⚡Algorithms & Data Structures
Hardware geometry dictates algorithmic performance. This volume examines memory hierarchy, B-Trees vs LSM-Trees, cache-oblivious designs, and consistent hashing rings.
Foundational Invariants & Core Principles:
Stage 1: Trees & Graphs
Sequential learning progression covering core mechanics of trees & graphs.
Array Manipulation Techniques
Array Manipulation Techniques is a foundational topic in Algorithms & Data Structures. Engineers use it to make predictable trade-offs under load, failure, and evolving requirements.
String Matching Algorithms
String Matching Algorithms is a foundational topic in Algorithms & Data Structures. Engineers use it to make predictable trade-offs under load, failure, and evolving requirements.
Linked List Patterns
Linked List Patterns is a foundational topic in Algorithms & Data Structures. Engineers use it to make predictable trade-offs under load, failure, and evolving requirements.
Stack & Queue Data Structures & Monotonic Stack Pattern
Stack & Queue Data Structures & Monotonic Stack Pattern provides core foundational patterns in Algorithms & Data Structures. Manage LIFO / FIFO orderings and optimize range queries with Monotonic Stacks in linear time.
Sliding Window Maximum Patterns
Sliding Window Maximum Patterns is a foundational topic in Algorithms & Data Structures. Engineers use it to make predictable trade-offs under load, failure, and evolving requirements.
Stage 2: B-Trees vs LSM-Trees
Sequential learning progression covering core mechanics of b-trees vs lsm-trees.
Monotonic Deque Techniques
Monotonic Deque Techniques is a foundational topic in Algorithms & Data Structures. Engineers use it to make predictable trade-offs under load, failure, and evolving requirements.
Tree Data Structures & Traversal Mechanics
Tree Data Structures & Traversal Mechanics provides core foundational patterns in Algorithms & Data Structures. Master hierarchical data models including Binary Trees, BSTs, AVL Trees, and In-Order/Pre-Order/Post-Order traversals.
Heaps & Priority Queues
A binary heap stores elements in a complete tree where each parent is smaller (min-heap) or larger (max-heap) than its children, enabling efficient priority queue operations.
Segment Trees for Range Queries
Segment Trees for Range Queries is a foundational topic in Algorithms & Data Structures. Engineers use it to make predictable trade-offs under load, failure, and evolving requirements.
Fenwick Trees (Binary Indexed Trees)
Fenwick Trees (Binary Indexed Trees) is a foundational topic in Algorithms & Data Structures. Engineers use it to make predictable trade-offs under load, failure, and evolving requirements.
Stage 3: Dynamic Programming
Sequential learning progression covering core mechanics of dynamic programming.
Graph Traversal & Pathfinding: BFS, DFS & Dijkstra
Graph Traversal & Pathfinding: BFS, DFS & Dijkstra provides core foundational patterns in Algorithms & Data Structures. Traverse graphs efficiently using Breadth-First Search, Depth-First Search, and Dijkstra shortest path algorithms.
Flood Fill on Grids & Graphs
Flood Fill on Grids & Graphs is a foundational topic in Algorithms & Data Structures. Engineers use it to make predictable trade-offs under load, failure, and evolving requirements.
Matrix Traversal Patterns
Matrix Traversal Patterns is a foundational topic in Algorithms & Data Structures. Engineers use it to make predictable trade-offs under load, failure, and evolving requirements.
Bellman-Ford Shortest Paths
Bellman-Ford Shortest Paths is a foundational topic in Algorithms & Data Structures. Engineers use it to make predictable trade-offs under load, failure, and evolving requirements.
Floyd-Warshall All-Pairs Shortest Paths
Floyd-Warshall All-Pairs Shortest Paths is a foundational topic in Algorithms & Data Structures. Engineers use it to make predictable trade-offs under load, failure, and evolving requirements.
Stage 4: Monotonic Stacks
Sequential learning progression covering core mechanics of monotonic stacks.
Kruskal Minimum Spanning Tree
Kruskal Minimum Spanning Tree is a foundational topic in Algorithms & Data Structures. Engineers use it to make predictable trade-offs under load, failure, and evolving requirements.
Prim's Minimum Spanning Tree
Prim's Minimum Spanning Tree is a foundational topic in Algorithms & Data Structures. Engineers use it to make predictable trade-offs under load, failure, and evolving requirements.
