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Computing Simple #linked-list#doubly-linked#lru

Doubly Linked List Operations

O(1) insert and delete given a node pointer. The basis for LRU caches and deques.

A free, animated doubly linked list operations you can read here or embed on any website, from Scrollchart.

Doubly Linked List Operations

Doubly Linked ListO(1) insert/delete given a pointer; four pointer rewrites vs O(n) array shiftNULLNULLprevAnextprevBnextprevCnextprevDnextprevEnextnext pointersprev pointersXnew node1 B.next=X2 X.next=C3 C.prev=X4 X.prev=BInsert or delete anywhere: 4 pointer writes, O(1) time. Array mid-insert: O(n) element shifts. Basis for LRU caches and deques.ComplexityInsert (given ptr)O(1)Delete (given ptr)O(1)Array mid-insertO(n)

Nodes with prev and next pointers. Insertion and deletion shown as four pointer rewrites. Compared with arrays where mid-insert costs O(n).

Good for

  • Data structures courses teaching pointer manipulation and linked list variants
  • LRU cache explainers showing why doubly linked lists enable O(1) splice-to-front
  • Systems programming articles on deque and deque-backed queue implementations

Source & accuracy

This doubly linked list operations is an editorial illustration built to represent the concept accurately. Where it shows figures, they are typical or representative values chosen to make the relationship clear, not a single underlying dataset. The diagram and its explainer are reviewed and maintained centrally, and updated over time as understanding improves.

Bidirectional traversal and in-place edits

A doubly linked list node holds a value, a next pointer, and a previous pointer. This bidirectional structure enables traversal in both directions and crucially, enables insertion and deletion in O(1) time given a node pointer, without scanning. A singly linked list requires a preceding node to delete; a doubly linked list does not.

This property makes doubly linked lists the foundation of LRU (Least Recently Used) caches. When a cache item is accessed, it is moved to the front of the list in O(1). When eviction is needed, the least recently used item (at the back) is removed in O(1). A hash map stores node pointers for O(1) lookups, completing the cache.

Deques and advanced operations

A doubly linked list naturally supports deque (double-ended queue) operations: push/pop from both front and back in O(1). This is faster than resizable arrays for heavy deque workloads because array resizing is O(n). Splice operations (transferring a sublist from one list to another) also run in O(1) with proper pointer updates.

Memory overhead is higher than arrays (extra pointer per node), and cache locality is poor compared to contiguous storage. For workloads with frequent insertions/deletions in the middle or bidirectional traversal, the O(1) operations justify the overhead. For simple iteration or sequential access, arrays are superior.

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Reference

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