Algorithms & Data Structures Mastery
From physical memory models & asymptotic complexity to dynamic programming, trees, and graph algorithms.
A first-principles, visual-first engineering curriculum mastering the fundamental building blocks of computation. Learn how data structures organize memory in RAM, and how algorithms manipulate them with optimal time and space complexity.
Course Overview
Welcome to Algorithms & Data Structures Mastery on codeworking.org. This track is engineered to take you from the physical reality of RAM memory addresses and CPU cache lines to the mathematical mastery of asymptotic complexity, trees, graphs, and dynamic programming.
What You Will Master
- First-Principles Computational Complexity: Understand
Big-O,Big-Ω, andBig-Θnot as arbitrary trivia, but as the mathematical laws governing scale and performance. - Physical Memory Architecture: Discover why an array scan in contiguous RAM can be 50x faster than a linked list traversal despite identical
O(n)time complexity, mastering CPU cache lines (L1/L2/L3) and spatial locality. - Foundational Data Structures: Implement dynamic arrays, linked lists, stacks, queues, hash tables with collision resolution, and self-balancing trees from scratch.
- Core Algorithmic Paradigms: Master Divide & Conquer, Two Pointers, Sliding Windows, Greedy strategies, and Dynamic Programming (Memoization and Tabulation).
- Graph & Network Theory: Solve complex dependency systems, shortest path routing (Dijkstra), and minimum spanning trees (Kruskal/Prim).
Prerequisites
- Basic familiarity with at least one programming language (C, Java, Python, TypeScript, or Rust).
- No prior theoretical computer science background required. We start at the hardware memory layer and build upward step by step.
Structured Learning Roadmap
Foundations of Algorithmic Thinking & Memory Models
Asymptotic notation (Big-O, Omega, Theta), physical RAM addressability, CPU cache lines, and recurrence trees.
Deep Dive: Introduction to Algorithms & Asymptotic Complexity
Master the mathematical foundations of algorithmic analysis. Explore Big-O, Big-Omega, Big-Theta, time vs space tradeoffs, and amortized complexity.
Deep Dive: Introduction to Data Structures & Physical Memory Models
Discover how data structures interface with physical RAM, 64-byte CPU cache lines (L1/L2/L3), spatial vs temporal locality, and the memory wall.
Mathematical Foundations: Recursion & The Master Theorem
Master recurrence relations, call stack frame mechanics, recursion trees, and the Master Theorem for divide-and-conquer algorithms.
Linear Data Structures
Dynamic arrays, singly and doubly linked lists, stacks, queues, and hash table collision resolution.
Arrays, Dynamic Arrays & Memory Allocation
PlannedContiguous indexing, geometric resizing (2x vs 1.5x), and amortized insertion analysis.
Singly & Doubly Linked Lists
PlannedNode pointers, sentinel dummy nodes, in-place list reversal, and Floyd's cycle detection.
Stacks & Stack-Based Algorithms
PlannedLIFO invariant, parentheses matching, monotonic stacks, and postfix expression evaluation.
Queues, Deques & Circular Ring Buffers
PlannedFIFO mechanics, double-ended queues, and circular index wrapping in OS drivers.
Hash Tables, Hash Functions & Collision Resolution
PlannedHash distribution, separate chaining, open addressing (linear probing), and load factors.
Sorting, Searching & Array Techniques
Divide-and-conquer sorts, linear counting/radix sorts, binary search, and sliding window paradigms.
Elementary Sorting: Bubble, Selection & Insertion Sort
PlannedIn-place comparison sorting, best/worst case behavior, and sorting stability.
Divide & Conquer Sorting: Mergesort & Quicksort
PlannedMerge trees, Lomuto vs Hoare partitioning, randomized pivots, and tail recursion.
Non-Comparison Linear Sorting: Counting, Radix & Bucket Sort
PlannedBreaking the Omega(n log n) comparison barrier with positional digit passes.
Binary Search & Discrete Search Spaces
PlannedSorted array lookups, lower/upper bounds, and binary search on monotonic answer spaces.
Two Pointers & Sliding Window Techniques
PlannedOpposite-direction scanning, fast/slow pointers, and dynamic window expansion/contraction.
Trees & Hierarchical Structures
Binary search trees, self-balancing AVL & Red-Black trees, binary heaps, and prefix tries.
Binary Trees & Tree Traversal Algorithms
PlannedPre-order, In-order, Post-order DFS traversals, and level-order BFS queues.
Binary Search Trees (BST) & Invariants
PlannedSearch, insert, minimum/maximum, and 3-case node deletion with successor replacement.
Self-Balancing Trees: AVL & Red-Black Trees
PlannedTree rotations, balance factors, color invariants, and Linux/Java standard library trees.
Binary Heaps & Priority Queues
PlannedArray-backed complete binary trees, sift-up/sift-down, Floyd's O(n) buildHeap, and Heapsort.
Tries (Prefix Trees) & Radix Trees
PlannedCharacter edge graphs, autocomplete dictionaries, and Patricia tree path compression.
Graphs & Network Algorithms
Graph representations, topological sorting, shortest path trees, and minimum spanning forests.
Graph Representations & Traversal: BFS & DFS
PlannedAdjacency matrix vs adjacency list, unweighted shortest paths, and cycle detection.
Directed Acyclic Graphs (DAG) & Topological Sorting
PlannedDependency resolution, Kahn's indegree algorithm, and DFS post-order reversal.
Shortest Path Algorithms: Dijkstra & Bellman-Ford
PlannedGreedy edge relaxation with min-heaps, and detecting negative weight cycles.
Minimum Spanning Trees: Kruskal & Prim
PlannedCut property, Disjoint Set Union (DSU) with path compression, and priority queues.
Advanced Paradigms & Dynamic Programming
Greedy choice strategies, 1D/2D dynamic programming memoization/tabulation, and backtracking.
Greedy Algorithms & Interval Scheduling
PlannedLocally optimal choices, greedy choice property, and Huffman compression trees.
Dynamic Programming 1: Memoization & Tabulation
PlannedOverlapping subproblems, top-down caching vs bottom-up arrays, and space reduction.
Dynamic Programming 2: Classic Multi-Dimensional Problems
Planned0/1 Knapsack, Longest Common Subsequence (LCS), and Edit Distance matrices.
Backtracking & Combinatorial Search
PlannedState space trees, recursive choice pruning, N-Queens, subsets, and permutations.