Math and counting

Number theory, combinatorics, and geometry

Under construction

Still being built. Things may change

Total results13,153 problems

Möbius Strip
Hard9
Math, Combinatorics+2
No attempts yet
Time limit
1s
Memory limit
128 MB
Judgeable
Fence Watch
Hard9
Geometry, Greedy+1
No attempts yet
Time limit
1s
Memory limit
128 MB
Judgeable
Mineshaft
Hard9
Geometry, Graph+1
No attempts yet
Time limit
1s
Memory limit
128 MB
Judgeable
Anchored Balloon
Hard9
Geometry, Binary search+1
No attempts yet
Time limit
1s
Memory limit
128 MB
Judgeable
Adriatic
Hard9
Graph, Prefix sum+1
No attempts yet
Time limit
2s
Memory limit
256 MB
Judgeable
Lonely Mountain
Hard9
Geometry, Math+2
No attempts yet
Time limit
2s
Memory limit
256 MB
Judgeable
Largest and Smallest Triangle
Hard9
Geometry, Sorting+1
No attempts yet
Time limit
6s
Memory limit
128 MB
Judgeable
Chain & Co.
Hard9
Geometry, Graph+1
No attempts yet
Time limit
10s
Memory limit
128 MB
Judgeable
Cactus Automorphisms
Hard9
Tree, Dynamic programming+2
No attempts yet
Time limit
5s
Memory limit
256 MB
Judgeable
Green Energy
Hard9
Geometry, Greedy+1
No attempts yet
Time limit
1s
Memory limit
128 MB
Judgeable
Teaching Hazard
Hard9
Number theory, Math+1
No attempts yet
Time limit
5s
Memory limit
128 MB
Judgeable
Recurrence
Hard9
Combinatorics, Number theory+1
No attempts yet
Time limit
1s
Memory limit
128 MB
Judgeable
Even cycle partition of a planar graph
Hard9
Graph, Math
No attempts yet
Time limit
1s
Memory limit
128 MB
Judgeable
GRAD
Hard9
Shortest path, Graph+2
No attempts yet
Time limit
2s
Memory limit
256 MB
Judgeable
Rail Station Recovery
Hard9
Graph, Sorting+1
No attempts yet
Time limit
3s
Memory limit
512 MB
Judgeable
Gondola replacement count
Hard9
Combinatorics, Math
No attempts yet
Time limit
1s
Memory limit
256 MB
Judgeable
Orbit
Hard9
Geometry, Math+1
No attempts yet
Time limit
2s
Memory limit
256 MB
Judgeable
Bisecting the Island
Hard9
Geometry, Brute force
No attempts yet
Time limit
1s
Memory limit
256 MB
Judgeable
The Forest of Fangorn
Hard9
Geometry, Graph
No attempts yet
Time limit
3s
Memory limit
64 MB
Judgeable
Solar Lamps
Hard9
Geometry, Segment tree+1
No attempts yet
Time limit
1s
Memory limit
256 MB
Judgeable
Parking
Hard9
Geometry, Graph+2
No attempts yet
Time limit
3s
Memory limit
256 MB
Judgeable
Sequence Center
Hard9
Math, Binary search
No attempts yet
Time limit
3s
Memory limit
256 MB
Judgeable
Museum
Hard9
Graph, Geometry+1
No attempts yet
Time limit
1s
Memory limit
256 MB
Judgeable
Tollgate
Hard9
Shortest path, Graph+2
No attempts yet
Time limit
2s
Memory limit
256 MB
Judgeable
Watering the Bean Plants
Hard9
Geometry, Greedy+1
No attempts yet
Time limit
10s
Memory limit
256 MB
Judgeable
Exhibition
Hard9
Dynamic programming, Math+1
No attempts yet
Time limit
10s
Memory limit
256 MB
Judgeable
Growing Orthogonal Spiral
Hard9
Math, Number theory+1
No attempts yet
Time limit
1s
Memory limit
256 MB
Judgeable
Red and Black Stepping Stones
Hard9
Game theory, Graph+1
No attempts yet
Time limit
9s
Memory limit
256 MB
Judgeable
Hidden Maze
Hard9
Divide and conquer, Tree+2
No attempts yet
Time limit
2s
Memory limit
256 MB
Judgeable
Overwriting Game
Hard9
Probability, Matrix+1
No attempts yet
Time limit
8s
Memory limit
512 MB
Judgeable
Slave to Achievements 2
Hard9
Probability, Dynamic programming+1
No attempts yet
Time limit
3s
Memory limit
256 MB
Judgeable
Believer in I 2
Hard9
Combinatorics, Dynamic programming+2
No attempts yet
Time limit
3s
Memory limit
256 MB
Judgeable
Followers of I 3
Hard9
Dynamic programming, Combinatorics+1
No attempts yet
Time limit
3s
