Math and counting

Number theory, combinatorics, and geometry

Under construction

Still being built. Things may change

Total results13,164 problems

Race
Hard8
Math, Greedy+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Cafebazaar's Chess Tournament
Hard8
Geometry, Sorting+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
The Big Surprise
Hard8
Geometry, Shortest path+1
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Gift Puzzle
Hard8
Geometry, Dynamic programming+1
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Perfect Pilgrimage
Hard8
Geometry, Math+1
No attempts yet
Time limit
1s
Memory limit
1024 MB
Judgeable
The End of the Pilgrimage
Hard8
Probability, Dynamic programming+1
No attempts yet
Time limit
1s
Memory limit
1024 MB
Judgeable
Polynomial and Queries 2
Hard8
Math, Number theory+2
No attempts yet
Time limit
5s
Memory limit
512 MB
Judgeable
Squares
Hard8
Dynamic programming, Math+1
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Logistics
Hard8
Greedy, Sorting+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Strawberry
Hard8
Dynamic programming, Greedy+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Rock-Scissors-Paper Expression
Hard8
Dynamic programming, Divide and conquer+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Zapina
Hard8
Combinatorics, Dynamic programming+2
No attempts yet
Time limit
1s
Memory limit
512 MB
Judgeable
Expected Value
Hard8
Graph, Math+1
No attempts yet
Time limit
1.5s
Memory limit
512 MB
Judgeable
Disjoint LIS
Hard8
Dynamic programming, Combinatorics
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Farm of Monsters
Hard8
Greedy, Sorting+2
No attempts yet
Time limit
1s
Memory limit
512 MB
Judgeable
Horrible Cycles
Hard8
Graph, Combinatorics+1
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Ignore Submasks
Hard8
Bit manipulation, Dynamic programming+2
No attempts yet
Time limit
1s
Memory limit
512 MB
Judgeable
Face Recognition Algorithm
Hard8
Geometry, Graph+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Euclid's Algorithm
Hard8
Number theory, Math+2
No attempts yet
Time limit
1s
Memory limit
512 MB
Judgeable
Not Our Problem
Hard8
Dynamic programming, Math
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Tree of Charge
Hard8
Tree, Math+1
No attempts yet
Time limit
4s
Memory limit
512 MB
Judgeable
Pick Your Own Nim
Hard8
Bit manipulation, Math+1
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Battle Royale
Hard8
Probability, Math+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Bomas
Hard8
Geometry, Tree+1
No attempts yet
Time limit
6s
Memory limit
512 MB
Judgeable
All Kill
Hard8
Dynamic programming, Combinatorics+1
No attempts yet
Time limit
1s
Memory limit
512 MB
Judgeable
Scored Nim
Hard8
Game theory, Dynamic programming+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
The Zong of the Zee
Hard8
String, Combinatorics+1
No attempts yet
Time limit
3s
Memory limit
512 MB
Judgeable
Expected Value
Hard8
Dynamic programming, Probability+2
No attempts yet
Time limit
3s
Memory limit
16 MB
Judgeable
Game X
Hard8
Math, Greedy+2
No attempts yet
Time limit
1s
Memory limit
512 MB
Judgeable
Count the Sequences
Hard8
Dynamic programming, Combinatorics+1
No attempts yet
Time limit
1s
Memory limit
512 MB
Judgeable
Fireflies
Hard8
Combinatorics, Math+1
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Glad You Came
Hard8
Segment tree, Implementation+2
No attempts yet
Time limit
4s
Memory limit
512 MB
Judgeable
Innocence
Hard8
Bit manipulation, Dynamic programming+1
No attempts yet
Time limit
1s
Memory limit
512 MB
Judgeable
Bus Stop
Hard8
