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| id | title | toc_max_heading_level |
|---|---|---|
| linked-list | Linked list | 2 |
Introduction
Like arrays, a linked list is used to represent sequential data. It is a linear collection of data elements whose order is not given by their physical placement in memory, as opposed to arrays, where data is stored in sequential blocks of memory. Instead, each element contains an address of the next element. It is a data structure consisting of a collection of nodes which together represent a sequence.
In its most basic form, each node contains: data, and a reference (in other words, a link) to the next node in the sequence.
Advantages
Insertion and deletion of a node in the list (given its location) is O(1) whereas in arrays the following elements will have to be shifted.
Disadvantages
Access time is linear because directly accessing elements by its position in the list is not possible (in arrays you can do arr[4] for example). You have to traverse from the start.
Singly linked list
A linked list where each node points to the next node and the last node points to null.
Doubly linked list
A linked list where each node has two pointers, next which points to the next node and prev which points to the previous node. The prev pointer of the first node and the next pointer of the last node point to null.
Circular linked list
A singly linked list where the last node points back to the first node.
There is a circular doubly linked list variant where the prev pointer of the first node points to the last node and the next pointer of the last node points to the first node.
Implementations
Out of the common languages, only Java provides a linked list implementation. Thankfully it's easy to write your own linked list regardless of language.
| Language | API |
|---|---|
| C++ | N/A |
| Java | java.util.LinkedList |
| Python | N/A |
| JavaScript | N/A |
Time complexity
| Operation | Big-O | Note |
|---|---|---|
| Access | O(n) | |
| Search | O(n) | |
| Insert | O(1) | Assumes you have traversed to the insertion position |
| Remove | O(1) | Assumes you have traversed to the node to be removed |
Learning resources
- Readings
- Videos
- Singly-linked lists, University of California San Diego
- Doubly linked lists, University of California San Diego
Common routines
Be familiar with the following routines because many linked list questions make use of one or more of these routines in the solution:
- Counting the number of nodes in the linked list
- Reversing a linked list in-place
- Finding the middle node of the linked list using two pointers (fast/slow)
- Merging two linked lists together
Corner cases
- Empty linked list (head is
null) - Single node
- Two nodes
- Linked list has cycles. Tip: Clarify beforehand with the interviewer whether there can be a cycle in the list. Usually the answer is no and you don't have to handle it in the code
Techniques
Sentinel/dummy nodes
Adding a sentinel/dummy node at the head and/or tail might help to handle many edge cases where operations have to be performed at the head or the tail. The presence of dummy nodes essentially ensures that operations will never have be done on the head or the tail, thereby removing a lot of headache in writing conditional checks to dealing with null pointers. Be sure to remember to remove them at the end of the operation.
Two pointers
Two pointer approaches are also common for linked lists. This approach is used for many classic linked list problems.
- Getting the kth from last node - Have two pointers, where one is k nodes ahead of the other. When the node ahead reaches the end, the other node is k nodes behind
- Detecting cycles - Have two pointers, where one pointer increments twice as much as the other, if the two pointers meet, means that there is a cycle
- Getting the middle node - Have two pointers, where one pointer increments twice as much as the other. When the faster node reaches the end of the list, the slower node will be at the middle
Using space
Many linked list problems can be easily solved by creating a new linked list and adding nodes to the new linked list with the final result. However, this takes up extra space and makes the question much less challenging. The interviewer will usually request that you modify the linked list in-place and the solve the problem without additional storage. You can borrow ideas from the Reverse a Linked List problem.
Elegant modification operations
As mentioned earlier, a linked list's non-sequential nature of memory allows for efficient modification of its contents. Unlike arrays where you can only modify the value at a position, for linked lists you can also modify the next pointer in addition to the value.
Here are some common operations and how they can be achieved easily:
- Truncate a list - Set the
nextpointer tonullat the last element - Swapping values of nodes - Just like arrays, just swap the value of the two nodes, there's no need to swap the
nextpointer - Combining two lists - attach the head of the second list to the tail of the first list
Recommended questions
- Reverse a Linked List
- Detect Cycle in a Linked List
- Merge Two Sorted Lists
- Merge K Sorted Lists
- Remove Nth Node From End Of List
- Reorder List
Recommended courses
import AlgorithmCourses from '../_courses/AlgorithmCourses.md'