00 · ACTIVE-LEARNING SYNTHESIS
Complete Unit 3 & Unit 4 study guide synthesised from the VCE Algorithmics (HESS) curriculum notes — formal ADT signatures, graph theory, shortest-path & MST proofs, recurrence relations, Master Theorem, complexity classes, Turing machines, and philosophy of AI.
Every module below is distilled directly from the VCE Algorithmics (HESS) study vault. Select any lesson to study formal ADT signatures, graph proofs, recurrence derivations, complexity classes, Turing machine configurations, and interactive self-checks.
Formal ADT specification (name, import, ops), List vs Unsorted/Sorted Array complexity bounds, LIFO Stacks, FIFO Circular & Linked Queues, Sets, Priority Queues, and Dictionaries.
study →Formal graph definitions G=(V,E), order, size, degree, diameter, density, transitive closure, DAGs, bridges, trees, and complete BFS, DFS (iterative & recursive), cycle detection, and Best-First Search analyses.
study →Prim's Cut Property & Loop Invariant proof, Kruskal's MST, Dijkstra's PQ relaxation, Bellman-Ford negative cycles, Warshall's & Floyd-Warshall's Θ(|V|³) DP recurrences, A* heuristics, and Google PageRank iteration tables.
study →Word RAM model, Big-O/Ω/Θ bounds, solving recurrences by Iteration & Telescoping, the Master Theorem (including Strassen a=7, b=2), Binary Search induction proof, Design Paradigms, Merge Sort, and Quick Sort.
study →P, NP, NP-Complete & NP-Hard, Cobham's vs Church-Turing thesis, TSP, N-Queens, 0-1 Knapsack, Graph Colouring bounds, Hill Climbing, Simulated Annealing, Hilbert's Program, Gödel, Halting Problem, Turing Machines, Chinese Room, SVMs, Neural Networks, and AI Ethics.
study →
Covers formal Abstract Data Type (ADT) signatures (name, import, ops), concrete implementations for Lists, Arrays, Stacks, Queues, Sets, Priority Queues, and Dictionaries, mathematical graph definitions, BFS/DFS traversals, cycle detection, MSTs (Prim & Kruskal), shortest paths (Dijkstra, Bellman-Ford, Warshall, Floyd-Warshall, A*), and Google's PageRank algorithm.
Covers the Word RAM model, asymptotic bounds (), solving recurrence relations via Iteration and Telescoping sums, the Master Theorem, loop invariant induction proofs, algorithm design paradigms, Merge Sort & Quick Sort, complexity classes (), metaheuristics, Hilbert's Program, Gödel, the Halting Problem, Turing Machines, Searle's Chinese Room, SVMs, and Neural Networks.