Probability, Math+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Calculating Average
Hard8
Prefix sum, Geometry+1
No attempts yet
Time limit
5s
Memory limit
512 MB
Judgeable
Fractional XOR Maximization
Hard8
Bit manipulation, Greedy+1
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Jimp Numbers
Hard8
Number theory, Math
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Cake Distribution
Hard8
Math, Number theory+2
No attempts yet
Time limit
1s
Memory limit
512 MB
Judgeable
Nonsense Time
Hard8
Dynamic programming, Binary search+2
No attempts yet
Time limit
12s
Memory limit
512 MB
Judgeable
Support or Not
Hard8
Geometry, Binary search+1
No attempts yet
Time limit
8s
Memory limit
512 MB
Judgeable
Game Prediction
Hard8
Dynamic programming, Game theory+2
No attempts yet
Time limit
1s
Memory limit
512 MB
Judgeable
Minimum Spanning Trees
Hard8
Dynamic programming, Probability+2
No attempts yet
Time limit
4s
Memory limit
512 MB
Judgeable
Square Root Partitioning
Hard8
Brute force, Math+2
No attempts yet
Time limit
3s
Memory limit
512 MB
Judgeable
Alakazam
Hard8
Math, Probability+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Restoring a Permutation
Hard8
Greedy, Sorting+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Challenge
Hard8
Tree, Greedy+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Graph Measurement
Hard8
Probability, Math
No attempts yet
Time limit
30s
Memory limit
512 MB
Judgeable
Spaceship
Hard8
Geometry, Math+1
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Erase Nodes
Hard8
Probability, Graph+2
No attempts yet
Time limit
7s
Memory limit
512 MB
Judgeable
Power of Function
Hard8
Math, Number theory+1
No attempts yet
Time limit
4s
Memory limit
512 MB
Judgeable
Quicksort
Hard8
Combinatorics, Probability+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Pyramid
Hard8
Math, Number theory+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Find the Vertex
Hard8
Graph, BFS+2
No attempts yet
Time limit
1s
Memory limit
512 MB
Judgeable
Baklawa
Hard8
Game theory, Geometry+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
This Means War
Hard8
Dynamic programming, Geometry
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Awesome Shawarma
Hard8
Tree, DFS+2
No attempts yet
Time limit
14s
Memory limit
512 MB
Judgeable
Dull Chocolates
Hard8
Prefix sum, Sorting+2
No attempts yet
Time limit
9s
Memory limit
512 MB
Judgeable
Khoshaf
Hard8
Dynamic programming, Combinatorics+2
No attempts yet
Time limit
12s
Memory limit
512 MB
Judgeable
Contamination
Hard8
Union-find, Geometry+1
No attempts yet
Time limit
10s
Memory limit
512 MB
Judgeable
Invited Speakers
Hard8
Geometry, Greedy+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Balls
Hard8
Array, Math+2
No attempts yet
Time limit
1s
Memory limit
512 MB
Judgeable
Bin
Hard8
Dynamic programming, Combinatorics+1
No attempts yet
Time limit
15s
Memory limit
512 MB
Judgeable
Exp
Hard8
Probability, Dynamic programming+2
No attempts yet
Time limit
5s
Memory limit
512 MB
Judgeable
Flip
Hard8
Combinatorics, Math+1
No attempts yet
Time limit
10s
Memory limit
512 MB
Judgeable
Joy
Hard8
Divide and conquer, Dynamic programming+1
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Help Yourself (Gold)
Hard8
Combinatorics, Sorting+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Delegation (Gold)
Hard8
Tree, Dynamic programming+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Bridge Construction
Hard8
Combinatorics, Dynamic programming+2
No attempts yet
Time limit
2s
Memory limit
256 MB
Judgeable
Fabulous Photos
Hard8
Union-find, Bit manipulation+1
No attempts yet