Memory limit
256 MB
Judgeable
Tile Cutting
Hard9
Number theory, Math+1
No attempts yet
Time limit
15s
Memory limit
256 MB
Judgeable
Art Gallery
Hard9
Geometry, Shortest path
No attempts yet
Time limit
1s
Memory limit
256 MB
Judgeable
Dictionary Survey
Hard9
Trie, Math+1
No attempts yet
Time limit
3s
Memory limit
256 MB
Judgeable
Phibonacci
Hard9
Number theory, Math
No attempts yet
Time limit
1s
Memory limit
256 MB
Judgeable
Random signals
Hard9
Geometry, Probability+1
No attempts yet
Time limit
12s
Memory limit
256 MB
Judgeable
Sorting under interference
Hard9
Math, Greedy
No attempts yet
Time limit
1s
Memory limit
512 MB
Judgeable
Card Rarity Encoding
Hard9
Greedy, Heap+2
No attempts yet
Time limit
3s
Memory limit
128 MB
Judgeable
Development of Small Flying Robots
Hard9
Shortest path, Graph+1
No attempts yet
Time limit
1s
Memory limit
256 MB
Judgeable
Frogger
Hard9
Math, BFS+1
No attempts yet
Time limit
1s
Memory limit
256 MB
Judgeable
Join My Team
Hard9
Graph, Game theory
No attempts yet
Time limit
1s
Memory limit
256 MB
Judgeable
Hogwarts staircases
Hard9
BFS, Shortest path+2
No attempts yet
Time limit
1s
Memory limit
256 MB
Judgeable
Canyon Mapping
Hard9
Geometry, Binary search+1
No attempts yet
Time limit
1s
Memory limit
256 MB
Judgeable
Nim with a Robot Referee
Hard9
Game theory, Number theory
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Counting Distinct Suffix Arrays
Hard9
Combinatorics, String+1
No attempts yet
Time limit
1s
Memory limit
512 MB
Judgeable
Quaternary Computer
Hard9
Bit manipulation, Math+2
No attempts yet
Time limit
1s
Memory limit
512 MB
Judgeable
Balancing Line
Hard9
Geometry, Brute force+1
No attempts yet
Time limit
10s
Memory limit
256 MB
Judgeable
Kernel
Hard9
Geometry
No attempts yet
Time limit
1s
Memory limit
256 MB
Judgeable
Highways and Counties
Hard9
Minimum spanning tree, Dynamic programming+2
No attempts yet
Time limit
2s
Memory limit
64 MB
Judgeable
Dungeon Creation
Hard9
Dynamic programming, Graph+1
No attempts yet
Time limit
3s
Memory limit
512 MB
Judgeable
Casino
Hard9
Probability, Dynamic programming+1
No attempts yet
Time limit
2s
Memory limit
256 MB
Judgeable
Runner and Sniper
Hard9
Game theory, Geometry+1
No attempts yet
Time limit
2s
Memory limit
256 MB
Judgeable
Wall Making Game
Hard9
Game theory, Divide and conquer+1
No attempts yet
Time limit
2s
Memory limit
256 MB
Judgeable
Cactus edge move
Hard9
Graph, Combinatorics
No attempts yet
Time limit
1s
Memory limit
256 MB
Judgeable
Rotating Cutter Bits
Hard9
Geometry, Simulation+1
No attempts yet
Time limit
3s
Memory limit
256 MB
Judgeable
Lights Out in the Barn
Hard9
Dynamic programming, Game theory+1
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Gauss
Hard9
Dynamic programming, Shortest path+2
No attempts yet
Time limit
2s
Memory limit
256 MB
Judgeable
Willow
Hard9
Game theory, Tree+1
No attempts yet
Time limit
5s
Memory limit
512 MB
Judgeable
Twirling Towards Freedom (Large)
Hard9
Geometry, Number theory+2
No attempts yet
Time limit
5s
Memory limit
512 MB
Judgeable
Children Wearing Hats (Large)
Hard9
Dynamic programming, Game theory+1
No attempts yet
Time limit
5s
Memory limit
512 MB
Judgeable
Ace in the Hole
Hard9
Game theory, Greedy+2
No attempts yet
Time limit
60s
Memory limit
512 MB
Judgeable
Expensive Dinner (Large)
Hard9
Number theory, Math
No attempts yet
Time limit
5s
Memory limit
512 MB
Judgeable
Sheepwalking
Hard9
Probability, Game theory+1
No attempts yet
Time limit
20s
Memory limit
1024 MB
Judgeable
Ninjutsu (Large)
Hard9
Geometry, Dynamic programming+1
No attempts yet
Time limit
60s
Memory limit
512 MB
