Math and counting

Number theory, combinatorics, and geometry

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Still being built. Things may change

Total results13,153 problems

Allowed swaps
Hard9
Union-find, Implementation+2
No attempts yet
Time limit
6s
Memory limit
512 MB
Judgeable
Appropriate Coordinate Map
Hard9
Geometry, Greedy+1
No attempts yet
Time limit
5s
Memory limit
512 MB
Judgeable
Game Moves
Hard9
Dynamic programming, Backtracking+1
No attempts yet
Time limit
1s
Memory limit
512 MB
Judgeable
Jumping Impala
Hard9
Binary search, Graph+2
No attempts yet
Time limit
8s
Memory limit
512 MB
Judgeable
Mobile Network Bandwidth
Hard9
Graph, Greedy+2
No attempts yet
Time limit
8s
Memory limit
512 MB
Judgeable
Blue Forest
Hard9
Geometry, Graph+2
No attempts yet
Time limit
8s
Memory limit
512 MB
Judgeable
Sequence and queries 12
Hard9
Segment tree, Hash map+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Triple tree
Hard9
Math, Number theory+2
No attempts yet
Time limit
1s
Memory limit
512 MB
Judgeable
Risky Lottery
Hard9
Game theory, Probability+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Acrobat
Hard9
Graph, Bit manipulation+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Large Ping Pong Tournament
Hard9
Greedy, Sorting+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Eggscavation
Hard9
Geometry, Prefix sum+2
No attempts yet
Time limit
10s
Memory limit
512 MB
Judgeable
Pirates
Hard9
Greedy, Dynamic programming+2
No attempts yet
Time limit
10s
Memory limit
512 MB
Judgeable
Miner
Hard9
Geometry, Binary search+2
No attempts yet
Time limit
1.5s
Memory limit
512 MB
Judgeable
Robotic Cow Herd
Hard9
Heap, Greedy+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Function and Queries
Hard9
Dynamic programming, Divide and conquer+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Unlucky 89
Hard9
Number theory, Math+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Find the Sequence
Hard9
Number theory, Math+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Soldiers (Large)
Hard9
Game theory, Dynamic programming+1
No attempts yet
Time limit
5s
Memory limit
512 MB
Judgeable
Ronald
Hard9
Graph, Bit manipulation+2
No attempts yet
Time limit
1s
Memory limit
64 MB
Judgeable
Rides 2
Hard9
Segment tree, Sorting+2
No attempts yet
Time limit
2s
Memory limit
256 MB
Judgeable
Building a Tall Barn
Hard9
Greedy, Heap+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Incremental Double Free Strings
Hard9
Combinatorics, Dynamic programming+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Maximum Color Clique
Hard9
Graph, Combinatorics+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
The Enormous Sequence
Hard9
Math, Number theory+2
No attempts yet
Time limit
2s
Memory limit
128 MB
Judgeable
Tarot Sham Boast
Hard9
String matching, Probability+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Shifty Grid
Hard9
Simulation, Implementation+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Rolling the Bottle
Hard9
Geometry, Sorting+2
No attempts yet
Time limit
2.5s
Memory limit
512 MB
Judgeable
Largest window sum
Hard9
Greedy, Prefix sum+2
No attempts yet
Time limit
1s
Memory limit
512 MB
Judgeable
Creating Fake News
Hard9
Math, Graph+1
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Fashion Show
Hard9
Greedy, Graph+2
No attempts yet
Time limit
5s
Memory limit
512 MB
Judgeable
Slate Modern (Large)
Hard9
Graph, Shortest path+2
No attempts yet
Time limit
80s
Memory limit
512 MB
Judgeable
Omnicircumnavigation (Large)
Hard9
Geometry, Math+2
No attempts yet
Time limit
120s
Memory limit
512 MB
Judgeable
Stack Management (Small)
Hard9
Game theory, Simulation+2
No attempts yet
Time limit
5s
Memory limit
512 MB
Judgeable
Sequence and Transformation
Hard9
Combinatorics, Math+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Expected value of the greatest common divisor
Hard9
Probability, Math+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Polynomial and Queries
Hard9
Number theory, Divide and conquer+2
No attempts yet
Time limit
10s
Memory limit
512 MB
Judgeable
NPM998244353 (Hard)
Hard9
Combinatorics, Dynamic programming+2
No attempts yet
Time limit
5s
Memory limit
512 MB
Judgeable
Counting multiples with a bounded digit sum
