🧠 Computer Science Fundamentals: Complete Curriculum Index

Welcome to the Computer Science Fundamentals guide series. This collection spans mathematical complexity theory, fundamental and advanced data structures, algorithmic design paradigms, graph algorithms, low-level binary arithmetic, and modern public-key cryptography.

Every guide in this series is standardized into a two-part learning structure:

  • ⚡ Quick Dive: Executive complexity matrices, cheat sheets, and practical code one-liners for instant lookup.
  • 📖 Extended Guide: Deep technical breakdowns, mathematical proofs, step-by-step algorithms with visual diagrams, Go code implementations, and systems-level tradeoffs.

📚 Complete Curriculum Roadmap

Part 1: Algorithmic Foundations & Complexity

# Guide Primary Topics Covered
01 Introduction to Algorithms & Big-O Asymptotic analysis ($O, \Omega, \Theta$), growth rates, Master Theorem for recurrences, loop invariants & correctness proofs, and space-time tradeoffs.
06 Divide and Conquer Recursive decomposition (Divide, Conquer, Combine), Karatsuba fast multiplication, Strassen's matrix multiplication, and Closest Pair of Points in 2D.
07 Dynamic Programming Optimal substructure, overlapping subproblems, Memoization vs. Tabulation, state design, 0/1 Knapsack (1D array optimization), LCS, and LIS ($O(n \log n)$).
08 Greedy Algorithms Greedy choice property, Activity Selection / Interval Scheduling, Huffman lossless compression, Dijkstra/Kruskal heuristics, and Greedy vs. DP decision matrix.

Part 2: Data Structures Architecture

# Guide Primary Topics Covered
02 Fundamental Data Structures Memory layout & CPU cache locality, Dynamic Array growth & amortized analysis, Doubly Linked Lists with sentinels, Stacks, Queues, and Circular Ring Buffers.
03 Trees, Heaps & Tries Binary Trees, BST properties, Self-Balancing Trees (AVL vs. Red-Black invariants), Binary Min/Max Heaps ($O(n)$ heapify), and Prefix Trees (Tries).
10 Hashing & String Algorithms Hash functions & load factor ($\alpha$), Collision resolution (Separate Chaining, Open Addressing, Robin Hood), Bloom Filters, KMP ($\pi$ table), and Rabin-Karp.

Part 3: Graphs, Low-Level Math & Cryptography

# Guide Primary Topics Covered
04 Graph Algorithms & Traversals Graph representations (Adjacency List vs. Matrix), BFS, 3-color DFS cycle detection, Topological Sort (Kahn's), Dijkstra's SSSP, and Kruskal/Prim MST.
09 Bit Manipulation & Binary Math Two's complement arithmetic, bitwise operators (&, `
11 Public-Key Cryptography Trapdoor one-way functions, RSA cryptosystem, Elliptic Curve Cryptography (Curve25519), ECDHE Forward Secrecy, Digital Signatures, and Hybrid TLS 1.3 architecture.
⌂ All Guides