Time limit
6s
Memory limit
512 MB
Judgeable
Solving a Problem (Park Seungwon)
Hard8
Dynamic programming, Combinatorics+1
No attempts yet
Time limit
1s
Memory limit
512 MB
Judgeable
Longest Increasing Subsequence K
Hard8
Dynamic programming, Binary search+1
No attempts yet
Time limit
0.25s
Memory limit
512 MB
Judgeable
Hamburg Steak
Hard8
Backtracking, Geometry+1
No attempts yet
Time limit
3s
Memory limit
1024 MB
Judgeable
Lingering Regret
Hard8
Tree, DFS+1
No attempts yet
Time limit
3s
Memory limit
1024 MB
Judgeable
Everything Is New
Hard8
Math, Graph+1
No attempts yet
Time limit
1s
Memory limit
1024 MB
Judgeable
O Life of My Youth
Hard8
Sorting, Greedy+2
No attempts yet
Time limit
2s
Memory limit
1024 MB
Judgeable
Circus
Hard8
Tree, Divide and conquer+1
No attempts yet
Time limit
1s
Memory limit
512 MB
Judgeable
Haircut
Hard8
Sorting, Prefix sum+2
No attempts yet
Time limit
1s
Memory limit
512 MB
Judgeable
New Year and Castle Construction
Hard8
Geometry, Combinatorics+2
No attempts yet
Time limit
3s
Memory limit
512 MB
Judgeable
Longest Increasing Subsequence ks
Hard8
Dynamic programming, Greedy+2
No attempts yet
Time limit
0.25s
Memory limit
512 MB
Judgeable
Nam Hyeon-uk
Hard8
Combinatorics, Math+1
No attempts yet
Time limit
2s
Memory limit
1024 MB
Judgeable
Daycare Children
Hard8
Combinatorics, Greedy+2
No attempts yet
Time limit
2s
Memory limit
64 MB
Judgeable
Encryption Function
Hard8
Math, Dynamic programming+2
No attempts yet
Time limit
1s
Memory limit
64 MB
Judgeable
Minimal Variance Tree
Hard8
Minimum spanning tree, Sorting+1
No attempts yet
Time limit
1s
Memory limit
256 MB
Judgeable
Alice and Bob
Hard8
Game theory, Dynamic programming+2
No attempts yet
Time limit
1s
Memory limit
512 MB
Judgeable
Joining Points
Hard8
Dynamic programming, Combinatorics
No attempts yet
Time limit
1s
Memory limit
512 MB
Judgeable
Disk Troubles
Hard8
Math, Bit manipulation+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Fox Labeling
Hard8
Probability, Combinatorics+1
No attempts yet
Time limit
3s
Memory limit
512 MB
Judgeable
Lands of Infinistan
Hard8
Geometry, Math+1
No attempts yet
Time limit
1s
Memory limit
512 MB
Judgeable
Non-Decreasing Subarray Game
Hard8
Game theory, Dynamic programming+2
No attempts yet
Time limit
2s
Memory limit
256 MB
Judgeable
Knapsack
Hard8
Dynamic programming, Greedy+2
No attempts yet
Time limit
3s
Memory limit
512 MB
Judgeable
Algebra on Segment
Hard8
Segment tree, Number theory+1
No attempts yet
Time limit
10s
Memory limit
512 MB
Judgeable
Partition into Teams
Hard8
Combinatorics, Math+2
No attempts yet
Time limit
1s
Memory limit
256 MB
Judgeable
Classic Quotation
Hard8
String matching, Prefix sum+2
No attempts yet
Time limit
1s
Memory limit
512 MB
Judgeable
Counting Divisors
Hard8
Number theory, Math+2
No attempts yet
Time limit
7s
Memory limit
512 MB
Judgeable
Lazy Running
Hard8
Shortest path, Dynamic programming+2
No attempts yet
Time limit
1s
Memory limit
256 MB
Judgeable
Matching In Multiplication
Hard8
Graph, Math+2
No attempts yet
Time limit
1s
Memory limit
512 MB
Judgeable
Questionnaire
Hard8
Math, Number theory+2
No attempts yet
Time limit
1s
Memory limit
512 MB
Judgeable
Stable Permutation
Hard8
Combinatorics, Math+1
No attempts yet
Time limit
3s
Memory limit
256 MB
Judgeable
Rikka with XOR
Hard8
Bit manipulation, Number theory+1
No attempts yet
Time limit
1s
Memory limit
512 MB
Judgeable
Road Connectivity
Hard8
Probability, Matrix+2
No attempts yet
Time limit
2s
Memory limit
256 MB
Judgeable

Title	Level	Topics	Solved	Time limit	Memory limit	Judge