Hard9
Dynamic programming, Combinatorics+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Good triples of paths
Hard9
Combinatorics, Tree+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Strongly Matchable
Hard9
Graph, Math+2
No attempts yet
Time limit
3s
Memory limit
512 MB
Judgeable
Equivalent Deformation
Hard9
Geometry, Implementation+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Leapfrog
Hard9
Number theory, Math+1
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Fractal Tree
Hard9
Tree, Recursion+2
No attempts yet
Time limit
7s
Memory limit
512 MB
Judgeable
Arranging tiles
Hard9
Dynamic programming, Geometry+2
No attempts yet
Time limit
1s
Memory limit
1024 MB
Judgeable
Craters
Hard9
Geometry, Dynamic programming+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Enlarging Enthusiasm
Hard9
Dynamic programming, Combinatorics+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Jupiter Rock Paper Scissors
Hard9
Game theory, Implementation+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Crazy Rotations
Hard9
String matching, Combinatorics+2
No attempts yet
Time limit
15s
Memory limit
512 MB
Judgeable
GCD Sum
Hard9
Number theory, Greedy+2
No attempts yet
Time limit
2s
Memory limit
1024 MB
Judgeable
Skiing
Hard9
Geometry, Greedy+2
No attempts yet
Time limit
1s
Memory limit
1024 MB
Judgeable
Restaurant Bribes
Hard9
Graph, Math+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Lunar Landscape
Hard9
Geometry, Sorting+1
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Toys
Hard9
Combinatorics, Number theory+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Workbook Algorithms
Hard9
Combinatorics, Graph+2
No attempts yet
Time limit
1s
Memory limit
512 MB
Judgeable
Secret Agent
Hard9
Graph, Geometry+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Garage
Hard9
Segment tree, Number theory+2
No attempts yet
Time limit
4s
Memory limit
256 MB
Judgeable
Counting Cycles
Hard9
Graph, DFS+2
No attempts yet
Time limit
4s
Memory limit
512 MB
Judgeable
Leaders
Hard9
Game theory, Dynamic programming+2
No attempts yet
Time limit
3s
Memory limit
512 MB
Judgeable
Disco Dance Debacle
Hard9
Graph, Greedy+2
No attempts yet
Time limit
5s
Memory limit
512 MB
Judgeable
Kabobs
Hard9
Dynamic programming, String+2
No attempts yet
Time limit
5s
Memory limit
512 MB
Judgeable
Vera and Love Triangles
Hard9
Combinatorics, Number theory+2
No attempts yet
Time limit
2s
Memory limit
256 MB
Judgeable
Drama
Hard9
Combinatorics, Dynamic programming+1
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
L-th K-th number
Hard9
Binary search, Array+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Revenge of the Endless BFS
Hard9
Graph, BFS+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Conveyor Belt
Hard9
Math, Greedy+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Blocks 2
Hard9
Combinatorics, Dynamic programming+2
No attempts yet
Time limit
1s
Memory limit
256 MB
Judgeable
Stamp Painting
Hard9
Dynamic programming, Combinatorics+1
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Euclidean Nim
Hard9
Game theory, Math+1
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Maximal polygon brightness
Hard9
Geometry, Dynamic programming+2
No attempts yet
Time limit
3s
Memory limit
1024 MB
Judgeable
In honor of Taekhee's graduation
Hard9
Math, Simulation+2
No attempts yet
Time limit
3s
Memory limit
128 MB
Judgeable
Want to solve a problem?
Hard9
String matching, Math+2
No attempts yet
Time limit
1s
Memory limit
128 MB
Judgeable
The Number of Sequences
Hard9
Bit manipulation, Combinatorics+2
No attempts yet
Time limit
1s
Memory limit
128 MB
Judgeable
Uncrossed Knight's Tour
Hard9
Greedy, Dynamic programming+2
No attempts yet
Time limit
2s
Memory limit
1024 MB
Judgeable
Tteokpire
Hard9
Combinatorics, Math+2
No attempts yet
Time limit
1s
Memory limit
128 MB
Judgeable
Circle Selection
Hard9
Geometry, Sorting+2
No attempts yet
Time limit
3s
Memory limit
1024 MB
Judgeable
United States of Eurasia
Hard9
Binary search, Dynamic programming+2
No attempts yet
Time limit
20s
Memory limit
1024 MB
Judgeable
Voronoi Diagram
Hard9
Graph, Shortest path+2
No attempts yet
Time limit
2s
Memory limit
1024 MB
Judgeable
Cryptarithm?!
