Expert-level data structures covering arrays, linked lists, trees, heaps, hash tables, graphs, and advanced structures like segment trees, tries, and union-find.
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Array: O(1) random access, O(n) insert/delete middle, cache-friendly. Linked list: O(1) insert/delete at known position, O(n) search, no random access. Stack: LIFO, O(1) push/pop. Applications: function calls, expression parsing, DFS. Queue: FIFO, O(1) enqueue/dequeue. Applications: BFS, scheduling, buffers. Deque: double-ended queue, O(1) both ends. Sliding window problems.
BST: O(log n) avg search/insert/delete, O(n) worst case (degenerate). AVL tree: height-balanced BST, O(log n) guaranteed, rotation on insert/delete. Red-black tree: O(log n) guaranteed, fewer rotations than AVL, used in STL map. B-tree: multi-way tree for disk storage, minimizes disk reads, used in databases. Segment tree: range queries and updates, O(log n), build O(n). Trie: prefix tree for strings, O(m) operations where m is string length.
Binary heap: complete binary tree, O(log n) insert/delete-max, O(1) peek. Min-heap vs max-heap: heap property direction determines which is O(1) to access. Fibonacci heap: O(1) amortized insert and decrease-key, O(log n) delete-min. Applications: priority queue, Dijkstra, Prim, heap sort, k-th largest.
Hash function: maps key to index, good function minimizes collisions. Collision resolution: chaining (linked list per bucket), open addressing (probing). Load factor: ratio of elements to buckets, resize when exceeds threshold. O(1) average insert/search/delete, O(n) worst case with many collisions.
Disjoint set union: tracks connected components. Path compression and union by rank: nearly O(1) amortized per operation. Applications: Kruskal MST, cycle detection, dynamic connectivity.
| Pitfall | Fix |
|---|---|
| Using linked list for random access | Use array or dynamic array instead |
| Hash table with bad hash function | Test distribution of hash values |
| BST degenerating to O(n) | Use balanced variant like AVL or RB tree |
| Segment tree off-by-one | Use 1-indexed and carefully define ranges |
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Expert-level abstract algebra knowledge. Use when working with groups, rings, fields, modules, Galois theory, representation theory, or algebraic structures. Also use when the user mentions 'group', 'ring', 'field', 'homomorphism', 'isomorphism', 'normal subgroup', 'quotient group', 'Sylow theorem', 'Galois theory', 'polynomial ring', 'ideal', 'module', 'vector space', or 'representation theory'.
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Expert-level acoustics knowledge. Use when working with sound waves, acoustic propagation, resonance, standing waves, Doppler effect, room acoustics, ultrasound, noise control, musical acoustics, or architectural acoustics. Also use when the user mentions 'sound wave', 'decibel', 'frequency', 'resonance', 'standing wave', 'Doppler effect', 'acoustic impedance', 'reverberation', 'ultrasound', 'noise control', 'harmonics', or 'sound intensity'.
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Expert-level aerodynamics covering subsonic and supersonic flow, lift and drag, airfoil theory, boundary layers, compressible flow, and CFD methods.
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Expert-level air quality engineering covering pollutant sources, atmospheric dispersion, air quality standards, emission controls, and air quality modeling.
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Expert-level aircraft structures covering structural design philosophy, wing and fuselage analysis, fatigue and damage tolerance, composite structures, and certification.
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Expert-level algorithms and complexity theory covering sorting, searching, graph algorithms, dynamic programming, greedy algorithms, NP-completeness, and algorithm design paradigms.
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