RaceGiven race length K and finish-speed cap X, find the minimum number of seconds for Bessie to cover at least K meters, with N queries.	Hard8	MathGreedy+2	No attempts yet	2s	512 MB	Judgeable
Cafebazaar's Chess TournamentGiven n players each with an opening and ending skill, count how many distinct tournament scores a new player with freely chosen distinct skills can achieve.	Hard8	GeometrySorting+2	No attempts yet	2s	512 MB	Judgeable
The Big SurpriseGiven up to 100 axis-aligned boxes, find the shortest rectilinear (Manhattan) 3D path between two points that avoids the boxes' interiors.	Hard8	GeometryShortest path+1	No attempts yet	2s	512 MB	Judgeable
Gift PuzzleGiven n horizontal rails with sliding obstacles on a board, find the shortest thread from the top-left to the bottom-right corner that avoids all obstacles.	Hard8	GeometryDynamic programming+1	No attempts yet	2s	512 MB	Judgeable
Perfect PilgrimageChoose N lattice points forming a counterclockwise polygon with no crossing edges and at least K equal sides, or report that no such choice exists.	Hard8	GeometryMath+1	No attempts yet	1s	1024 MB	Judgeable
The End of the PilgrimageGiven the last N visited sites, find the expected time until the last N visits are all distinct, printed modulo the prime X.	Hard8	ProbabilityDynamic programming+1	No attempts yet	1s	1024 MB	Judgeable
Polynomial and Queries 2Given a degree-N polynomial and K query points, evaluate the polynomial at every point modulo 1,030,307.	Hard8	MathNumber theory+2	No attempts yet	5s	512 MB	Judgeable
SquaresGiven n up to 10^18, find the smallest possible largest base k(n) in a sum of distinct squares equal to n, and count the overgrown integers up to n.	Hard8	Dynamic programmingMath+1	No attempts yet	2s	512 MB	Judgeable
LogisticsFor each query, decide whether c drivers who can each drive at most their own mileage limit can cover a route of s km in one convoy, given the drivers may swap at stops.	Hard8	GreedySorting+2	No attempts yet	2s	512 MB	Judgeable
StrawberryStrawberries at positions ripen at given times; starting and ending at 0, move at speed 1 and find the minimum time to harvest all after they ripen.	Hard8	Dynamic programmingGreedy+2	No attempts yet	2s	512 MB	Judgeable
Rock-Scissors-Paper ExpressionCount the assignments of R, S, P to the ? symbols in a fixed arithmetic expression, under rock-scissors-paper defined operators, so that evaluation gives A.	Hard8	Dynamic programmingDivide and conquer+2	No attempts yet	2s	512 MB	Judgeable
ZapinaCount the ways to assign N distinct tasks to N programmers so that at least one programmer i receives exactly i tasks, modulo 1e9+7.	Hard8	CombinatoricsDynamic programming+2	No attempts yet	1s	512 MB	Judgeable
Expected ValueGiven a connected plane straight-line graph, find the expected first hitting time of vertex n from vertex 1 in a random walk, modulo 998244353.	Hard8	GraphMath+1	No attempts yet	1.5s	512 MB	Judgeable
Disjoint LISCount the permutations of n elements that contain two disjoint increasing subsequences, each as long as the LIS, modulo 998244353.	Hard8	Dynamic programmingCombinatorics	No attempts yet	2s	512 MB	Judgeable
Farm of MonstersYou and a fixed greedy opponent alternate attacking monsters; you choose targets to maximize the number of monsters you personally kill.	Hard8	GreedySorting+2	No attempts yet	1s	512 MB	Judgeable
Horrible CyclesCount the simple cycles in a bipartite graph where each left vertex i connects to the right prefix 1 to a_i, modulo 998244353, with n up to 5000.	Hard8	GraphCombinatorics+1	No attempts yet	2s	512 MB	Judgeable