Hard9
Backtracking, Math+2
No attempts yet
Time limit
1s
Memory limit
128 MB
Judgeable
Koala Game
Hard9
Game theory, Greedy+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Tree Escape
Hard9
Game theory, Tree+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
The Sprawl
Hard9
Graph, BFS+2
No attempts yet
Time limit
5s
Memory limit
768 MB
Judgeable
Pia's Atelier: The Alchemist of Mysterious Life
Hard9
Union-find, Prefix sum+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Booster
Hard9
Graph, Union-find+2
No attempts yet
Time limit
8s
Memory limit
512 MB
Judgeable
Team Building
Hard9
Union-find, Implementation+1
No attempts yet
Time limit
1s
Memory limit
512 MB
Judgeable
Flipping
Hard9
Graph, Union-find+2
No attempts yet
Time limit
5s
Memory limit
256 MB
Judgeable
Cloud computing
Hard9
Dynamic programming, Greedy+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Buildings
Hard9
Combinatorics, Math+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Banner
Hard9
String, Dynamic programming+1
No attempts yet
Time limit
6s
Memory limit
512 MB
Judgeable
Growing Microorganisms
Hard9
Math, Greedy+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Game Theory
Hard9
Game theory, Graph+1
No attempts yet
Time limit
1s
Memory limit
256 MB
Judgeable
Constellation
Hard9
Math, Geometry+2
No attempts yet
Time limit
1.5s
Memory limit
512 MB
Judgeable
N and M
Hard9
Math, Number theory+1
No attempts yet
Time limit
1s
Memory limit
1024 MB
Judgeable
Satellites
Hard9
Geometry, Dynamic programming+2
No attempts yet
Time limit
4s
Memory limit
512 MB
Judgeable
Black Chain
Hard9
Greedy, Combinatorics+2
No attempts yet
Time limit
0.1s
Memory limit
512 MB
Judgeable
Matching
Hard9
Geometry, Math
No attempts yet
Time limit
1s
Memory limit
512 MB
Judgeable
Numbers
Hard9
Dynamic programming, Math+1
No attempts yet
Time limit
1s
Memory limit
512 MB
Judgeable
Simple Polygon
Hard9
Geometry, Dynamic programming+1
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Prime Tree - 2
Hard9
Number theory, Tree+2
No attempts yet
Time limit
10s
Memory limit
512 MB
Judgeable
Prime Tree - 4
Hard9
Greedy, Number theory+2
No attempts yet
Time limit
10s
Memory limit
512 MB
Judgeable

Title	Level	Topics	Solved	Time limit	Memory limit	Judge
Allowed swapsMaintain an array under swaps and union operations, answering whether it can be sorted and counting pairs of clouds whose merge would fix both.	Hard9	Union-findImplementation+2	No attempts yet	6s	512 MB	Judgeable
Appropriate Coordinate MapGiven N points, choose a ring through all of them and endpoints A, B so the two legs are monotone in the projection onto AB, maximizing the smallest gap in that projection.	Hard9	GeometryGreedy+1	No attempts yet	5s	512 MB	Judgeable
Game MovesGiven a reachable 2048 board and its score, find the minimum number of moves that could have produced that state, using the merge rules and random tile births.	Hard9	Dynamic programmingBacktracking+1	No attempts yet	1s	512 MB	Judgeable
Jumping ImpalaGiven a lake, a central island, and S unit rocks, find the minimum leap distance letting Vlad reach the island and return twice without landing on any rock twice.	Hard9	Binary searchGraph+2	No attempts yet	8s	512 MB	Judgeable
Mobile Network BandwidthGiven a graph whose edge capacities are polynomials in x, output the max-flow polynomial from node 1 to node N for large x.	Hard9	GraphGreedy+2	No attempts yet	8s	512 MB	Judgeable
Blue ForestGiven several planar floor maps that may be rigid-motion duplicates, unify matching maps, merge their warp gates, then find the shortest route from entrance to exit.	Hard9	GeometryGraph+2	No attempts yet	8s	512 MB	Judgeable
Sequence and queries 12Maintain a dynamic sequence under point updates, deletions, and insertions, answering range queries for distinct count and the sum of triple products of distinct values.	Hard9	Segment treeHash map+2	No attempts yet	2s	512 MB	Judgeable
Triple treeGenerate triples (a,b,c) satisfying a^2+b^2+c^2 = k(ab+bc+ca)+1 by two sweep operations from (1,k,k+k^2), then greedily print triples whose numbers are all new.	Hard9	MathNumber theory+2	No attempts yet	1s	512 MB	Judgeable