Judgeable
Paths of Yin and Yang (Small)
Hard9
Combinatorics, Backtracking+1
No attempts yet
Time limit
30s
Memory limit
512 MB
Judgeable
The Paths of Yin Yang (Large)
Hard9
Combinatorics, Graph
No attempts yet
Time limit
120s
Memory limit
512 MB
Judgeable
Watering Plants (Large)
Hard9
Geometry, Binary search+2
No attempts yet
Time limit
60s
Memory limit
512 MB
Judgeable
King Game
Hard9
Game theory, Graph+2
No attempts yet
Time limit
5s
Memory limit
512 MB
Judgeable
Coloring Practice (Large)
Hard9
Combinatorics, Math+2
No attempts yet
Time limit
3s
Memory limit
512 MB
Judgeable
Polygonal Puzzle
Hard9
Geometry, Brute force+2
No attempts yet
Time limit
20s
Memory limit
512 MB
Judgeable
Road Times
Hard9
Shortest path, Math+2
No attempts yet
Time limit
5s
Memory limit
512 MB
Judgeable
Spin Doctor
Hard9
Geometry, Sorting+2
No attempts yet
Time limit
5s
Memory limit
512 MB
Judgeable
Connect Highways
Hard9
Geometry, Sorting+2
No attempts yet
Time limit
0.4s
Memory limit
32 MB
Judgeable
Covering posters
Hard9
Segment tree, Prefix sum+2
No attempts yet
Time limit
2s
Memory limit
1024 MB
Judgeable
Half-plane land grab 2
Hard9
Dynamic programming, Divide and conquer+2
No attempts yet
Time limit
4s
Memory limit
512 MB
Judgeable
Counting Strings
Hard9
Dynamic programming, String matching+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Number of walks
Hard9
Graph, Dynamic programming+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Dinner
Hard9
Graph, Math+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
New Track
Hard9
Implementation, Combinatorics+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Growing a Binary Tree
Hard9
Tree, DFS+2
No attempts yet
Time limit
4s
Memory limit
512 MB
Judgeable
Tree Transformation
Hard9
Tree, Dynamic programming+2
No attempts yet
Time limit
1s
Memory limit
512 MB
Judgeable
Array
Hard9
Array, Implementation+2
No attempts yet
Time limit
1s
Memory limit
512 MB
Judgeable
Flowey's Love
Hard9
Geometry, Dynamic programming+2
No attempts yet
Time limit
1s
Memory limit
512 MB
Judgeable
Solve this one too
Hard9
Matrix, Dynamic programming+2
No attempts yet
Time limit
5s
Memory limit
512 MB
Judgeable
Posters
Hard9
Geometry, Divide and conquer+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Colored Brackets
Hard9
Combinatorics, Math+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Drawing lots
Hard9
Probability, Math+1
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Laser Sensors
Hard9
Divide and conquer, Geometry+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Distant Stars
Hard9
Geometry, Divide and conquer+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Dangerous Hashing
Hard9
Math, Number theory+2
No attempts yet
Time limit
5s
Memory limit
512 MB
Judgeable
Almost Euler graphs
Hard9
Combinatorics, Graph+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Binary cryptarithm decryption
Hard9
Backtracking, Dynamic programming+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Three Kingdoms of Bourdelot
Hard9
Graph, Union-find+2
No attempts yet
Time limit
4s
Memory limit
512 MB
Judgeable
Oracle
Hard9
Dynamic programming, Divide and conquer+2
No attempts yet
Time limit
3s
Memory limit
256 MB
Judgeable
Fencing off the darkness
Hard9
Graph, Minimum spanning tree+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Counting points inside a circle
Hard9
Geometry, Divide and conquer+2
No attempts yet
Time limit
8s
Memory limit
512 MB
Judgeable
Polygon Shrinking Kit
Hard9
Geometry, Dynamic programming+2
No attempts yet
Time limit
1s
Memory limit
512 MB
Judgeable
Where are the bubbles?
