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Six worlds · start with Academy

World 1 · Kestrel Academy · Foundations

Academy.

One module after another. Each module has short sections: lessons teach, practice problems build the skill, and a checkpoint quiz ends the section. Everything is open: go in any order.

Academy progress0 of 25 modules done

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Part 1Toolkit

Read problems and their limits, count operations, and feel how running time grows.

2 modules · being written

Part 2Data structures

See each structure in memory, try its operations, build it yourself, then solve warm-up problems.

9 modules · 8 ready now

Part 3Algorithms

Watch each algorithm run step by step on your own input, see why it works, build it, then use it.

12 modules · 7 ready now

Part 4Patterns

Recognise the classic problem patterns, such as two pointers and sliding windows, and solve with them.

2 modules · 2 ready now

doneaheadbeing written

2.2 · Hash House · Payments app

Hashing

The records hall of a payments app lives here. You learn to trade memory for time, so that finding a key takes one step instead of a scan.

Section 1 · Inside a hash table0 / 50 of 5 steps done

Lesson · Hash table internals, next
Practice problem: The busiest payment shard, open
Practice problem: Growing a session table, open
Practice problem: Order codes that land in the same bucket, open
Checkpoint quiz + 2 problems, open
Next section: 2 · Seen-set and complement, open

Read the lesson ▶ Lecture

Module review · Hash House reviewbeing written

Browse everything · 218 lessons and problems, lectures, shorts, cheat sheets

LecturesWatch each lesson animated →ShortsOne idea in two minutes →Cheat sheetsEvery pattern on one page →

Lessons ready to learn

2.2 HashingHash table internalsExplain buckets, collisions, load factor and resizing.
2.2 HashingSeen-set and complementFind pairs and duplicates in one pass by remembering what you have seen.
4.1 Two pointersOpposite endsMove pointers inward from both ends of a sorted sequence.
4.1 Two pointersRead and write pointersFilter or compact an array in place with a read pointer and a write pointer.
4.1 Two pointersThree-way partitionSplit values into less, equal and greater in one pass.
4.1 Two pointersMerging sorted sequencesMerge two sorted lists in linear time.
4.1 Two pointers3-sumCombine sorting and two pointers to find triples without duplicates.
4.2 Sliding windowSliding window: fixed and variable windowsAnswer questions about contiguous stretches in one pass, with a window of fixed size or one that grows and shrinks.
4.2 Sliding windowWindows with countsKeep a frequency map inside the window to compare stretches with a pattern.
4.2 Sliding windowAt most K and exactly KFind the longest window with at most K of something, and count windows with exactly K.
4.2 Sliding windowMinimum covering windowFind the shortest window that contains every required item.
2.3 Linked listsLinked listsPicture nodes and next pointers in memory, know what each operation costs, and build a linked list yourself.
2.4 StacksStacksPush and pop at one end, see a stack on an array and on a linked list, follow the call stack, and build your own stack.
2.5 Queues and dequesQueues and dequesAdd at the back and remove from the front, see a queue on a ring buffer and on a linked list, work at both ends with a deque, and build your own ring buffer.
2.6 Trees and binary search treesTrees and binary search treesPicture a tree, walk it in the four orders, search, insert and delete in a binary search tree, see why a sorted insertion order makes it a chain, and build your own.
2.7 Heaps and priority queuesHeaps and priority queuesPicture a heap as a tree and as an array, push and pop with sift up and sift down, build one with heapify, keep the best k of a stream, and build your own min-heap.
2.8 GraphsGraphsMeet vertices and edges, directed, undirected and weighted, see a graph as an adjacency list and as a matrix, count degrees, build a graph from a list of pairs, and build your own.
2.9 TriesTriesStore words letter by letter so words that start the same share a path, insert, search and ask about a prefix, see why the end mark matters, and build your own trie.
3.4 BFS and DFSBFS and DFS on a gridExplore a grid in rings with a queue for the fewest steps, or deep first with a stack to reach every cell, and build both yourself.
3.5 Shortest pathsDijkstra's shortest pathsFind the cheapest route when steps cost different amounts, with a heap of tentative distances.
3.6 Topological sortTopological sortOrder tasks after their dependencies, and detect the cycle that makes an order impossible.
3.7 Union-findUnion-findMerge groups and ask whether two items are connected, almost in constant time.
3.8 GreedyGreedy choicesTake the best choice at each step, and prove when that is also the best overall.
3.9 Dynamic programmingDynamic programming from recursionSpot repeated subproblems, then cache them or fill a table in the right order.
3.10 String basicsString basicsCount, compare and search strings efficiently, up to a first rolling hash.