Risky LotteryFind the unique symmetric Nash equilibrium mixed strategy for a lottery where the winner is the player holding the smallest number written exactly once, and print each pick probability to five decimals.	Hard9	Game theoryProbability+2	No attempts yet	2s	512 MB	Judgeable
AcrobatGiven a bipartite multigraph between two sets of N assistants, each rope may be swapped (i,j)->(j,i) at most once; find the minimum swaps so the edges form an Eulerian circuit, or report -1.	Hard9	GraphBit manipulation+2	No attempts yet	2s	512 MB	Judgeable
Large Ping Pong TournamentGiven the total points each of 2^N players scored in a knockout ping pong tournament, decide if Dudu, who always wins ties, could have been champion.	Hard9	GreedySorting+2	No attempts yet	2s	512 MB	Judgeable
EggscavationGiven up to 100000 shell species (each in at most 4 cells) and egg insertions, answer queries for the probability that a random K x K scoop covers at least V species and no egg.	Hard9	GeometryPrefix sum+2	No attempts yet	10s	512 MB	Judgeable
PiratesFor every prefix of pirates, compute the oldest pirate's share under the stated voting and tie-breaking rules.	Hard9	GreedyDynamic programming+2	No attempts yet	10s	512 MB	Judgeable
MinerFor each lamp position above a polyline mine floor, find the reachable floor interval lit without crossing the floor.	Hard9	GeometryBinary search+2	No attempts yet	1.5s	512 MB	Judgeable
Robotic Cow HerdEach robot picks one model per location, and all K robots must differ somewhere; find the minimum total cost of K distinct robots.	Hard9	HeapGreedy+2	No attempts yet	2s	512 MB	Judgeable
Function and QueriesGiven an array and a recurrence f(i,j)=min(f(i-1,j),f(i-1,j-1))+a_j, answer up to 1e5 offline queries for f(x,y).	Hard9	Dynamic programmingDivide and conquer+2	No attempts yet	2s	512 MB	Judgeable
Unlucky 89Average the circumferences of all integer right triangles whose hypotenuse is k*sqrt(89) with k up to n, printed as exact mixed numbers in an ASCII box.	Hard9	Number theoryMath+2	No attempts yet	2s	512 MB	Judgeable
Find the SequenceGiven B, decide whether there exist distinct integers A_i > 1 such that A_i^{B_i} is divisible by the product of all the other A_j.	Hard9	Number theoryMath+2	No attempts yet	2s	512 MB	Judgeable
Soldiers (Large)Two players alternately pick soldiers, each new pick must beat all previous picks in attack or in defense; decide if the first player can end up with strictly more picks.	Hard9	Game theoryDynamic programming+1	No attempts yet	5s	512 MB	Judgeable
RonaldGiven a graph on N vertices, a move toggles all edges incident to one chosen vertex; decide whether the complete graph is reachable.	Hard9	GraphBit manipulation+2	No attempts yet	1s	64 MB	Judgeable
Rides 2Each day one child grows by 1 or 2, and we must report how many of Q fixed child-pair and ride triples become valid that day.	Hard9	Segment treeSorting+2	No attempts yet	2s	256 MB	Judgeable
Building a Tall BarnAssign K cows to N ordered floors, each with work a_i, so each floor gets at least one cow; minimize the sum of a_i/c_i over valid allocations, rounded to nearest integer.	Hard9	GreedyHeap+2	No attempts yet	2s	512 MB	Judgeable
Incremental Double Free StringsFind the nth string of length k(k+1)/2 that uses one letter j times for each j up to k and has no two equal adjacent letters, in alphabetical order.	Hard9	CombinatoricsDynamic programming+2	No attempts yet	2s	512 MB	Judgeable
Maximum Color CliqueGiven a complete graph whose every cycle has two adjacent same-color edges, sum over all nonempty node subsets the size of the largest same-color clique inside each subset, modulo 1e9+7.	Hard9	GraphCombinatorics+2	No attempts yet	2s	512 MB	Judgeable
The Enormous SequenceDefine a_n by summing every nonempty subset sum of the first n-1 terms, then answer queries about gcd, 2-adic valuation of lcm, prefix sums, or a single term for various starting values.	Hard9	MathNumber theory+2	No attempts yet	2s	128 MB	Judgeable
Tarot Sham BoastGiven up to 10 equal-length strings over {R,P,S} and a length n random string, sort the strings by the probability each occurs as a contiguous block.	Hard9	String matchingProbability+2	No attempts yet	2s	512 MB	Judgeable