Hard9
Implementation, Greedy+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable

Title	Level	Topics	Solved	Time limit	Memory limit	Judge
Möbius StripGiven m and n, compute the average graph distance over all ordered square pairs on the m by 2n Mobius grid.	Hard9	MathCombinatorics+2	No attempts yet	1s	128 MB	Judgeable
Fence WatchPlace the fewest sensors on a convex polygon boundary so every boundary point forms an angle from alpha to 360 degrees minus alpha with some sensor pair.	Hard9	GeometryGreedy+1	No attempts yet	1s	128 MB	Judgeable
MineshaftRun a pipe of straight segments up a winding polygonal shaft so each segment touches the walls in at least two places and the number of bends is minimal.	Hard9	GeometryGraph+1	No attempts yet	1s	128 MB	Judgeable
Anchored BalloonFind the greatest height a balloon tied to ground anchors by fixed-length ropes can reach while all ropes hold and none cross.	Hard9	GeometryBinary search+1	No attempts yet	1s	128 MB	Judgeable
AdriaticOn a 2500 by 2500 grid, islands ordered alike from northwest to southeast connect in one hop, and each island needs the sum of fewest hops from all others.	Hard9	GraphPrefix sum+1	No attempts yet	2s	256 MB	Judgeable
Lonely MountainGiven two orthogonal mountain silhouettes, decide whether any solid casts both and print the largest possible volume modulo 1000000007.	Hard9	GeometryMath+2	No attempts yet	2s	256 MB	Judgeable
Largest and Smallest TriangleGiven n points in the plane, compute the largest and smallest areas among all triangles formed by triples of the points.	Hard9	GeometrySorting+1	No attempts yet	6s	128 MB	Judgeable
Chain & Co.Decide whether axis-aligned square links split into two nonempty groups with every cross pair linked.	Hard9	GeometryGraph+1	No attempts yet	10s	128 MB	Judgeable
Cactus AutomorphismsCount the automorphisms of a given cactus graph with up to 50000 vertices and print the count as a prime factorization.	Hard9	TreeDynamic programming+2	No attempts yet	5s	256 MB	Judgeable
Green EnergyPlace towers of given heights on a polygonal terrain to maximize the total length lit by parallel sun rays blocked by terrain and other towers.	Hard9	GeometryGreedy+1	No attempts yet	1s	128 MB	Judgeable
Teaching HazardGiven n and x, count pairs of bases b1 < b2 where n! ends in the same number of trailing zeros p with p at least x.	Hard9	Number theoryMath+1	No attempts yet	5s	128 MB	Judgeable
RecurrenceCount the decrement orders that reduce the given partition to all zeros while staying nonincreasing, modulo 1,000,000,009.	Hard9	CombinatoricsNumber theory+1	No attempts yet	1s	128 MB	Judgeable
Even cycle partition of a planar graphGiven a vertex-biconnected planar graph with at most two odd faces, decide whether its edges partition into even simple cycles.	Hard9	GraphMath	No attempts yet	1s	128 MB	Judgeable
GRADCities join the road network one by one with two roads each, and each query asks the shortest road distance between two cities.	Hard9	Shortest pathGraph+2	No attempts yet	2s	256 MB	Judgeable
Rail Station RecoveryRecover every station's block number and C or D type from the all-pairs shortest-route distances and station 0's block.	Hard9	GraphSorting+1	No attempts yet	3s	512 MB	Judgeable
Gondola replacement countCount the replacement orders that can produce the given circular gondola sequence, modulo 1000000009.	Hard9	CombinatoricsMath	No attempts yet	1s	256 MB	Judgeable
OrbitPlace two opposite sensors on the radius-R circle so their brightest-star readings match, and print the pair with the smallest angle.	Hard9	GeometryMath+1	No attempts yet	2s	256 MB	Judgeable
Bisecting the IslandSplit an axis-parallel simple polygon into two congruent pieces with one axis-parallel cut on integer coordinates, or report that none exists.	Hard9	GeometryBrute force	No attempts yet	1s	256 MB	Judgeable
The Forest of FangornFind which border camps connect to the start by a path where no tree ever hides behind another tree.	Hard9	GeometryGraph	No attempts yet	3s	64 MB	Judgeable
Solar LampsCompute each lamp turn-on time from its place in the power-on order and the count of already lit lamps shining on it.	Hard9	GeometrySegment tree+1	No attempts yet	1s	256 MB	Judgeable
ParkingDecide whether axis-aligned cars in a strip of height w can be slid without overlap or rotation from the start layout to the target layout.	Hard9	GeometryGraph+2	No attempts yet	3s	256 MB	Judgeable
