efficient and works faster than quick sort in case of larger array size or datasets. whereas Quick sort is more efficient and works faster than merge sort in case of smaller array size or datasets.
When comparing the three main data structures, Doubly Linked Lists are most efficient in all major tasks and operations when looking at time complexity.
Doubly linked list is more efficient. When memory is not the problem and we need better performance while searching, we use doubly linked list. Solve DSA problems on GfG Practice.
Due to the fact that a circular doubly linked list contains three parts in its structure therefore, it demands more space per node and more expensive basic operations. However, a circular doubly linked list provides easy manipulation of the pointers and the searching becomes twice as efficient.
All elements in the ArrayList are located next to each other in the same memory space. This is why retrieving an element from an ArrayList is so fast: given the location of the start of the ArrayList, you can know exactly where any element is located in memory. LinkedLists, on the other hand, use non-contiguous memory.
Arrays have fixed sizes as we remember. Besides, ArrayList resizes itself and this operation slows its performance. Furthermore, ArrayLists can hold only Objects, and they usually store more place than Arrays. Even though Arrays are faster than ArrayLists, fast execution consumes more memory than ArrayList.
To add or remove the element from HashSet, the time complexity is O(1). For adding or removing the element from TreeSet, the time complexity is O(log(n)). Only one null element can be stored in the HashSet. No null elements are allowed.
Slower Search Time:
Linked list have slower search times than arrays as random access is not allowed. Unlike arrays where the elements can be search by index, linked list require iteration.
Arrays are best suited for situations where the size of the collection is known in advance and where elements need to be accessed or manipulated quickly. Linked lists are more flexible and adaptable and are best suited for situations where the size of the collection is not known.
What is the difference between LinkedList and ArrayList?
ArrayList internally uses a dynamic array to store its elements. LinkedList uses Doubly Linked List to store its elements. ArrayList is slow as array manipulation is slower. LinkedList is faster being node based as not much bit shifting required.
Deletion of nodes is easy as compared to a Singly Linked List. A singly linked list deletion requires a pointer to the node and previous node to be deleted but in the doubly linked list, it only required the pointer which is to be deleted.
Why insertion and deletion are faster in a linked list? Insertion and deletion are faster in a linked list because less memory needs to be manipulated.
It is said that the complexity of the LinkedList remove and the add operation is of O(1) . and in case of ArrayList it is of O(n) .
What is the best case time complexity of deleting a node in a Singly Linked list? Explanation: Deletion of the head node in the linked list is taken as the best case. The successor of the head node is changed to head and deletes the predecessor of the newly assigned head node. This process completes in O(1) time.
What is the optimal time complexity to count the number of nodes in a linked list? Answer: A) Explanation: We can count the number of nodes in a linked list in O(n) where n is the number of nodes in the linked list.
Omega Notation
It defines the best case of an algorithm's time complexity, the Omega notation defines whether the set of functions will grow faster or at the same rate as the expression. Furthermore, it explains the minimum amount of time an algorithm requires to consider all input values.
From a memory allocation point of view, linked lists are more efficient than arrays. Unlike arrays, the size for a linked list is not pre-defined, allowing the linked list to increase or decrease in size as the program runs.
Linked lists also have some advantages over arrays when it comes to memory usage. Because linked lists only allocate memory for the nodes that are currently in use, they can be more memory-efficient than arrays for collections that are not always fully populated.
ArrayList is faster in storing and accessing data. LinkedList is faster in manipulation of data.
What is the time complexity of linked list and array?
If the array is full, we first need to copy the array into another array and add a new element. In this case, the time complexity would be O(n). To insert an element at the end of the linked list, we have to traverse the whole list. If the linked list consists of n elements, then the time complexity would be O(n).
An array is faster and that is because ArrayList uses a fixed amount of array. However when you add an element to the ArrayList and it overflows.
ArrayList provides constant time for search operation, so it is better to use ArrayList if searching is more frequent operation than add and remove operation. The LinkedList provides constant time for add and remove operations. So it is better to use LinkedList for manipulation.
Worst Case Time Complexity of insertion sort on linked list is O(n^2). Average Case Time Complexity of insertion sort on linked list is O(n^2). Best Case Time Complexity of insertion sort on linked list is O(n). Space Complexity of insertion sort on linked list O(1).
While the HashMap will be slower at first and take more memory, it will be faster for large values of n. The reason the ArrayList has O(n) performance is that every item must be checked for every insertion to make sure it is not already in the list. We will do n insertions, so it is O(n^2) for the whole operation.
The insertion, addition, and removal operations are faster in a LinkedList because there is no resizing of an array done in the background. When a new item is added somewhere in the middle of the list, only references in surrounding elements need to change.
The ArrayList in Java is backed by an array.
So let's focus first on the time complexity of the common operations at a high level: add() – takes O(1) time; however, worst-case scenario, when a new array has to be created and all the elements copied to it, it's O(n) add(index, element) – on average runs in O(n) time.
The time complexity of remove(int index) Method is O(N). Reason: ArrayList implements RandomAccess interface, so accessing any random element will be done in O(1) complexity. However, since the remaining elements also need to be shifted by one place to their left, the overall time complexity becomes O(N).