Shifty GridApply a fixed two-phase procedure of cyclic row and column shifts to sort a permutation grid into row-major order, following the exact TURN steps given.	Hard9	SimulationImplementation+2	No attempts yet	2s	512 MB	Judgeable
Rolling the BottleGiven a convex polygon as a bottle base and a water volume, find the minimum and maximum number of sides of the water region as the bottle rolls.	Hard9	GeometrySorting+2	No attempts yet	2.5s	512 MB	Judgeable
Largest window sumFor every window length K, find the largest possible sum of a length-K window over all non-negative arrays that satisfy each given length bound.	Hard9	GreedyPrefix sum+2	No attempts yet	1s	512 MB	Judgeable
Creating Fake NewsFind one story vector satisfying n linear equations, then the minimum number of starting people whose reach covers all n people.	Hard9	MathGraph+1	No attempts yet	2s	512 MB	Judgeable
Fashion ShowPlace models on an N by N grid (or upgrade existing ones) so every shared row or column has a plus and every shared diagonal has an x, maximizing style points.	Hard9	GreedyGraph+2	No attempts yet	5s	512 MB	Judgeable
Slate Modern (Large)Fill a huge R by C grid with positive integers so adjacent cells differ by at most D, matching N fixed cells, maximizing the total sum or reporting impossibility.	Hard9	GraphShortest path+2	No attempts yet	80s	512 MB	Judgeable
Omnicircumnavigation (Large)Given points on a unit sphere joined in order by shortest arcs, decide whether the closed path meets every great circle.	Hard9	GeometryMath+2	No attempts yet	120s	512 MB	Judgeable
Stack Management (Small)Decide whether a solitaire game on 2 to 4 short stacks of cards can be reduced to at most one card per stack using two allowed moves.	Hard9	Game theorySimulation+2	No attempts yet	5s	512 MB	Judgeable
Sequence and TransformationCount length-n sequences with entries in [1,m] whose image after applying a min-based affine transformation k times has the given max-minus-min value.	Hard9	CombinatoricsMath+2	No attempts yet	2s	512 MB	Judgeable
Expected value of the greatest common divisorEach of K values is chosen uniformly from its own interval; find the expected gcd of the K chosen numbers as a fraction mod 1e9+7.	Hard9	ProbabilityMath+2	No attempts yet	2s	512 MB	Judgeable
Polynomial and QueriesEvaluate a degree-N polynomial with integer coefficients at K given points, all modulo the prime 786433, with N and K up to 250000.	Hard9	Number theoryDivide and conquer+2	No attempts yet	10s	512 MB	Judgeable
NPM998244353 (Hard)For every digit-sum cap from 0 to MM, count length-N digit strings divisible by P, modulo 998244353.	Hard9	CombinatoricsDynamic programming+2	No attempts yet	5s	512 MB	Judgeable
Counting multiples with a bounded digit sumCount length-N digit strings divisible by P with digit sum at most M, for every M up to the limit, modulo 998244353.	Hard9	Dynamic programmingCombinatorics+2	No attempts yet	2s	512 MB	Judgeable
Good triples of pathsCount triples of simple paths in a tree that are either node-disjoint or pairwise intersecting, modulo 1e9+7.	Hard9	CombinatoricsTree+2	No attempts yet	2s	512 MB	Judgeable
Strongly MatchableDecide whether an even-order graph admits a perfect bipartite matching for every balanced partition of its vertices.	Hard9	GraphMath+2	No attempts yet	3s	512 MB	Judgeable
Equivalent DeformationGiven two equal-area triangles, find the minimum number of vertex-sliding operations that map the first exactly onto the second.	Hard9	GeometryImplementation+2	No attempts yet	2s	512 MB	Judgeable
LeapfrogGiven up to 40 frogs, each starting at x_i with prime jump d_i, find the smallest position where the number of frogs that land there is largest.	Hard9	Number theoryMath+1	No attempts yet	2s	512 MB	Judgeable
Fractal TreeFor a recursively defined fractal tree F_k, answer queries giving the distance between two DFS-labeled vertices.	Hard9	TreeRecursion+2	No attempts yet	7s	512 MB	Judgeable
Arranging tilesGiven up to 14 convex tiles of equal height with cut corners, find the ordering and horizontal placement that minimizes the total frame width when packed side by side.	Hard9	Dynamic programmingGeometry+2	No attempts yet	1s	1024 MB	Judgeable
CratersFind the shortest single closed fence that surrounds all circles at distance 10 or more, given each crater's center and radius.	Hard9	GeometryDynamic programming+2	No attempts yet	2s	512 MB	Judgeable
