data structures

Ways of organizing, storing, and accessing data so that algorithms can operate efficiently.

linear

• array: contiguous block of memory, O(1) random access
• linked list: nodes connected by pointers, O(1) insertion/deletion
• stack: last-in first-out (LIFO)
• queue: first-in first-out (FIFO)

hierarchical

• tree: nodes with parent-child relationships, binary trees, B-trees
• heap: tree satisfying the heap property, used in priority queues
• trie: prefix tree for fast string lookup

associative

• hash table: key-value storage with O(1) average lookup via hashing
• graphs: nodes and edges representing relationships, directed/undirected, weighted

graph

A graph is a set of vertices connected by edges. Foundation of knowledge graphs, neural networks, and network science. Represented as adjacency lists or adjacency matrices.

choosing

The right structure depends on access patterns: random access favors arrays, frequent insertions favor linked lists, key lookups favor hash tables, hierarchical queries favor trees. databases formalize these tradeoffs at scale.