Practice problems

Not solved yetRepaint a region of map tileseasy
Not solved yetCount the rack blocks on a warehouse flooreasy
Not solved yetFewest moves to a pickup pointeasy
Not solved yetMinutes until a config reaches every servereasy
Not solved yetCheapest delivery routeeasy
Not solved yetTime for a signal to reach every nodeeasy
Not solved yetPath with the least riskeasy
Not solved yetFewest tolls on the wayeasy
Not solved yetSpot a looping discounteasy
Not solved yetOrder of the build stepseasy
Not solved yetCan every course be finishedeasy
Not solved yetFind the cycle in dependencieseasy
Not solved yetTask order with ties alphabeticaleasy
Not solved yetIs this order valideasy
Not solved yetIs the network still in one pieceeasy
Not solved yetRedundant link in a networkeasy
Not solved yetAccounts merged by shared emaileasy
Not solved yetComponents after each added linkeasy
Not solved yetLargest group of linked walletseasy
Not solved yetMatch servers to jobseasy
Not solved yetKeep the worst delay smalleasy
Not solved yetChange at the lemonade standeasy
Not solved yetReach the last stopeasy
Not solved yetFewest jumps to the endeasy
Not solved yetCourses before their deadlineshard
Not solved yetClimb with step costseasy
Not solved yetBest non-adjacent deliverieseasy
Not solved yetRoutes around closed roadseasy
Not solved yetSplit a query into known wordseasy
Not solved yetLongest common subsequence of two logseasy
Not solved yetJob scheduling for the best profithard
Not solved yetLongest mirror from letter tileseasy
Not solved yetTotal of a scorecard lineeasy
Not solved yetTyped code one swap awayeasy
Not solved yetLabels in a custom shelf ordereasy
Not solved yetDetect a repeated blockeasy
Not solved yetGroup the product codes by lettersmedium
Not solved yetWords that are rotations of each othermedium
Not solved yetIsomorphic status codeseasy
Not solved yetGroup strings that differ by the same shiftmedium
Not solved yetFind all anagram starts in a logmedium
Not solved yetSort the buckets of a histogrameasy
Not solved yetWords made from a letter poolmedium
Not solved yetProduct of the others without divisionmedium
Not solved yetFirst error code that appears onceeasy
Not solved yetCount orders per customereasy
Not solved yetMajority payment methodeasy
Not solved yetValues that appear in more than a third of requestsmedium
Not solved yetTop three most active usersmedium
Not solved yetFewest distinct values after k removalsmedium
Not solved yetOverlap score of two ad profileseasy
Not solved yetAd banners with the same shapemedium
Not solved yetChats filled by requested sizemedium
Not solved yetThe busiest payment shardeasy
Not solved yetHow long are the chains?medium
Not solved yetGrowing a session tablemedium
Not solved yetLookup cost in a chained tablehard
Not solved yetOrder codes that land in the same bucketmedium
Not solved yetFour ledgers that balancemedium
Not solved yetThe first replayed requesteasy
Not solved yetThe farthest matching pairmedium
Not solved yetA refund pair for a totaleasy
Not solved yetTrack pairs that fill whole slotsmedium
Not solved yetComplement of a delivery windowmedium
Not solved yetLongest streak of consecutive idsmedium
Not solved yetMissing and repeated idsmedium
Not solved yetCount pairs of orders that match the totalmedium
Not solved yetPairs of readings a fixed distance apartmedium
Not solved yetPairs that differ by at most the tolerancemedium
Not solved yetMerge two devices' message logseasy
Not solved yetDocuments in both posting listseasy
Not solved yetWhen the dock and the driver are both freemedium
Not solved yetMerge two sorted inventories in placeeasy
Not solved yetFarthest pair across two falling listsmedium
Not solved yetBest-paying route for each drivermedium
Not solved yetMirror reference codeseasy
Not solved yetTwo parcels for the spare capacityeasy
Not solved yetGift pairs within the budgetmedium
Not solved yetSquared clock drifts in ordereasy
Not solved yetFewest cargo bikes for the roundmedium
Not solved yetSmallest pair sum above a thresholdmedium
Not solved yetDistinct team totalseasy
Not solved yetLargest charge with a matching refundeasy
Not solved yetMirror the letters, keep the symbolseasy
Not solved yetLargest tank of water between two wallsmedium
Not solved yetMost bundles that hit the pricemedium
Not solved yetPalindrome after one deletionmedium
Not solved yetShortest status strip after trimming matching endsmedium
Not solved yetTrack selections that fit the slotmedium
Not solved yetRain trapped between towershard
Not solved yetCompact the log buffereasy
Not solved yetTrim repeated postingsmedium
Not solved yetCompress repeated scansmedium
Not solved yetName typed on a sticky keyboardeasy
Not solved yetSlide a row of number tileseasy
Not solved yetInterleave odds and evensmedium
Not solved yetRobots on a one-lane railmedium