Enlarging EnthusiasmCount the distinct final rankings achievable when positive point bonuses summing to x are announced in increasing order, with the lead changing hands each time.	Hard9	Dynamic programmingCombinatorics+2	No attempts yet	2s	512 MB	Judgeable
Jupiter Rock Paper ScissorsEach player crops a length-k substring, Alice morphs one block, then the play phase awards 2/1/1 points by who reaches m round wins first; report the optimal outcome.	Hard9	Game theoryImplementation+2	No attempts yet	2s	512 MB	Judgeable
Crazy RotationsGiven a row of coloured lights, find the smallest rotation amount that can appear at position p in a non-decreasing sequence of rotation craziness values.	Hard9	String matchingCombinatorics+2	No attempts yet	15s	512 MB	Judgeable
GCD SumFor each k from 1 to n, split a multiset of n numbers into k nonempty groups to maximize the sum of the groups' gcds. n is up to 500000 and each value up to 10^12.	Hard9	Number theoryGreedy+2	No attempts yet	2s	1024 MB	Judgeable
SkiingFind the shortest polygonal path from S down to F that crosses n horizontal gates in top-to-bottom order, and output its breakpoints.	Hard9	GeometryGreedy+2	No attempts yet	1s	1024 MB	Judgeable
Restaurant BribesGiven a friendship graph and a list of k people to bribe, choose a real bribe for each so the total restaurant revenue minus bribe money is maximized, and print the answer as an exact reduced fraction.	Hard9	GraphMath+2	No attempts yet	2s	512 MB	Judgeable
Lunar LandscapeCompute the total area covered by axis-aligned squares and 45-degree rotated squares, counting overlaps once.	Hard9	GeometrySorting+1	No attempts yet	2s	512 MB	Judgeable
ToysCount the number of distinct toys formed by strings joining n evenly spaced clamps on one disc to m on another, where rotating each disc independently gives the same toy, modulo 1,000,000,007.	Hard9	CombinatoricsNumber theory+2	No attempts yet	2s	512 MB	Judgeable
Workbook AlgorithmsCount the number of undirected graphs X on N vertices whose number of permutations P satisfying G(P)=X lies between l and r, modulo 1e9+7.	Hard9	CombinatoricsGraph+2	No attempts yet	1s	512 MB	Judgeable
Secret AgentGiven a planar straight-line graph (castle walls) where crossing a wall costs its height, find the minimum cost to travel between successive query points, starting from infinity.	Hard9	GraphGeometry+2	No attempts yet	2s	512 MB	Judgeable
GarageMaintain a sequence under point updates, and for each range query count subarrays whose elements share a common divisor greater than 1.	Hard9	Segment treeNumber theory+2	No attempts yet	4s	256 MB	Judgeable
Counting CyclesA connected undirected graph with n vertices and at most n+15 edges is given; count all simple cycles, where a simple cycle is a connected subgraph with every degree exactly two.	Hard9	GraphDFS+2	No attempts yet	4s	512 MB	Judgeable
LeadersAnimals in a circle alternately raise a running number by 1 to K; whoever is forced to say M loses, and we find the winner of every start position.	Hard9	Game theoryDynamic programming+2	No attempts yet	3s	512 MB	Judgeable
Disco Dance DebacleGiven a grid where some cells are unlit (unions of rectangles), find the fewest cell states to flip so that a set of alternating row-column dances can cover all lit cells, each dance starting and ending on the same cell with different first and last feet.	Hard9	GraphGreedy+2	No attempts yet	5s	512 MB	Judgeable
KabobsCount length-K strings over the given alphabet that satisfy all substring-implication rules of the form b>e, modulo 10^7.	Hard9	Dynamic programmingString+2	No attempts yet	5s	512 MB	Judgeable
Vera and Love TrianglesFor each pair of friends, a crush direction is set by the parity of the bit-count of a modular power expression; count cyclic triples.	Hard9	CombinatoricsNumber theory+2	No attempts yet	2s	256 MB	Judgeable
DramaCount the number of valid pyramid colourings of an H by N grid with exactly N black cells, modulo 10^9+7.	Hard9	CombinatoricsDynamic programming+1	No attempts yet	2s	512 MB	Judgeable
L-th K-th numberGiven N cards, take the K-th smallest value of every contiguous block of length at least K, then report the L-th smallest of all those values.	Hard9	Binary searchArray+2	No attempts yet	2s	512 MB	Judgeable
