The realization that linked lists require $O(n)$ time for access, contrasting sharply with the $O(1)$ random access of arrays, forces a critical comparison.
The choice between an array and a linked list depends entirely on which operations are performed most frequently, balancing the costs of traversal versus data shifting.
Summary: When to Choose
- Choose Arrays when:
- Accessing elements by index (random access) is the most frequent operation ($O(1)$ performance).
- The size of the data structure is largely fixed or predictable.
- Memory efficiency is paramount and data items are small.
- Choose Linked Lists when:
- Frequent insertions or deletions are required, especially at the boundaries ($O(1)$ once the insertion point is known).
- The data size is highly dynamic and unpredictable.
- Sequential access or iteration is acceptable, and random access is rarely needed.
Complexity Trade-offs ($n$ elements)
| Operation | Array (Fixed Size) | Linked List (Singly) | Key Difference |
|---|---|---|---|
| Find/Access (Index $i$) | $O(1)$ | $O(n)$ | Contiguous vs. sequential access. |
| Insert/Delete (At start/end) | $O(n)$ | $O(1)$ | Shifting required in arrays. |
| Insert/Delete (Known middle position $i$) | $O(n)$ | $O(1)$ | Linked lists use pointer relinking (no shifting). |
| Insert/Delete (Search first) | $O(n)$ | $O(n)$ | Search cost dominates for both. |
| Space Overhead | $O(1)$ (No pointer storage) | $O(n)$ (Pointer overhead) | Every node holds an extra `next` pointer. |