Data Structures

Interactive guides to master the building blocks of algorithms.

Arrays & Strings

Why Learn Data Structures?

The right container changes everything — speed, memory, and elegance

A row of numbered boxes — fast to grab, fixed in size

An array that grows automatically when it runs out of space

Two fingers tracing an array to solve problems in one pass

A picture frame scanning over an array to solve sub-array problems in \(O(n)\) time

Pre-calculate a running total so you can sum any subarray in instant \(O(1)\) time

Linked Lists

Singly Linked List

A chain of boxes — each one knows only where the next box is

Doubly Linked List

A two-way chain — each node knows both its neighbour ahead and the one behind

Circular Linked List

A chain with no end — the last link points back to the first

Floyd's Cycle Detection

Catch a loop in a linked list using just two pointers and no extra memory

Reversing a Linked List

Flip the entire chain so the last node becomes first — iteratively or recursively

Stacks & Queues

A pile of plates — the last one you put on is the first one you take off

A line of people waiting — the first one in is the first one served

A line you can join or leave from either end — front or back, your choice

Monotonic Stack

A stack that stays sorted — used to find the next bigger or smaller element fast

Monotonic Queue

A queue that tracks the max or min of a sliding window in constant time

Hash Tables

Turn any key into a bucket number — instantly

Collisions? Just grow a list at that bucket

Instant membership and key-value lookup — the everyday hash table

Frequency Patterns

Count once, answer anything — the hash map superpower

Trees

A family tree where every parent has at most two children

Binary Search Tree

A sorted binary tree — left is smaller, right is bigger

An unbalanced BST is just a slow linked list in disguise

A self-balancing BST that rebalances itself after every insert or delete

A self-balancing BST used inside Java's TreeMap and C++'s std::map

Answer range queries in \(O(\log n)\) with \(O(\log n)\) point updates

Fenwick Tree (BIT)

Prefix sums in \(O(\log n)\) with elegant bit manipulation — simpler than a segment tree

Trie (Prefix Tree)

Store strings by their prefixes — autocomplete in \(O(L)\) time

When nodes can have any number of children — file systems, DOM, org charts

Heaps & Priority Queues

Always know the smallest (or largest) in \(O(1)\) — with \(O(\log n)\) updates

Sort in-place with guaranteed \(O(n \log n)\) — no extra memory needed

Priority Queue Patterns

K-th largest, merge K lists, top-K frequent — solved with a small heap

Two-Heap Pattern

Split the data in half — find the median in \(O(1)\) always

Graphs

Graph Representation

How to store a map of cities and roads in memory

Breadth-First Search

Explore a city map ring by ring — nearest neighbors first

Depth-First Search

Follow one road as far as it goes before backtracking

Topological Sort

Order cities so every one-way road points forward, never backward

Union-Find (Disjoint Set Union)

Track connected groups — merge them near-instantly

Minimum Spanning Tree

Connect all cities with the least total road construction cost

Dijkstra's Algorithm

GPS for graphs — find the cheapest route from one node to all others

Bellman-Ford Algorithm

Shortest paths with negative weights — and negative cycle detection

Floyd-Warshall Algorithm

All-pairs shortest paths in one elegant triple loop

Advanced / Specialized

A linked list with express lanes — search in \(O(\log n)\) on average

Ask 'is this here?' in \(O(1)\) — maybe yes, definitely no

Keep the most recent items fast — evict the forgotten ones

Answer range minimum queries in \(O(1)\) after \(O(n \log n)\) setup

Suffix Array & LCP Array

Sort every suffix of a string — unlock powerful substring queries