Data Structures reference data
Fundamental data structures with properties and complexity analysis.
Topic guide
What Data Structures covers
Data-structure reference data describes how information is organized in memory so that operations are fast: arrays, linked lists, hash tables, trees, heaps and graphs, plus the specialized structures built for particular problems (probabilistic filters, spatial indexes, concurrent containers) and the algorithms that run on them. The usual comparison is by time and space complexity in Big-O terms, which says how cost grows with input size and ignores constants, caches and implementation quality. Choosing a structure means matching its strong operations to the program's access pattern.
Key ideas
- Big-O
- A notation for how an operation's cost grows with input size n, ignoring constant factors. O(1) is constant, O(log n) logarithmic, O(n) linear, O(n^2) quadratic.
- Amortized cost
- The average cost per operation over a sequence, even when some single operations are expensive, as with appending to a dynamic array.
- Balanced tree
- A search tree that keeps its height near log n by rebalancing, so lookups, insertions and deletions stay logarithmic.
- Hash table
- A structure that maps keys to buckets by a hash function, giving average O(1) lookup, with collisions handled by chaining or open addressing.
- Heap
- A tree-based structure that keeps the minimum or maximum at the root, the basis of priority queues.
- Graph
- A set of nodes and edges, stored as an adjacency list (sparse graphs) or matrix (dense graphs).
- Probabilistic data structure
- A compact structure that answers membership or counting queries approximately, trading a bounded error for much less space.
Common pitfalls
- Quoting average-case complexity as the guaranteed bound. Hash tables and quicksort have worse worst cases.
- Ignoring constants and cache behavior: an array often beats a linked list in practice even when Big-O suggests otherwise.
- Using a structure whose strong operation is not the one your program performs most.
- Forgetting that probabilistic structures can give false positives (Bloom filters) or approximate counts.
Using it from an agent
- State the operation, the structure and the case (best, average or worst) when quoting a complexity.
- Ask what operations dominate and how large the data is before recommending a structure.
- Mention the standard-library equivalent in the user's language (for example HashMap, dict, TreeMap) with the structure name.
Start with: Data Structure Complexity Analysis · Hash Tables & Hash Functions
Datasets in Data Structures
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Advanced Graph Algorithms
Advanced graph algorithms: strongly connected components (Tarjan's, Kosaraju's), max flow (Ford-Fulkerson, Edmonds-Karp, Dinic), matching, and graph coloring.
8 entries -
Concurrent Data Structures
Thread-safe data structures: concurrent hash maps, skip lists, queues, stacks, read-write locks, lock-free algorithms, and compare-and-swap patterns.
8 entries -
Data Structure Complexity Analysis
Time and space complexity analysis of common data structures: Array, Linked List, Binary Search Tree, Hash Table, Heap, and Graph with Big-O notation.
15 entries -
Graph Algorithms
Essential graph algorithms: traversals (BFS, DFS), shortest path (Dijkstra, Bellman-Ford), minimum spanning tree (Prim, Kruskal), topological sort, and network flow.
10 entries -
Hash Tables & Hash Functions
Hash table implementations, collision resolution strategies, hash functions, load factor, and performance characteristics.
6 entries -
Probabilistic Data Structures: Bloom Filters & Beyond
Probabilistic data structures for approximate set membership, counting, and cardinality estimation: Bloom filters, Count-Min Sketch, HyperLogLog, and Cuckoo filters.
6 entries -
Sorting Algorithms Comparison
Time and space complexity comparison of sorting algorithms: Bubble, Selection, Insertion, Merge, Quick, Heap, Counting, and Radix Sort with stability notes.
12 entries -
Spatial Data Structures
Spatial indexing structures for multi-dimensional data: k-d trees, R-trees, quadtrees, octrees, grid files, and space-filling curves (Z-order, Hilbert).
7 entries -
String Algorithms and Pattern Matching
String processing algorithms: KMP, Rabin-Karp, Z-algorithm, suffix trees/arrays, Aho-Corasick, and edit distance (Levenshtein).
7 entries -
Tree Data Structures
Complete reference of tree data structures: binary trees, BST, AVL, Red-Black, B-trees, B+ trees, segment trees, and trie.
8 entries
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