Sequence CenterGiven k integer sequences of length n, find an integer sequence that minimizes the maximum Manhattan distance to them.	Hard9	MathBinary search	No attempts yet	3s	256 MB	Judgeable
MuseumA burglar picks guards to bribe to maximize the value of exhibits no remaining guard sees minus bribe costs under downward cone views.	Hard9	GraphGeometry+1	No attempts yet	1s	256 MB	Judgeable
TollgateFind the road with the largest expected toll income when every resident visits every restaurant by a random shortest round trip.	Hard9	Shortest pathGraph+2	No attempts yet	2s	256 MB	Judgeable
Watering the Bean PlantsPlace at most one disk of radius R and cover the uncovered parts of N segments with unit-length sticks at minimum total cost.	Hard9	GeometryGreedy+1	No attempts yet	10s	256 MB	Judgeable
ExhibitionFind the cheapest linear-cost cuts to product 1's price, size and weight that put it in some k-set tying the best set without it.	Hard9	Dynamic programmingMath+1	No attempts yet	10s	256 MB	Judgeable
Growing Orthogonal SpiralDecide whether an orthogonal spiral whose segment lengths grow by at least 1 can end exactly at (x, y) and print the shortest such lengths.	Hard9	MathNumber theory+1	No attempts yet	1s	256 MB	Judgeable
Red and Black Stepping StonesFind the smallest lookahead queue size that lets the mover survive forever on a red-black directed graph against an adversarial color chooser.	Hard9	Game theoryGraph+1	No attempts yet	9s	256 MB	Judgeable
Hidden MazeCompute the expected median edge weight over all tree node pairs at odd distance, and print it as a reduced fraction.	Hard9	Divide and conquerTree+2	No attempts yet	2s	256 MB	Judgeable
Overwriting GameYou repeat random prefix-rectangle repaints until the board matches the target, and report the expected total of painted cells as a reduced fraction.	Hard9	ProbabilityMatrix+1	No attempts yet	8s	512 MB	Judgeable
Slave to Achievements 2Repeatedly craft as many N-scrap daggers as possible and reclaim 0 to K scraps per dagger, then find the distribution of the final leftover under N scraps.	Hard9	ProbabilityDynamic programming+1	No attempts yet	3s	256 MB	Judgeable
Believer in I 2Over every ordering of A push, B add, and C multiply cards on an infinite stack of I, report the total of each of the top K stack values modulo 1,000,000,007.	Hard9	CombinatoricsDynamic programming+2	No attempts yet	3s	256 MB	Judgeable
Followers of I 3Sum, over every distinct order of the I, plus, and times cards run on an infinite I stack, the top K stack values modulo 1000000007.	Hard9	Dynamic programmingCombinatorics+1	No attempts yet	3s	256 MB	Judgeable
Tile CuttingFor each query range, find the area with the largest count of inscribed parallelogram cuts and report that count, breaking ties by the smaller area.	Hard9	Number theoryMath+1	No attempts yet	15s	256 MB	Judgeable
Art GalleryFind the vertex sequence of the shortest interior path between two given vertices of a polygon lit from edge v0-v1.	Hard9	GeometryShortest path	No attempts yet	1s	256 MB	Judgeable
Dictionary SurveyFind how many leading pages of the integers from A to B in lexicographic order pin down both A and B.	Hard9	TrieMath+1	No attempts yet	3s	256 MB	Judgeable
PhibonacciGiven n and k, decide whether (P_n)^k equals A φ^k + B for integers A and B and print them modulo 1,000,000,007, or -1.	Hard9	Number theoryMath	No attempts yet	1s	256 MB	Judgeable
Random signalsCompute the expected plane integral of the strongest covering signal when each of up to 20 stations draws an independent uniform power that activates its disks.	Hard9	GeometryProbability+1	No attempts yet	12s	256 MB	Judgeable
Sorting under interferenceFind the fewest rounds of one swap per round that sort a permutation despite known interfering swaps, with the smallest move list on ties.	Hard9	MathGreedy	No attempts yet	1s	512 MB	Judgeable
Card Rarity EncodingGiven N draws over four rarities with known probabilities, find the smallest possible expected length of a prefix-free binary code for the N-draw sequences.	Hard9	GreedyHeap+2	No attempts yet	3s	128 MB	Judgeable
Development of Small Flying RobotsEach robot moves sideways for 1 energy and rises through a hole for 100, and all must meet on one hole-free cell of the top floor for the least total energy.	Hard9	Shortest pathGraph+1	No attempts yet	1s	256 MB	Judgeable
FroggerFind the fewest frogs to place left of the y-axis so peg jumps can bring one frog to (X, 0), or print frogger when it is impossible.	Hard9	MathBFS+1	No attempts yet	1s	256 MB	Judgeable