Ignore SubmasksFor each k-bit mask x, find the first array element that does not contain x as a submask, and sum these indices modulo 998244353.	Hard8	Bit manipulationDynamic programming+2	No attempts yet	1s	512 MB	Judgeable
Face Recognition AlgorithmGiven a planar straight-line embedding of a connected graph, decide whether every face, including the outer one, is bounded by exactly three edges.	Hard8	GeometryGraph+2	No attempts yet	2s	512 MB	Judgeable
Euclid's AlgorithmGiven d and k, find the largest integer that divides (a+d)^k - a^k for every positive integer a.	Hard8	Number theoryMath+2	No attempts yet	1s	512 MB	Judgeable
Not Our ProblemCount the ways to fill the -1 entries so every adjacent pair satisfies a_i * a_{i+1} * min(a_i, a_{i+1}) <= C, or print -1 if there are infinitely many.	Hard8	Dynamic programmingMath	No attempts yet	2s	512 MB	Judgeable
Tree of ChargeCharges on a rooted tree move up to parents, split down equally among children, or get added at a vertex. Print each final charge modulo 1e9+7.	Hard8	TreeMath+1	No attempts yet	4s	512 MB	Judgeable
Pick Your Own NimBob picks one heap from each of his boxes so that he wins for every nonempty subset Alice can choose from her heaps, or the task reports that he cannot.	Hard8	Bit manipulationMath+1	No attempts yet	2s	512 MB	Judgeable
Battle RoyaleGiven house positions x_i and survival times a_i, find each player's probability of being the last survivor when the final safe point M is random in [L, R].	Hard8	ProbabilityMath+2	No attempts yet	2s	512 MB	Judgeable
BomasGiven non-touching circular fences that may nest, find how many animal types fit in each query boma when adjacent areas cannot both hold animals.	Hard8	GeometryTree+1	No attempts yet	6s	512 MB	Judgeable
All KillGiven n coding times and a contest of t minutes, find p times t^n mod 998244353, where p is the chance that all problems are coded in full, each as one contiguous block, before the end.	Hard8	Dynamic programmingCombinatorics+1	No attempts yet	1s	512 MB	Judgeable
Scored NimPlayers alternately split a heap into two colored heaps until all heaps are size one; find Alice's optimal final white-stone count.	Hard8	Game theoryDynamic programming+2	No attempts yet	2s	512 MB	Judgeable
The Zong of the ZeeGiven m lines of length n with at most one unknown letter per line, count the permutations that turn each line into the next one, modulo 1e9+7.	Hard8	StringCombinatorics+1	No attempts yet	3s	512 MB	Judgeable
Expected ValueRepeatedly pick a random adjacent pair, replace the left value by its difference with the right, drop the right. Find the expected final value modulo 1e9+7.	Hard8	Dynamic programmingProbability+2	No attempts yet	3s	16 MB	Judgeable
Game XGiven n and k, decide whether exactly k pairs of nonzero, distinct-magnitude integers can have positive sum, and if so maximize the number of pairs whose product is positive.	Hard8	MathGreedy+2	No attempts yet	1s	512 MB	Judgeable
Count the SequencesCount sequences x_1 to x_m where each 0 <= x_i <= b^i - c and the sum is below n, modulo 998244353.	Hard8	Dynamic programmingCombinatorics+1	No attempts yet	1s	512 MB	Judgeable
FirefliesFind the fewest fireflies needed to cover every unit of an n-dimensional box, where each firefly moves one unit step at a time, printed mod 1e9+7.	Hard8	CombinatoricsMath+1	No attempts yet	2s	512 MB	Judgeable
Glad You CameApply m range-max updates (a_j = max(a_j, v_i)) to a zero array, where each l, r, v comes from a fixed 32-bit RNG, then output the XOR of i*a_i.	Hard8	Segment treeImplementation+2	No attempts yet	4s	512 MB	Judgeable
