Data Structures terms
The right container makes every algorithm faster
Choosing the right data structure is often the difference between an algorithm that runs in milliseconds and one that times out. This category covers arrays, linked lists, trees, graphs, heaps, hash tables, and more complex structures — with focus on when to use each, what operations are fast or slow, and how they underpin the algorithms built on top of them.
More on Data Structures
History
Data structures emerged as a formal discipline in computer science during the 1960s–1970s, when pioneers like Donald Knuth systematized the study of how data organization affects algorithm performance. Early work focused on foundational structures—arrays, linked lists, trees, and graphs—driven by the practical need to manage memory efficiently on severely resource-constrained machines. The publication of seminal texts like Knuth's "The Art of Computer Programming" and the rise of complexity analysis established that choosing the right data structure was as critical as the algorithm itself. By the 1980s–1990s, as systems grew more complex, specialized structures like B-trees, hash tables, and heaps became standard tools for databases, file systems, and real-time applications. Today, data structures remain a core concern in software engineering: modern practice combines classical structures with variants (skip lists, bloom filters, segment trees) optimized for specific domains like caching, streaming, and distributed systems.
Key concepts
- Arrays
- Linked List
- Stacks
- Queues
- Hash Table
- Binary Trees
- Graphs
- Heaps & Priority Queues
Best references
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Introduction to Algorithms (CLRS) The definitive computer science textbook covering data structures with rigorous analysis. Chapters on arrays, linked lists, trees, graphs, heaps, and hash tables are standard reference material for understanding correctness and complexity.
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Competitive Programming — Data Structures Chapters Comprehensive reference for implementing and applying data structures efficiently, covering standard and advanced structures used in algorithmic problem-solving.
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GeeksforGeeks Data Structures Practical reference with code examples across multiple languages, covering implementation details and use cases for all major data structures in this category.
✦ Latest in Data Structures
Typed relationships here
Edges touching a Data Structures term.
- Skip Lists Contrasts with Hash Table Sep 10
- B-Trees & B+ Trees Contrasts with Hash Table Sep 10
- Covering Index Leverages B-Trees & B+ Trees Sep 10
- Composite Index Design Leverages B-Trees & B+ Trees Sep 10
- Database Indexing Leverages B-Trees & B+ Trees Sep 10
Binary trees connect to pagination through database indexing, which is the structure that actually carries the benefit between them. The index is typically a B-tree variant of the binary tree concept, and its ordered, logarithmic-lookup structure is exactly what lets efficient pagination seek directly to a page's starting key (keyset pagination) instead of scanning and counting rows. Without the index sitting in the middle, the tree's ordering properties would never reach pagination at all — it's the index that translates tree structure into fast page boundaries.
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Quadtree
A tree where each internal node has exactly four children, recursively partitioning 2D space for efficient spatial queries.
3mo ago
Data Structures advanced
Merkle Tree
PHP 7.0+
A binary tree where each non-leaf node holds the hash of its children, enabling efficient verification that data is intact and untampered.
4mo ago
Data Structures advanced
Fenwick Tree (Binary Indexed Tree)
PHP 7.4+
1
A compact array-backed structure giving O(log n) prefix-sum queries and O(log n) point updates with minimal code and memory overhead.
5mo ago
Data Structures advanced
Trie (Prefix Tree)
A tree where each node represents a character — paths from root to leaf spell out keys, enabling O(m) lookup, prefix search, and autocomplete where m is key length, independent of dataset size.
7mo ago
Data Structures intermediate
Adjacency Matrix vs Adjacency List
1
Two ways to represent a graph — adjacency matrix (2D array, O(1) edge lookup, O(V²) space) vs adjacency list (array of lists, O(V+E) space, better for sparse graphs).
7mo ago
Data Structures intermediate
B-Trees & B+ Trees
5
Self-balancing tree structures used in database indexes — each node holds multiple keys, keeping the tree shallow and minimising disk I/O for range queries.
7mo ago
Data Structures advanced
Circular Buffer / Ring Buffer
PHP 5.0+
1
A fixed-size array treated as circular — the write pointer wraps around when it reaches the end, overwriting the oldest data. Used for logs, audio streaming, and producer-consumer queues.
7mo ago
Data Structures intermediate
Disjoint Set / Union-Find
A data structure tracking which elements belong to the same group — supporting near-O(1) union and find operations. Used for network connectivity, Kruskal's MST, and cycle detection.
7mo ago
Data Structures advanced
Graphs
3
A collection of nodes (vertices) connected by edges — directed or undirected, weighted or unweighted. The most general data structure, modelling networks, dependencies, and relationships.
7mo ago
Data Structures intermediate
Queues
PHP 5.3+ A FIFO (First In, First Out) data structure — the first element enqueued is the first dequeued. Used for BFS traversal, job queues, rate limiting, and buffer management.
7mo ago
Data Structures beginner
Segment Trees
A tree data structure for O(log n) range queries and point updates — supporting sum, min, max over arbitrary array ranges.
7mo ago
Data Structures advanced
Skip Lists
4
A probabilistic data structure providing O(log n) search, insert, and delete — used internally in Redis sorted sets for ZADD/ZRANGE operations.
7mo ago
Data Structures advanced
Sparse Matrix Representations
COO, CSR, and DOK formats efficiently store matrices where most values are zero — avoiding storing terabytes of zeros for recommendation systems and graphs.
7mo ago
Data Structures advanced
Stacks
PHP 5.3+ A LIFO (Last In, First Out) data structure — the last element pushed is the first popped. Used for function call stacks, undo history, expression parsing, and DFS traversal.
7mo ago
Data Structures beginner
Tries (Prefix Trees)
PHP 5.0+
A tree where each path from root to node spells a prefix — enabling O(m) insert, lookup, and prefix search where m is the string length, regardless of dictionary size.
7mo ago
Data Structures advanced
Arrays
PHP 5.0+
10
The most fundamental data structure — a contiguous block of memory holding elements of the same type, offering O(1) index access but O(n) insertion and deletion in the middle.
7mo ago
Data Structures beginner
Binary Trees
PHP 5.0+
5
A hierarchical structure where each node has at most two children — Binary Search Trees enable O(log n) search, while balanced variants (AVL, Red-Black) guarantee it.
7mo ago
Data Structures intermediate
Bloom Filter
PHP 7.0+ A probabilistic data structure that tests set membership in O(1) time and O(1) space, with a tunable false-positive rate and zero false negatives.
7mo ago
Data Structures advanced
Hash Table
PHP 5.0+
3
A data structure that maps keys to values using a hash function, providing amortised O(1) average-case lookups, insertions, and deletions.
7mo ago
Data Structures intermediate
Heaps & Priority Queues
PHP 5.3+
2
A tree-based structure satisfying the heap property — min-heap: parent ≤ children; max-heap: parent ≥ children — enabling O(1) peek and O(log n) insert/extract for priority queues.
7mo ago
Data Structures intermediate