While the scattered memory organization of linked lists results in slower $O(n)$ element access, this same flexibility provides crucial benefits in terms of dynamism and efficiency for modification.
- Linked lists are designed for situations where the structure changes frequently, offering two major advantages over fixed-size, contiguous structures like arrays:
- Dynamic Size (Flexibility): Unlike arrays, which require fixed memory allocation, linked lists can grow or shrink dynamically at runtime.
- New nodes are allocated from memory only when needed, making them highly efficient when the required size $n$ is unknown or highly variable.
- Efficient Modification ($O(1)$ Insertion/Deletion): The key benefit is the time complexity for inserting or deleting an element at a known position $i$ (or after a known pointer $p$).
- This operation requires only changing **two or three pointers**, regardless of the size $n$ of the list.
- For arrays, insertion or deletion at index $i$ requires shifting up to $n$ elements, resulting in an $O(n)$ operation. Linked lists perform these modifications in $O(1)$ time.
Complexity Comparison (Modification)
| Operation | Array (Avg) | Linked List (Avg) |
|---|---|---|
| Access (by index) | $O(1)$ | $O(n)$ |
| Insertion (Start) | $O(n)$ | $O(1)$ |
| Insertion (Middle) | $O(n)$ | $O(1)$* |
| Deletion (Middle) | $O(n)$ | $O(1)$* |
* Assumes the predecessor node is already known (e.g., found via traversal).