InnocenceCount arrays of length N with every element in [L, R] whose XOR equals K, modulo 1e9+7, for several K values per test case.	Hard8	Bit manipulationDynamic programming+1	No attempts yet	1s	512 MB	Judgeable
Bus StopEach of n bus routes has independent waiting time uniform on [0, di]; find the expected minimum, output as a fraction modulo 998244353.	Hard8	ProbabilityMath+2	No attempts yet	2s	512 MB	Judgeable
Calculating AverageFor each index k, find the maximum average of a consecutive segment that contains position k.	Hard8	Prefix sumGeometry+1	No attempts yet	5s	512 MB	Judgeable
Fractional XOR MaximizationGiven rational intervals [a, b] and [c, d], find the supremum of the XOR of binary expansions of one number from each interval.	Hard8	Bit manipulationGreedy+1	No attempts yet	2s	512 MB	Judgeable
Jimp NumbersCount the jimp numbers k up to n, where exactly one arithmetic triple (a, b, c) satisfies a^2 + b^2 + k = c^2.	Hard8	Number theoryMath	No attempts yet	2s	512 MB	Judgeable
Cake DistributionChoose up to 5000 positive integer cake pieces so that for each of A, B, C guests they can be split evenly, labeling each piece with its recipient for each case.	Hard8	MathNumber theory+2	No attempts yet	1s	512 MB	Judgeable
Nonsense TimeElements of a random permutation are unfrozen one at a time; after each unfreeze report the longest increasing subsequence length among the currently available elements.	Hard8	Dynamic programmingBinary search+2	No attempts yet	12s	512 MB	Judgeable
Support or NotGiven n spheres in 3D, find the k smallest gap distances between pairs of spheres and print each one rounded up.	Hard8	GeometryBinary search+1	No attempts yet	8s	512 MB	Judgeable
Game PredictionFor each subarray query, compute both players' final scores when they alternately take the leftmost or rightmost element, playing optimally.	Hard8	Dynamic programmingGame theory+2	No attempts yet	1s	512 MB	Judgeable
Minimum Spanning TreesGiven a random graph where each edge has weight 0 to k or is absent, find for each s the probability that the graph is connected with MST weight s, modulo 1e9+7.	Hard8	Dynamic programmingProbability+2	No attempts yet	4s	512 MB	Judgeable
Square Root PartitioningGiven n numbers (n up to 36) with values up to 10^100000, count the sign choices + or - that make the signed sum of their square roots equal zero.	Hard8	Brute forceMath+2	No attempts yet	3s	512 MB	Judgeable
AlakazamGiven an array and range shuffle operations that permute a segment uniformly at random, answer point queries for the expected value at a position.	Hard8	MathProbability+2	No attempts yet	2s	512 MB	Judgeable
Restoring a PermutationGiven arrays a and b, construct a permutation p where a[i] is the LIS ending at i and b[i] is the longest decreasing subsequence starting at i.	Hard8	GreedySorting+2	No attempts yet	2s	512 MB	Judgeable
ChallengeConstruct a tree with at most n vertices whose recursive center-removal decomposition puts some vertex in at least floor(sqrt(n)) different pieces.	Hard8	TreeGreedy+2	No attempts yet	2s	512 MB	Judgeable
Graph MeasurementGiven k random black/white colorings of an unknown graph's edges, recover the graph from the per-vertex counts of black edges.	Hard8	ProbabilityMath	No attempts yet	30s	512 MB	Judgeable
SpaceshipGiven a start point and direction and a target point and direction in 3D, build a path of lines and circular arcs with radius at least r0 that joins them with matching tangent directions.	Hard8	GeometryMath+1	No attempts yet	2s	512 MB	Judgeable
Erase NodesNodes of a connected graph with n nodes and n edges are removed in random order; find the expected number of BFS updates, modulo 998244353.	Hard8	ProbabilityGraph+2	No attempts yet	7s	512 MB	Judgeable
