Once by the book.
Once where it earns its place.

Time and space complexity

Count repeated work and growing storage over the same release batch before a small input hides the difference

Recursion

Solve a nested recipe from its base case upward, then choose between the call stack and explicit frames

Dynamic programming

Reuse overlapping postage subproblems with a memo or a bottom-up table, then compare the state-space cost

Builds on recursion · memoization

Dynamic array

Record finishers in order, follow capacity growth, and correct indexed results

Linked list

Edit a theatre cue sheet: find a node, keep its handle, and change its links

Stack

Last in, first out — follow the operations, then give an editor undo and redo

Queue and deque

Add to queue, play next, skip: run a music player’s up-next list on a ring that wraps at both ends

Ring buffer

Keep a weather station’s latest readings in fixed slots, and decide whether a full buffer overwrites or refuses

Hash map

Join CRM customers to their orders: hash each email to a bucket, compare keys, and grow when full

Hash set

Keep a birder’s life list once each: hash a species code, probe past collisions, and leave a tombstone when you remove one

Ordered map

Edit a podcast’s chapter markers: find the chapter at the playhead, jump to the next, keep markers 10 seconds apart, and list what is in view

LRU cache

Resolve a café’s short links from memory: a hash map finds each link, a linked list keeps recency, the least recently used is evicted, and a changed link is invalidated

Binary heap

Keep the highest-priority item within reach without sorting everything

Trie

Suggest emoji as someone types a shortcode: share prefixes, complete by popularity, prune removed codes, and weigh the cost of the nodes

Binary search tree

Find a conference badge by name: branch left or right, watch a sorted export build one long branch, and rotate to keep lookups short

B+ trees and indexes

Index a bakery’s orders by day: keep sorted records in linked leaf pages, split a full page and grow a new root, and read a range of days down one path and along the leaves

Builds on binary-search-tree · ordered-map

Adjacency list

Map an island airline’s nonstop routes: keep each airport’s departures and arrivals as lists, check a route, close an airport, and compare with a matrix

Union-find

Group duplicate photos from matching pairs: merge groups, check whether two photos belong together, and rebuild when a photo is taken out

Breadth-first and depth-first search

Search a project folder: find the nearest package.json one layer at a time, add up folder sizes branch by branch, and survive a symlink loop

Topological sort

Calculate an invoice sheet: order cells so each formula runs after what it reads, recalculate only what an edit reaches, and catch a circular reference

Graph overview

Model a trip’s shared tab as a graph: people as nodes, debts as directed, weighted edges, and balances, groups, circles, and settling up as questions about it

Bloom filter

Screen sign-up passwords against a common-password list: hash to a few bits, trust a no, and ask the full list only on a maybe

Count-min sketch

Spot a neighborhood forum’s trending hashtags: count into a small table of counters, never undercount, and rotate each hour

HyperLogLog

Count a transit line’s different riders from card taps: keep the longest run of zeros per bucket, merge stations and days, and trade 1.6% error for kilobytes

Binary search

Read a day of tide predictions: halve the range on every probe, find insertion positions, and keep the boundary conditions honest

Sorting

Shelve a library’s returned books: insertion-sort small piles, merge them stably, and see why the built-in sorts work the same way

Sliding window

Excerpt a product review: grow a window on the right, shrink it on the left, and keep a running summary instead of rereading

Two pointers and prefix sums

Find two sorted book prices that use up a gift card exactly, and answer repeated contiguous totals with stored prefix boundaries

Divide and conquer, greedy choices, and backtracking

Choose a strategy by its proof: split the day to find when the crowd grew most, schedule talks by earliest finish, and undo choices until lightning talks fill a gap exactly

Builds on recursion · sorting · dynamic-programming

Monotonic stacks, interval problems, and string matching

Keep unresolved readings ordered, merge overlapping maintenance windows after sorting, and reuse pattern borders when searching logs

Builds on stack · two-pointers-prefix-sums · divide-conquer-greedy-backtracking