Learning track · 27 concepts

DSA & Implementation

Fast, clean implementation ability: arrays, graphs, trees, dynamic programming, and the core algorithmic patterns.

What mastery looks like

This track contains 27 connected concepts rather than an unordered reading list. Mastery means you can move from vocabulary to mechanisms, predict how the system behaves under pressure, and support a design decision with code, measurements, or a failure-recovery exercise. For DSA & Implementation, use the track description as the boundary: learn enough detail to reason clearly about fast, clean implementation ability: arrays, graphs, trees, dynamic programming, and the core algorithmic patterns.

A useful explanation names the state involved, the operation that changes it, the resource or safety constraint, and the observable signal that tells you whether the mechanism works. Avoid stopping at product names. Compare at least two approaches, state what each optimizes, and identify what breaks first as scale, concurrency, latency, or uncertainty increases.

Suggested study sequence

Start with Arrays & Hashing, Stack, Linked List, Complexity Analysis to establish the basic vocabulary. Continue through the core concepts by alternating explanation with an executable drill. Treat Backtracking, Graphs, Shortest Path, 1D DP as integration work: they should combine earlier mechanisms rather than introduce disconnected facts.

At the end of each session, record one decision you can now make, one failure mode you can now predict, and one unanswered question. Revisit that question through the linked primary sources, then prove the answer in the Playground or a real repository. The track is complete when you can transfer the reasoning to an unfamiliar system, not when every page has been opened.

Roadmaps

Concepts in this track

intro

Stack

LIFO, parsing, monotonic stack.

core

Binary Search

Halving sorted search space, predicate search.

intro

Linked List

Pointer manipulation, fast/slow, reversal.

core

Trees

Binary trees, BSTs, DFS/BFS.

core

Trie

Prefix trees.

advanced

Backtracking

DFS with state restoration, pruning.

advanced

Graphs

BFS/DFS, topo sort, union-find.

advanced

1D DP

Linear state recurrences.

advanced

2D DP

Grid DP, edit distance, knapsack.

core

Greedy

Local-optimal-as-global proofs.

intro

Complexity Analysis

Big-O, amortised cost, and space complexity — how to argue a bound before writing code.

core

Sorting

Comparison sorts, stability, in-place versus extra space, and when a linear-time sort is available.

core

Prefix Sums

Precomputed cumulative arrays that turn repeated range queries into O(1) lookups.

core

Monotonic Stack

A stack kept sorted so each element is pushed and popped once, answering next-greater questions in O(n).

core

String Matching

Finding a pattern in text in linear time — KMP's failure function and Rabin-Karp's rolling hash.

core

Quickselect

Finding the k-th smallest in expected O(n) by recursing into only one partition.