Friday is for fluency
The Algorithmic Forge is the parallel algorithmic spine of the course. Every Friday you sharpen a skill that supports the current phase - with four tiers so depth never blocks the core path.
Recurring Friday skill that directly supports the current phase
Guided lab or one representative problem
Reference material for future use or unusual interview prompts
A selected advanced problem integrated with a gate or capstone
| Weeks | Theme | Tier | Artifact |
|---|---|---|---|
| 1–6 | Complexity, arrays, prefix sums, two pointers, binary search, bitmasks | Core | Timed implementation drill with complexity note |
| 7–14 | Matrix multiplication, Gaussian elimination, matrix exponentiation, recurrences | Core | From-scratch matrix or recurrence solver |
| 15–22 | Numerical methods, binary search on answer, ternary search, Newton iteration | Supporting | Root-finding or optimization comparison |
| 23–30 | Probability simulation, expectation DP, combinatorics, inclusion-exclusion, number theory basics | Core | Expectation/counting lab; Week 30 mini-contest |
| 31–37 | Heaps, hashing, tries, linked structures, intervals, basic pattern matching | Core | Retrieval/cache primitive plus timed data-structure drill |
| 38–45 | Fenwick, segment trees, range queries, sketches, DSU, randomized hashing | Core | Range-query or routing primitive; Week 45 mini-contest |
| 46–52 | Graph representation, BFS/DFS, SCC, topological sort, shortest paths | Core | Dependency graph or routing implementation |
| 53–57 | MST, Euler paths, max flow, min-cost flow, matching | Core / Supporting | Resource-allocation design; Week 57 graph boss fight |
| 58–69 | DP, greedy, bitmask DP, probability DP, experiment assignment | Core | Evaluation or assignment tool with algorithmic analysis |
| 70–81 | KMP, Aho–Corasick, trie retrieval, sequence DP, suffix-array survey | Core / Supporting | Pattern detector or retrieval index; Week 81 string boss |
| 82–93 | Priority scheduling, interval allocation, capacity search, randomized load balancing | Core / Supporting | Scheduler benchmark; Week 93 inference boss |
| 94–102 | Euler indexing, subtree aggregation, DSU on Tree, HLD survey | Supporting / Boss | Tenant-tree query lab; Week 102 platform boss |
| 103–108 | Mo’s algorithm, capstone integration, tree forensics | Boss fights | Capstone 1 required; Capstone 2 optional at Week 108 |
Gaussian elimination, matrix exponentiation, or randomized SVD with numerical-stability notes.
Expectation DP, combinatorics, modular arithmetic, and one optimization search problem.
Fenwick/segment tree, DSU, hashing, and a range-query workload.
Euler indexing plus a flow or matching formulation for scheduling/resource allocation.
Experiment assignment, greedy rollout, or bandit allocation with a correctness and trade-off report.
Aho–Corasick tool/prompt detector or sequence-DP planner.
Priority scheduling, interval allocation, and binary search on capacity backed by a benchmark.
Euler Tour plus DSU-on-Tree subtree analytics, used as preparation for Capstone 2.
Mo’s algorithm over immutable LLM traces - the required algorithmic capstone.
Euler Tour + DSU on Tree over agent execution trees. Extra depth credit, not required for the LLM Platform badge.
| Algorithmic area | Treatment | Lands in |
|---|---|---|
| Complexity, arrays, prefix sums, binary search, greedy | Core | Weeks 1–6 and recurring |
| Matrix operations, Gaussian elimination, exponentiation, recurrences | Core | Weeks 7–18 |
| Probability, expectation DP, combinatorics, modular arithmetic, gcd/sieve | Core | Weeks 23–30 and Weeks 58–69 |
| Heaps, hashing, tries, Fenwick trees, segment trees, DSU | Core | Weeks 31–45 |
| BFS/DFS, SCCs, topological sort, shortest paths | Core | Weeks 46–52 |
| MST, Euler paths, flows, matching | Core concepts; selected Boss fights | Weeks 53–57 |
| Dynamic programming and state-space reduction | Core | Weeks 58–69 |
| KMP, Aho–Corasick, retrieval-oriented string matching | Core | Weeks 70–81 |
| Suffix arrays, suffix trees, suffix automata | Supporting / Archive | Weeks 70–81; project-driven promotion |
| Scheduling, interval structures, randomized algorithms, capacity search | Core / Supporting | Weeks 82–102 |
| Euler Tour, DSU on Tree, Mo’s algorithm | Boss fights | Weeks 103–108 |
| Computational geometry | Supporting basics; Archive advanced | Weeks 1–30 and project-driven |
| HLD, dynamic trees, Link-Cut Trees, exotic contest structures | Archive / Boss fight | Capstone extensions only |
Core drills are required and phase-aligned. Supporting labs are guided depth. Archive topics are reference-only. Boss fights are selected gate or capstone extensions. A learner is never blocked from the next phase by optional depth work.