Revenge of the Endless BFSDecide whether a buggy BFS that forgets visited vertices ever terminates on a given directed graph, and if so output the loop count modulo 1e9+7.	Hard9	GraphBFS+2	No attempts yet	2s	512 MB	Judgeable
Conveyor BeltAfter each of Q delivery requests (a, b, p) is added, report the minimum time to finish all tasks, given plates arrive one per second and each plate carries one product.	Hard9	MathGreedy+2	No attempts yet	2s	512 MB	Judgeable
Blocks 2Count the ways to tile an N x M rectangle with rotated k x N blocks (k=1..N), modulo 1999, where M can be as large as 10^10.	Hard9	CombinatoricsDynamic programming+2	No attempts yet	1s	256 MB	Judgeable
Stamp PaintingCount the distinct colorings of an N-unit canvas obtainable by stamping K-wide colored stamps so every unit ends up painted, modulo 1e9+7.	Hard9	Dynamic programmingCombinatorics+1	No attempts yet	2s	512 MB	Judgeable
Euclidean NimFor each pair of move sizes p and q and starting pile n, decide which player wins the take-or-add game, or that it draws.	Hard9	Game theoryMath+1	No attempts yet	2s	512 MB	Judgeable
Maximal polygon brightnessGiven a convex polygon and a sequence of vertex deletions, compute after each deletion the largest total length of edges that a single external light point can illuminate.	Hard9	GeometryDynamic programming+2	No attempts yet	3s	1024 MB	Judgeable
In honor of Taekhee's graduationDeer bounce on a line segment [0,T], each with strength; a statue at x falls when the net force of deer that have reached it exceeds W. Maximize the fall time over x.	Hard9	MathSimulation+2	No attempts yet	3s	128 MB	Judgeable
Want to solve a problem?For given K and C, choose A > 0 to maximize the characters saved by writing K+A repeated K+A times instead of K repeated K times, minus C times A.	Hard9	String matchingMath+2	No attempts yet	1s	128 MB	Judgeable
The Number of SequencesFor a given N and C, find the lexicographically smallest triple (X, Y, Z) such that exactly C ordered N-tuples of 31-bit integers have OR X, AND Y, XOR Z, or report none exists.	Hard9	Bit manipulationCombinatorics+2	No attempts yet	1s	128 MB	Judgeable
Uncrossed Knight's TourGiven an m by n board (m at most 8, n up to 1e15), find the maximum number of squares a closed knight tour can visit without crossing itself.	Hard9	GreedyDynamic programming+2	No attempts yet	2s	1024 MB	Judgeable
TteokpireCount the number of ways to write N as an ordered sequence of one or more positive integers; equivalently, count compositions of N, modulo 1e9+7, for N up to 1e12.	Hard9	CombinatoricsMath+2	No attempts yet	1s	128 MB	Judgeable
Circle SelectionProcess circles in decreasing radius order; each chosen circle removes all remaining circles that intersect it, and for every circle you must report which chosen circle eliminated it.	Hard9	GeometrySorting+2	No attempts yet	3s	1024 MB	Judgeable
United States of EurasiaSplit N points sorted by x into at most K contiguous groups, minimizing the largest squared diameter within any group.	Hard9	Binary searchDynamic programming+2	No attempts yet	20s	1024 MB	Judgeable
Voronoi DiagramGiven a connected weighted graph and a set of source vertices, assign every point on every edge to its nearest source (smallest index on ties) and report the total length each source owns.	Hard9	GraphShortest path+2	No attempts yet	2s	1024 MB	Judgeable
Cryptarithm?!Given three letter strings A+B=C, decide whether some assignment of distinct digits to letters makes the addition valid, columns up to 18 long.	Hard9	BacktrackingMath+2	No attempts yet	1s	128 MB	Judgeable
Koala GameDetermine properties of a hidden permutation by bidding stones in a game where Koala optimally maximizes the sum of values she wins, using as few rounds as possible.	Hard9	Game theoryGreedy+2	No attempts yet	2s	512 MB	Judgeable
Tree EscapeOn a rooted tree where each leaf starts with one piece, players alternately move a piece to its parent and remove it at the root; decide if the first player wins.	Hard9	Game theoryTree+2	No attempts yet	2s	512 MB	Judgeable
