The Holy Grail

The JVM as Your Operating System

Object layout, compressed OOPs, autoboxing costs, GC fundamentals, escape analysis, JIT compilation, and measuring memory with JOL.

Arrays — The Hard and Deep Way

Contiguous allocation, cache-friendly traversal, ArrayList from scratch with amortized proofs, circular buffers, sparse arrays, and bitsets.

Linked Structures

Reference semantics, singly and doubly linked lists from scratch, cache hostility measured on real hardware, Floyd's cycle detection, skip lists.

Stacks, Queues, and Deques

Array-backed and linked implementations, ArrayDeque from scratch, monotonic stacks, expression evaluation, and binary heaps.

Hashing — The Mathematics of O(1)

Hash function theory, collision resolution, HashMap from scratch, Java 8 treeification, consistent hashing, Bloom filters, HyperLogLog.

Trees — Binary to Balanced to Ugly

BST, AVL, Red-Black trees, B-trees, segment trees, Fenwick trees, tries, suffix arrays, treaps, and splay trees — all from scratch.

Heaps and Priority Structures

Binary heaps, d-ary heaps, binomial heaps, Fibonacci heaps with potential function proofs, pairing heaps, leftist and skew heaps.

Graphs — The Universal Structure

BFS, DFS, topological sort, SCCs, MSTs, Union-Find, Dijkstra, Bellman-Ford, max flow, bipartite matching, and A*.

Sorting and Searching

The comparison lower bound proof, merge sort, quicksort, heapsort, introsort, Timsort internals, radix sort, binary search variants.

Algorithmic Paradigms

Divide and conquer, dynamic programming, classic DP problems, greedy algorithms and matroids, backtracking, randomized algorithms, amortized analysis.

Strings — Behind Grep and Git

KMP, Rabin-Karp, Boyer-Moore, Aho-Corasick, Z-algorithm, Manacher's algorithm, and NFA/DFA regex engines.

The Frontier

Persistent structures, Van Emde Boas, wavelet trees, succinct data structures, LSM trees, CRDTs, lock-free programming, cache-oblivious algorithms.