Topological Sort, Inverted Index & Search Patterns
Topological Sort, Inverted Index & Search Patterns provides core foundational patterns in Algorithms & Data Structures. Solve dependency DAG ordering, inverted index search scans, and logarithmic searching in large datasets.
Counting & Radix Sort
Counting & Radix Sort is a foundational topic in Algorithms & Data Structures. Engineers use it to make predictable trade-offs under load, failure, and evolving requirements.
Hash Tables & Probabilistic Bloom Filters
Hash Tables & Probabilistic Bloom Filters provides core foundational patterns in Algorithms & Data Structures. Achieve O(1) constant time lookups and test set membership with zero false negatives using space-efficient Bloom filters.
Stage 5: Sorting & Searching
Sequential learning progression covering core mechanics of sorting & searching.
Divide & Conquer Algorithms
Divide & conquer splits input, solves subproblems recursively, and merges partial answers—classic examples include merge sort and binary search on answer space.
Core Algorithm Patterns: Two Pointers, Fast & Slow, Sliding Window & DP
Core Algorithm Patterns: Two Pointers, Fast & Slow, Sliding Window & DP provides core foundational patterns in Algorithms & Data Structures. Master top interview algorithm techniques including Two Pointers, Fast & Slow Pointers, Sliding Window, and Dynamic Programming.
Bit Manipulation Techniques
Bit Manipulation Techniques is a foundational topic in Algorithms & Data Structures. Engineers use it to make predictable trade-offs under load, failure, and evolving requirements.
Bitmask Dynamic Programming
Bitmask Dynamic Programming is a foundational topic in Algorithms & Data Structures. Engineers use it to make predictable trade-offs under load, failure, and evolving requirements.
Reservoir Sampling
Reservoir Sampling is a foundational topic in Algorithms & Data Structures. Engineers use it to make predictable trade-offs under load, failure, and evolving requirements.
Stage 6: Hash Tables
Sequential learning progression covering core mechanics of hash tables.
Randomized Algorithms
Randomized Algorithms is a foundational topic in Algorithms & Data Structures. Engineers use it to make predictable trade-offs under load, failure, and evolving requirements.
Amortized Analysis
Amortized Analysis is a foundational topic in Algorithms & Data Structures. Engineers use it to make predictable trade-offs under load, failure, and evolving requirements.
Database Indexing: B-Trees vs LSM-Trees
Database indexes turn linear O(N) table scans into logarithmic O(log N) lookups. B-Trees optimize point & range reads; LSM-Trees turn random writes into sequential disk writes.
B-Trees vs LSM-Trees Storage Engines
B-Trees vs LSM-Trees Storage Engines provides core foundational patterns in Algorithms & Data Structures. Compare B+ Tree read-optimized node layouts against LSM-Tree append-only SSTable write buffers.
ACID Transaction Fundamentals
ACID Transaction Fundamentals is a foundational topic in Databases & Storage Engines. Engineers use it to make predictable trade-offs under load, failure, and evolving requirements.
Stage 7: Stage 7
Sequential learning progression covering core mechanics of stage 7.
Database Isolation Levels & Transaction Anomalies
Database Isolation Levels & Transaction Anomalies provides core foundational patterns in Distributed Systems & Storage. Understand Dirty Reads, Non-Repeatable Reads, Phantom Reads, Write Skew, and SSI isolation in SQL and NoSQL engines.
SQL Query Tuning: Index Seeks, Scans, Clustered & Covering Indexes
Relational query execution hinges on whether the optimizer executes an Index Seek (direct O(log N) B-Tree root-to-leaf traversal) or an Index/Table Scan (O(N) sequential page reads). When non-clustered indexes lack requested SELECT columns, the engine must perform a Key/RID Lookup back to clustered index pages for every row, triggering catastrophic random disk I/O.
Full-Text Inverted Indexes
Full-Text Inverted Indexes is a foundational topic in Databases & Storage Engines. Engineers use it to make predictable trade-offs under load, failure, and evolving requirements.
Explore Other Domain Curriculums
Distributed Systems
High-availability replication, event loops, quorum consensus, and horizontal database sharding.
Software Architecture
Decoupled event streaming, microservice resilience, CQRS, and domain-driven design.
Design Patterns
GoF structural/behavioral patterns, circuit breakers, sagas, and transactional outbox patterns.
Software Engineering
Clean code craft, automated testing pyramids, CI/CD pipelines, refactoring, and technical debt.