The SprawlOn an infinite grid, N cities grow one cell per day in index order; sum over all pairs the first day the two cities' territories touch and connect.	Hard9	GraphBFS+2	No attempts yet	5s	768 MB	Judgeable
Pia's Atelier: The Alchemist of Mysterious LifeGiven 2x2 parity constraints on an n by n binary grid, decide for each day whether a grid exists satisfying all interval cell-fixing conditions active that day.	Hard9	Union-findPrefix sum+2	No attempts yet	2s	512 MB	Judgeable
BoosterFor each query, decide whether the character can travel from checkpoint A to checkpoint B with maximum HP X, given walking drains HP and the booster moves only along axes.	Hard9	GraphUnion-find+2	No attempts yet	8s	512 MB	Judgeable
Team BuildingMaintain teams under merge, a split that separates members by their remainder mod P, and size queries, for up to 100000 commands.	Hard9	Union-findImplementation+1	No attempts yet	1s	512 MB	Judgeable
FlippingCount initial black/white colorings of an N by M grid that can reach the given coloring when a press inverts the whole monochromatic connected component containing that cell, modulo 1e9+7.	Hard9	GraphUnion-find+2	No attempts yet	5s	256 MB	Judgeable
Cloud computingChoose a set of orders and a set of computers to buy so every accepted order gets enough cores at its minimum clock rate, maximizing payments minus computer costs.	Hard9	Dynamic programmingGreedy+2	No attempts yet	2s	512 MB	Judgeable
BuildingsCount the distinct houses formed by placing m walls of n by n colored squares around an m-gon, up to rotation, modulo 1e9+7.	Hard9	CombinatoricsMath+2	No attempts yet	2s	512 MB	Judgeable
BannerCount the orders of the 26 machines that let greedy longest-substring sewing finish a string of up to 35 letters in the fewest hours, modulo four primes.	Hard9	StringDynamic programming+1	No attempts yet	6s	512 MB	Judgeable
Growing MicroorganismsWith buy costs and production costs, buy microorganisms and make each kind produce others to reach x_i of every kind at minimum total cost.	Hard9	MathGreedy+2	No attempts yet	2s	512 MB	Judgeable
Game TheoryTwo players alternately remove stones from a vertex of a connected graph, then move along an edge or stay put; output who wins with optimal play from start vertex s.	Hard9	Game theoryGraph+1	No attempts yet	1s	256 MB	Judgeable
ConstellationChoose a subset of up to 2e5 points maximizing total brightness so that from any chosen point all others fall in the first or third quadrant, with the nearest point in each occupied quadrant within Chebyshev distance L.	Hard9	MathGeometry+2	No attempts yet	1.5s	512 MB	Judgeable
N and MFind the eventual constant residue modulo M of the power tower N, N^N, N^{N^N}, ... given N and M up to 1e9.	Hard9	MathNumber theory+1	No attempts yet	1s	1024 MB	Judgeable
SatellitesSatellites appear and disappear above a half-disc planet; for each query decide whether two satellites have a common coverage point outside the planet that no other live satellite covers.	Hard9	GeometryDynamic programming+2	No attempts yet	4s	512 MB	Judgeable
Black ChainGiven a chain of n rings (up to 10^18), find the fewest rings to open so the resulting pieces can be combined into every weight from 1 to n.	Hard9	GreedyCombinatorics+2	No attempts yet	0.1s	512 MB	Judgeable
MatchingGiven point sets A and B, find a translation of B that minimizes the width of the smallest strip containing both sets, and print that width.	Hard9	GeometryMath	No attempts yet	1s	512 MB	Judgeable
NumbersGiven n up to 10^18, count the ordered pairs of palindromes (a, b) whose sum is n.	Hard9	Dynamic programmingMath+1	No attempts yet	1s	512 MB	Judgeable
Simple PolygonGiven n segments with one endpoint on the x-axis, decide whether they can all lie on the boundary of one simple polygon, and find the minimum boundary length if so.	Hard9	GeometryDynamic programming+1	No attempts yet	2s	512 MB	Judgeable
Prime Tree - 2This output-only task asks for labels 1 to n on a tree's vertices so that as few edges as possible join two labels sharing a common divisor greater than 1.	Hard9	Number theoryTree+2	No attempts yet	10s	512 MB	Judgeable
Prime Tree - 4Relabel every vertex of each tree with 1 to n so the edges whose two labels share a divisor exceed 1 are as few as possible.	Hard9	GreedyNumber theory+2	No attempts yet	10s	512 MB	Judgeable