Data Structures & Algorithms
Data structures and algorithms, taught for data science and AI — not for whiteboard trivia. From Big-O and binary search to trees, graphs, dynamic programming, and the probabilistic structures (Bloom filters, MinHash-LSH) that power real dedup and retrieval. Python throughout, every idea animated.
- Chapter 01
Foundations
4 lessons - 01 Why DSA for Data Science The same correct code can take 3 hours or 3 seconds — the difference is the data structure you chose, not the language.
- 02 Big-O & Complexity How to measure whether an algorithm will still work when your data is 1,000× bigger — the one concept that separates working code from scalable code.
- 03 Recursion & the Call Stack Understand how a function calls itself, what happens in memory when it does, and why naive recursion can be exponentially wasteful.
- 04 Python Built-ins & Their Cost Every built-in operation has a hidden Big-O. Knowing a handful of them is 80% of writing fast Python.
- Chapter 02
Searching
3 lessons - 05 Linear Search The simplest search algorithm — scan items one by one until you find what you need. Slow at scale, but often exactly right.
- 06 Binary Search Search a sorted array in O(log n) — halve the range with each comparison so one million items need only twenty.
- 07 Search Patterns Binary search applied beyond sorted arrays — first/last occurrence, rotated arrays, 2D matrices, and searching on the answer space.
- Chapter 03
Sorting
4 lessons - 08 Bubble, Insertion & Selection The three elementary O(n²) sorts every programmer should understand — they teach the cost model that underpins every more efficient algorithm you'll ever use.
- 09 Merge Sort & Divide-and-Conquer Split the problem until it is trivial, then rebuild the answer — how merge sort achieves O(n log n) in every case and why that makes it the foundation of serious sorting.
- 10 Quicksort & Partitioning How quicksort picks a pivot, slices the array in a single pass, and recurses — plus why a bad pivot turns O(n log n) into O(n²) and how to avoid it.
- 11 Timsort, Stability & sorted() You will never write a sort from scratch in production — but you need to know exactly what Python's sorted() and list.sort() are doing under the hood, because it changes how you design data pipelines.
- Chapter 04
Core Data Structures
4 lessons - 12 Arrays vs Linked Lists Two ways to hold a sequence of values — one lives in a single contiguous block of memory, the other chains scattered nodes with pointers. The choice reshapes every operation's cost.
- 13 Stacks, Queues & Deques Three simple data structures that power the call stack, undo history, BFS, bracket validation, and sliding-window algorithms — and why Python's list is a silent O(n²) trap when you need a queue.
- 14 Hash Tables & Dicts The most important data structure for data work — how a hash function turns a key into an array index, why lookup is O(1) on average, and what happens when the math gets messy.
- 15 Heaps & Priority Queues How a heap keeps the best element always at the top — O(1) peek, O(log n) push/pop — and why it is the natural priority queue for Dijkstra, beam search, and streaming top-K.
- Chapter 05
Trees
4 lessons - 16 Trees & Traversals How trees model hierarchies — and the four canonical ways to walk every node, with the queue or stack that powers each one.
- 17 Binary Search Trees A tree that keeps the binary-search invariant alive — left < node < right — so every search and insert follows a single root-to-leaf path instead of scanning all n elements.
- 18 Tries (Prefix Trees) A tree where the path from root to a node spells a string. Tries give O(L) insert and lookup — independent of vocabulary size — and make prefix queries trivially fast.
- 19 Balanced Trees & B-Trees Why a plain BST can degenerate to O(n), how self-balancing trees fix it with rotations, and why databases use B+-trees — not binary trees — for their indexes.
- Chapter 06
Graphs
4 lessons - 20 Graph Representations How to store a graph in code — adjacency lists vs adjacency matrices — and how to pick the right one for the job.
- 21 Graph Traversal: BFS & DFS How to systematically visit every node in a graph — BFS expanding outward ring by ring, DFS plunging deep before backtracking — and which to reach for when.
- 22 Shortest Paths (Dijkstra) BFS finds the path with fewest hops; Dijkstra finds the path with least total cost. Learn relaxation, the min-heap frontier, and why non-negative weights are required.
- 23 Graphs for ML & Knowledge Graphs How the graph abstractions from this chapter — nodes, edges, BFS, adjacency — quietly power knowledge graphs, node embeddings, GNNs, and GraphRAG in production AI systems.
- Chapter 07
Algorithmic Techniques
5 lessons - 24 Two Pointers & Sliding Window Stop re-scanning. Keep one or two indices moving forward and reuse your previous work — the pattern that turns O(n²) into O(n) for a surprising number of real problems.
- 25 Divide & Conquer A three-step pattern that turns hard problems into smaller copies of themselves — and the reasoning behind why it works so efficiently.
- 26 Greedy Algorithms How to solve optimization problems by always picking the best available option right now — and how to know when that local optimism is provably correct versus dangerously wrong.
- 27 Dynamic Programming How to turn exponential recursion into polynomial-time solutions by solving each subproblem exactly once — the technique behind spell-check, sequence alignment, and optimal planning.
- 28 Backtracking How to search a combinatorial space by building solutions step-by-step, pruning dead branches early — the engine behind N-Queens, Sudoku, and constraint satisfaction.
- Chapter 08
DSA for Data Science
4 lessons - 29 When O(n²) Kills Your DataFrame How accidental quadratic complexity sneaks into real data pipelines — and the hash-based patterns that fix it.
- 30 Vectorization vs Loops Why two O(n) algorithms can differ by 50-100x in wall time — and how to push loops into C where NumPy can run them in a single tight pass over typed memory.
- 31 Sampling & Reservoir Sampling How to draw a perfectly uniform random sample of k items from a stream you cannot load into memory — in one pass, O(n) time, O(k) space.
- 32 Bloom Filters, HyperLogLog & MinHash-LSH Trade a little accuracy for enormous space and time savings — the probabilistic data structures every data engineer should have in their toolkit.
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Data Structures & Algorithms — frequently asked questions
Straight answers to the questions people ask most about data structures & algorithms.
How much DSA do I need for data science and ML?
The practical core: Big-O intuition to reason about cost, hash maps and sets for fast lookups and dedup, sorting and binary search, and a feel for when an O(n²) approach won't scale. You rarely implement exotic algorithms, but understanding complexity is what keeps data pipelines fast.
What is Big-O notation, simply?
Big-O describes how an algorithm's time or memory grows as the input grows, ignoring constants. O(n) doubles when the input doubles; O(n²) quadruples; O(log n) barely grows. It's the tool for predicting whether code will still be fast at 10× or 1000× the data.
When should I use a hash table?
Use a hash table (dict or set in Python) whenever you need fast lookups, membership tests, counting, or deduplication — it offers average O(1) access. It's the workhorse behind grouping, joins, and 'have I seen this before' checks across data work.
What's the difference between O(n log n) and O(n²)?
O(n log n) is the speed of good sorting algorithms and scales to millions of items; O(n²) compares every pair and becomes painfully slow past a few thousand. Turning a nested-loop O(n²) approach into a sort- or hash-based one is one of the highest-leverage optimisations.
What are Bloom filters and HyperLogLog used for?
They're probabilistic structures that trade a little accuracy for huge memory savings at scale. A Bloom filter answers 'have I probably seen this?' without storing every item; HyperLogLog estimates the count of distinct items in a stream using tiny memory. Both power real-world dedup and analytics.