Join My TeamPair N participants by ranked preference lists into the lexicographically smallest stable pairing with no blocking pair, or report NO SOLUTION.	Hard9	GraphGame theory	No attempts yet	1s	256 MB	Judgeable
Hogwarts staircasesFind the shortest sequence of red and green button presses that turns the current staircase layout into the desired one, breaking ties by lexicographic order.	Hard9	BFSShortest path+2	No attempts yet	1s	256 MB	Judgeable
Canyon MappingCover a simple polygon with k equal axis-aligned squares and print the smallest side length that covers it, rounded to two decimals.	Hard9	GeometryBinary search+1	No attempts yet	1s	256 MB	Judgeable
Nim with a Robot RefereeDecide each bag's winning first takes in a Nim variant where piles with forbidden divisor patterns vanish before every turn.	Hard9	Game theoryNumber theory	No attempts yet	2s	512 MB	Judgeable
Counting Distinct Suffix ArraysCount how many distinct suffix arrays length-N strings with at most M distinct letters produce, modulo 1e9+7.	Hard9	CombinatoricsString+1	No attempts yet	1s	512 MB	Judgeable
Quaternary ComputerGiven N base-4 variables, M add and xor commands, and one forbidden start value per variable, print each output total over all inputs modulo 4.	Hard9	Bit manipulationMath+2	No attempts yet	1s	512 MB	Judgeable
Balancing LineFind the shortest closed curve avoiding square lamp footprints that encloses a nonempty lamp group holding half the total energy.	Hard9	GeometryBrute force+1	No attempts yet	10s	256 MB	Judgeable
KernelDecide whether a rectilinear polygon contains a beacon point that attracts every other point under greedy distance-decreasing motion.	Hard9	Geometry	No attempts yet	1s	256 MB	Judgeable
Highways and CountiesFind the smallest road length limit so cities joined by shorter roads form a group whose populations hold a subset summing to a multiple of K.	Hard9	Minimum spanning treeDynamic programming+2	No attempts yet	2s	64 MB	Judgeable
Dungeon CreationCount the spanning trees of the obstacle-free grid graph for each test case, modulo 1,000,000,007.	Hard9	Dynamic programmingGraph+1	No attempts yet	3s	512 MB	Judgeable
CasinoWith m dollars, a goal of n dollars and win chance p percent per play, pick each stake to maximize the chance of reaching the goal.	Hard9	ProbabilityDynamic programming+1	No attempts yet	2s	256 MB	Judgeable
Runner and SniperYou give your start position and the gun's start angle and turn rate, then compute the fastest run speed at which the rotating gun still catches you.	Hard9	Game theoryGeometry+1	No attempts yet	2s	256 MB	Judgeable
Wall Making GameTwo players alternately pick an empty cell and turn its row and column lines into walls until blocked, and the player unable to move loses.	Hard9	Game theoryDivide and conquer+1	No attempts yet	2s	256 MB	Judgeable
Cactus edge moveCount the pairs of deleting one edge and inserting a different edge that keep the given graph a cactus.	Hard9	GraphCombinatorics	No attempts yet	1s	256 MB	Judgeable
Rotating Cutter BitsThe program counts interior lattice points of a polygonal workpiece that survive one full rotation against a second rotating polygonal cutter.	Hard9	GeometrySimulation+1	No attempts yet	3s	256 MB	Judgeable
Lights Out in the BarnStarting at an unknown vertex of a rectilinear barn, walk the walls to identify the position and reach the exit with the smallest worst-case extra distance.	Hard9	Dynamic programmingGame theory+1	No attempts yet	2s	512 MB	Judgeable
GaussStarting from A, pay divisor-based costs to shrink the number or stay on lucky numbers, and find the cheapest exact-move cost to end at B.	Hard9	Dynamic programmingShortest path+2	No attempts yet	2s	256 MB	Judgeable
WillowTwo players choose starting cities on a tree with coins and alternately collect cities, each road usable once, and Hanaa maximizes the final score difference.	Hard9	Game theoryTree+1	No attempts yet	5s	512 MB	Judgeable
Twirling Towards Freedom (Large)Each minute you stay put or rotate 90 degrees clockwise around a star, and must report the largest squared distance from the origin reachable in M minutes.	Hard9	GeometryNumber theory+2	No attempts yet	5s	512 MB	Judgeable
Children Wearing Hats (Large)Given B black and W white hats for k children, count color sequences where the i-th child from the back first deduces their hat color, modulo 32749.	Hard9	Dynamic programmingGame theory+1	No attempts yet	5s	512 MB	Judgeable
