Time and Space Complexity of Linked List

The time complexity of the Linked List is O(n) for Accessing, insertion, or deletion at the beginning and searching for an element, where n is the number of elements. However, insertion and deletion at the beginning or end take O(1) time in a doubly linked list due to direct access to the head and tail nodes.

Space complexity for both types of linked lists is O(n), as each element requires space for its data and pointers to the next (and possibly previous) node, resulting in linear space usage proportional to the number of elements.

Here’s a table summarizing the time and space complexity of common operations for a linked list:

Operation	Time Complexity (Singly Linked List)	Time Complexity (Doubly Linked List)	Space Complexity
Accessing by Index	O(n)	O(n)	O(1)
Insertion at Beginning	O(1)	O(1)	O(1)
Insertion at End	O(n)	O(1)	O(1)
Insertion at Given Position	O(n)	O(n)	O(1)
Deletion at Beginning	O(1)	O(1)	O(1)
Deletion at End	O(n)	O(1)	O(1)
Deletion at Given Position	O(n)	O(n)	O(1)
Searching	O(n)	O(n)	O(1)

Time Complexity of Searching (Finding an Element) in Linked List:

• Best Case: O(1) – If the element is found at the head of the list.
  • In the best case, the target element is located at the beginning of the linked list, so only one comparison is needed to find it.
• Worst Case: O(n) – If the element is at the end of the list or not present.
  • In the worst case, the target element is either at the end of the list, requiring traversal through all elements, or not present at all, resulting in full traversal.
• Average Case: O(n) – Similar to the worst case, as each element may need to be checked on average.
  • On average, the target element could be located anywhere within the list, requiring traversal through approximately half of the elements.

Time Complexity of Insertion (Adding an Element) in Linked List:

• Best Case: O(1) – If inserting at the beginning of the list.
  • Insertion at the beginning requires updating the head pointer, which can be done in constant time.
• Worst Case: O(n) – If inserting at the end or in the middle of the list, requiring traversal.
  • Inserting at the end or in the middle of the list requires traversing to the appropriate position, which may involve visiting all elements.
• Average Case: O(n) – Similar to the worst case, as traversal may be needed on average.
  • On average, insertion could occur anywhere within the list, requiring traversal through approximately half of the elements.

Time Complexity of Deletion (Removing an Element) in Linked List:

• Best Case: O(1) – If deleting the first element.
  • Deletion of the first element only requires updating the head pointer, which can be done in constant time.
• Worst Case: O(n) – If deleting the last element or one in the middle, requiring traversal.
  • Deleting the last element or one in the middle requires traversal to locate the target element, which may involve visiting all elements.
• Average Case: O(n) – Similar to the worst case, as traversal may be needed on average.
  • On average, the target element could be located anywhere within the list, requiring traversal through approximately half of the elements.

Time Complexity of Traversal in Linked List: O(n)

• Each element needs to be visited once to perform any operation.

Time Complexity of Accessing (Getting/Setting) an element in Linked List: O(n)

• Typically O(n), as access requires traversal from the head to the desired position.
• Accessing an arbitrary element in the linked list requires traversal from the head to the desired position, which may involve visiting all elements.

Auxiliary Space Complexity of Linked List:

The auxiliary space Complexity of above linked list operations mentioned above is O(1) because they do not require extra space beyond a fixed number of variables. However, for certain operations, extra space of the order of O(N) may be needed. For instance, sorting a linked list using a non-in-place sorting algorithm would require this additional space.