Not solved yetStrip every banned wordmedium
Not solved yetClosest balance snapshots of two accountsmedium
Not solved yetThree products for a gift cardmedium
Not solved yetThree parcels closest to the pallet limitmedium
Not solved yetFour batches that net to zerohard
Not solved yetAd slot triples under the page budgetmedium
Not solved yetEvenly spaced check-in triplesmedium
Not solved yetThree entries that cancel outmedium
Not solved yetValid triangles from stick lengthsmedium
Not solved yetRight-angle frames from rodsmedium
Not solved yetFour entries that hit the targetmedium
Not solved yetFirst use of each idempotency keyeasy
Not solved yetGroup parcels by priority classeasy
Not solved yetBids around the reserve pricemedium
Not solved yetTyped queries with backspacesmedium
Not solved yetThe k-th fastest pickupmedium
Not solved yetFee stretches within the allowancemedium
Not solved yetLongest segment covering at most two zonesmedium
Not solved yetStretches with exactly k clicksmedium
Not solved yetLongest healthy stretch with k re-runsmedium
Not solved yetSessions with exactly k categorieshard
Not solved yetBusiest stretch on the launch dashboardeasy
Not solved yetRepeated order inside k arrivalseasy
Not solved yetError bursts on the status pageeasy
Not solved yetFirst slow stretch in a surge zonemedium
Not solved yetLongest delivery run in one shiftmedium
Not solved yetLongest fresh listening sessionmedium
Not solved yetFewest hours to a revenue targetmedium
Not solved yetBest k days on a repeating rostereasy
Not solved yetMaximum of every window of khard
Not solved yetFewest parcels from both endshard
Not solved yetShortest log window with every required codemedium
Not solved yetShortest block to rebalance the build queuehard
Not solved yetShortest stretch where every member postsmedium
Not solved yetShortest browsing span with every wishlist itemhard
Not solved yetDistinct tracks in every k-play windoweasy
Not solved yetScrambled blocked terms in a descriptionmedium
Not solved yetWindows dominated by one topicmedium
Not solved yetReordered batch in a scan streammedium
Not solved yetBest bundle of distinct productsmedium
Not solved yetLargest number from the piecesmedium
Not solved yetBike convoys on a one-lane roadmedium
Not solved yetRelative order of a priority listeasy
Not solved yetSort by number of set bitseasy
Not solved yetSmallest gap between two orderseasy
Not solved yetH index of a creatormedium
Not solved yetMeeting time overlap checkeasy
Not solved yetMerge the overlapping slotsmedium
Not solved yetInsert a new slot and mergemedium
Not solved yetFewest clips to cover the showmedium
Not solved yetNext booking after each bookingmedium
Not solved yetRemove the covered slotsmedium
Not solved yetEmployee free timemedium
Not solved yetSplit the log into the most chunksmedium
Not solved yetCarve a blackout out of the free slotseasy
Not solved yetRooms needed for the meetingsmedium
Not solved yetFewest announcements to reach every showmedium
Not solved yetCar pool capacity checkmedium
Not solved yetMost offers you can claimmedium
Not solved yetAlerts firing at each query timemedium
Not solved yetTightest campaign for each dayhard
Not solved yetPairs processed out of ordermedium
Not solved yetNewest first in a chat threadeasy
Not solved yetThe middle of a reply chaineasy
Not solved yetMerge two shards' log chainseasy
Not solved yetUnsend the k-th newest messageeasy
Not solved yetBalanced brackets in a configeasy
Not solved yetCancel double scans in a conveyor logeasy
Not solved yetCheapest item in a cart with Undomedium
Not solved yetEvaluate a postfix fee formulamedium
Not solved yetHours until a slower responsemedium
Not solved yetMoving average of a streameasy
Not solved yetRequests in the last three secondseasy
Not solved yetA stack built from queueseasy
Not solved yetParcels left on the belteasy
Not solved yetCircular buffer of log linesmedium
Not solved yetTotal size of a foldereasy
Not solved yetDepth of the org charteasy
Not solved yetMirror the category treeeasy
Not solved yetIs it a valid search treemedium
Not solved yetLevel by level ordermedium
Not solved yetSmash the heaviest parcelseasy
Not solved yetKth largest score in a streameasy
Not solved yetCheapest k offerseasy
Not solved yetTop busiest endpointsmedium
Not solved yetK nearest driversmedium
Not solved yetBuild the follower grapheasy
Not solved yetCount the connectionseasy
Not solved yetFind the isolated stationseasy
Not solved yetFind the town judgeeasy
Not solved yetCount the mutual followersmedium
Not solved yetCount the contacts that match what you typedeasy
Not solved yetCount the distinct prefixes in a word listeasy
Not solved yetLongest common prefix of route pathseasy
Not solved yetBuild the autocomplete indexmedium
Not solved yetSearch a word list with a wildcardmedium

all problems →