Ace in the HoleGiven Ben's examination order, restore the lexicographically greatest deck with no decreasing triple that makes his optimal search follow it.	Hard9	Game theoryGreedy+2	No attempts yet	60s	512 MB	Judgeable
Expensive Dinner (Large)Friends 1 to N arrive in any order and raise the shared bill to multiples of their numbers, and you report the gap between the most and fewest waiter calls.	Hard9	Number theoryMath	No attempts yet	5s	512 MB	Judgeable
SheepwalkingTwo sheepdogs block two neighboring cells each turn to steer a randomly moving sheep home and minimize its expected number of moves there.	Hard9	ProbabilityGame theory+1	No attempts yet	20s	1024 MB	Judgeable
Ninjutsu (Large)Pick a starting rope length so the counterclockwise swing catches as many targets as possible before settling into orbit.	Hard9	GeometryDynamic programming+1	No attempts yet	60s	512 MB	Judgeable
Paths of Yin and Yang (Small)Count the black-and-white colorings of an N by M grid in which each color class forms a single path with two ends.	Hard9	CombinatoricsBacktracking+1	No attempts yet	30s	512 MB	Judgeable
The Paths of Yin Yang (Large)Count the black-and-white colorings of an N by M grid in which each color forms one edge-adjacent path.	Hard9	CombinatoricsGraph	No attempts yet	120s	512 MB	Judgeable
Watering Plants (Large)Given non-overlapping plant disks, find the smallest radius R so that two disks of radius R together cover every plant disk completely.	Hard9	GeometryBinary search+2	No attempts yet	60s	512 MB	Judgeable
King GameOn a small board with burned squares, two players alternately move a king to an unvisited neighboring square; report who wins under optimal play.	Hard9	Game theoryGraph+2	No attempts yet	5s	512 MB	Judgeable
Coloring Practice (Large)Count colorings of a regular n-gon up to rotation, reflection, and arbitrary permutation of the k colors, modulo 1e9+7.	Hard9	CombinatoricsMath+2	No attempts yet	3s	512 MB	Judgeable
Polygonal PuzzleGiven two simple polygons, translate and rotate them without reflection so their interiors stay disjoint and their shared boundary is as long as possible; print that maximum length.	Hard9	GeometryBrute force+2	No attempts yet	20s	512 MB	Judgeable
Road TimesGiven a unique shortest route for each ordered city pair, recorded delivery times constrain 30 to 60 km/h road speeds; for each query find the minimum and maximum travel time consistent with all records.	Hard9	Shortest pathMath+2	No attempts yet	5s	512 MB	Judgeable
Spin DoctorGiven n points (a_i, b_i) labeled 1 or 0, choose a direction (S, T); with ties broken adversarially, minimize the span covering all label-1 points.	Hard9	GeometrySorting+2	No attempts yet	5s	512 MB	Judgeable
Connect HighwaysGiven two planar connected networks, find the Red-Blue junction pair allowed to be joined by a segment, following a fixed angular tie-breaking rule.	Hard9	GeometrySorting+2	No attempts yet	0.4s	32 MB	Judgeable
Covering postersFor each new axis-aligned rectangle, compute the total area of the given union of rectangles that it covers.	Hard9	Segment treePrefix sum+2	No attempts yet	2s	1024 MB	Judgeable
Half-plane land grab 2Maintain a dynamic set of lines under insertions and deletions and answer maximum-at-x queries online.	Hard9	Dynamic programmingDivide and conquer+2	No attempts yet	4s	512 MB	Judgeable
Counting StringsCount strings over the lowercase alphabet whose length lies between LK and LK+N and in which at most K non-overlapping copies of a given pattern S can be found.	Hard9	Dynamic programmingString matching+2	No attempts yet	2s	512 MB	Judgeable
Number of walksGiven a directed graph as an adjacency matrix, find the smallest K such that the number of walks of length L grows as O(L^K), or -1 if none exists.	Hard9	GraphDynamic programming+2	No attempts yet	2s	512 MB	Judgeable
DinnerGiven ages, decide whether all people can be split into round tables of size at least 3 so that every pair of adjacent ages sums to a prime.	Hard9	GraphMath+2	No attempts yet	2s	512 MB	Judgeable
New TrackConstruct a fixed alternating axis-parallel polyline through a formula that encodes exactly k crossings, using a zigzag permutation of y coordinates to place them.	Hard9	ImplementationCombinatorics+2	No attempts yet	2s	512 MB	Judgeable
Growing a Binary TreeFor each tree, pick a root and count the fewest vertices to add so that the result becomes a complete binary tree (every internal vertex has exactly two children, all leaves equidistant from the root), minimizing that count and then the vertex index; output the count mod 1e9+7.	Hard9	TreeDFS+2	No attempts yet	4s	512 MB	Judgeable
Tree TransformationCount the minimum-size sets of edges whose removal splits the tree into components of power-of-two sizes, modulo 1e9+7.	Hard9	TreeDynamic programming+2	No attempts yet	1s	512 MB	Judgeable
ArrayStart with array a_i = i, apply up to 300000 queries that reverse or rotate subarrays and ask for range min, max, sum, value at index, or index of a value, then print the final array.	Hard9	ArrayImplementation+2	No attempts yet	1s	512 MB	Judgeable
Flowey's LoveA soul starting at the origin moves at speed at most 1 inside a rectangle; N moving points travel along fixed lines, and you must find the maximum number of points the soul can touch.	Hard9	GeometryDynamic programming+2	No attempts yet	1s	512 MB	Judgeable
Solve this one tooGiven an N x L matrix, find windows of 3N columns split into matrices A, B, C with A*B=C; pick disjoint windows to maximize total colored cells.	Hard9	MatrixDynamic programming+2	No attempts yet	5s	512 MB	Judgeable
PostersCompute the visible area of each of N rectangles pasted in order on the plane, where later rectangles cover earlier ones.	Hard9	GeometryDivide and conquer+2	No attempts yet	2s	512 MB	Judgeable
Colored BracketsCount valid bracket strings of 2N brackets over K colors that equal their own reversal, modulo 1e9+7.	Hard9	CombinatoricsMath+2	No attempts yet	2s	512 MB	Judgeable
Drawing lotsCompute the expected number of draws until a blue lot has been drawn K times, where red lots are removed and green and blue lots are returned.	Hard9	ProbabilityMath+1	No attempts yet	2s	512 MB	Judgeable
Laser SensorsGiven N blue points and 2N red points in general position, build the particular non-crossing perfect matching prescribed by the paper's recursive angular-sweep Solve/Attach procedure.	Hard9	Divide and conquerGeometry+2	No attempts yet	2s	512 MB	Judgeable
Distant StarsEach star moves at constant integer velocity; for each day 0 to T find the maximum pairwise squared distance, and report the earliest day attaining the minimum of that maximum.	Hard9	GeometryDivide and conquer+2	No attempts yet	2s	512 MB	Judgeable
Dangerous HashingFind two distinct lowercase strings of equal length (at most 300000) that collide under ten polynomial hashes with bases 29, 31, 37, 41, 43, 47, 53, 59, 61, 67 modulo 1e9+7.	Hard9	MathNumber theory+2	No attempts yet	5s	512 MB	Judgeable
Almost Euler graphsCount the simple graphs on N labeled vertices that become Eulerian after adding or removing one edge, modulo 1e9+7.	Hard9	CombinatoricsGraph+2	No attempts yet	2s	512 MB	Judgeable
Binary cryptarithm decryptionGiven a short cipher string where letters replace some characters of an unknown binary equation, count how many valid equations from the given grammar match it.	Hard9	BacktrackingDynamic programming+2	No attempts yet	2s	512 MB	Judgeable
Three Kingdoms of BourdelotDecide whether some assignment of positive or negative polarity to each document is consistent with the hypothesis that person p is an ancestor of person q.	Hard9	GraphUnion-find+2	No attempts yet	4s	512 MB	Judgeable
OracleGiven multipliers p_i and bet sizes j^2+aj+b for the j-th entered game, she picks a subsequence of exactly k games to maximize total profit, for every k.	Hard9	Dynamic programmingDivide and conquer+2	No attempts yet	3s	256 MB	Judgeable
Fencing off the darknessGiven a grid of bulb strengths and a ceiling height, compute each square's light level, mark the dark ones, then find the cheapest set of interior squares that contains all dark squares and minimizes the perimeter cost.	Hard9	GraphMinimum spanning tree+2	No attempts yet	2s	512 MB	Judgeable
Counting points inside a circleFor each of M circle queries, count how many of N fixed points lie inside or on the circle, printing the count per query.	Hard9	GeometryDivide and conquer+2	No attempts yet	8s	512 MB	Judgeable
Polygon Shrinking KitEach polygon vertex is replaced by the midpoint toward A or toward B; among all choices keeping the vertices in convex order, find the minimum possible area.	Hard9	GeometryDynamic programming+2	No attempts yet	1s	512 MB	Judgeable
Where are the bubbles?Given the per-turn swap counts of bubblesort, reconstruct the lexicographically largest permutation that produces exactly those swap counts.	Hard9	ImplementationGreedy+2	No attempts yet	2s	512 MB	Judgeable