Power of FunctionFind the largest m such that f^m(n) = 1 for some n in [l, r], plus the smallest and largest such n for that m.	Hard8	MathNumber theory+1	No attempts yet	4s	512 MB	Judgeable
QuicksortGiven a flawed quicksort with recursion depth limit k, find the expected number of inversions after running it on a uniformly random permutation of size n, times n! modulo 998244353.	Hard8	CombinatoricsProbability+2	No attempts yet	2s	512 MB	Judgeable
PyramidCount the ways to pick three vertices forming an equilateral triangle among the pyramid vertices on levels l to r, for up to 300000 queries.	Hard8	MathNumber theory+2	No attempts yet	2s	512 MB	Judgeable
Find the VertexGiven a connected graph and the shortest-path distances from an unknown vertex s to all vertices modulo 3, find s.	Hard8	GraphBFS+2	No attempts yet	1s	512 MB	Judgeable
BaklawaGiven a huge cuboid with up to 100 poisonous unit cells, players alternate cutting off a safe cuboid half; decide who wins under optimal play.	Hard8	Game theoryGeometry+2	No attempts yet	2s	512 MB	Judgeable
This Means WarSplit sorted soldiers into contiguous groups to maximize the sum of f_a(x_b) over each group, where a is the group's leftmost and b its rightmost soldier.	Hard8	Dynamic programmingGeometry	No attempts yet	2s	512 MB	Judgeable
Awesome ShawarmaGiven a tree, count the unordered pairs of nodes whose added edge leaves the number of bridges in [L, R].	Hard8	TreeDFS+2	No attempts yet	14s	512 MB	Judgeable
Dull ChocolatesCount prefix rectangles of a huge grid whose parity of white cells is odd versus even, given at most 1000 white cells.	Hard8	Prefix sumSorting+2	No attempts yet	9s	512 MB	Judgeable
KhoshafCount arrays of length N with entries in [L, R] that have exactly K contiguous subarrays whose sum is divisible by 3, modulo 1e9+7.	Hard8	Dynamic programmingCombinatorics+2	No attempts yet	12s	512 MB	Judgeable
ContaminationGiven disjoint contaminated circles, answer for each query whether two points can be connected without entering any circle while staying within a horizontal latitude band.	Hard8	Union-findGeometry+1	No attempts yet	10s	512 MB	Judgeable
Invited SpeakersGiven n red and n blue points in the plane with distinct x and y coordinates and no three collinear, draw n disjoint polygonal chains pairing each red point with a blue point.	Hard8	GeometryGreedy+2	No attempts yet	2s	512 MB	Judgeable
BallsGiven a row of colored balls, repeatedly pick a consecutive segment with a strict majority color and delete all other balls in it; count which colors can remain at the end.	Hard8	ArrayMath+2	No attempts yet	1s	512 MB	Judgeable
BinCount full binary trees with n leaves where each node's left leaf count exceeds its right leaf count by at most k, modulo 998244353.	Hard8	Dynamic programmingCombinatorics+1	No attempts yet	15s	512 MB	Judgeable
ExpEach of n independent monsters grants i experience (0 to k) with probability p_i, totals are capped at x, and the expected capped total must be computed modulo 998244353.	Hard8	ProbabilityDynamic programming+2	No attempts yet	5s	512 MB	Judgeable
FlipGiven sets of people numbered 1 to 2n, find for each set the probability that all its members land on the same team under the coin-flip assignment, modulo 998244353.	Hard8	CombinatoricsMath+1	No attempts yet	10s	512 MB	Judgeable
JoyGiven a queue of n-1 players and your skill x, find for each of the n insertion positions the probability that you win the knockout tournament.	Hard8	Divide and conquerDynamic programming+1	No attempts yet	2s	512 MB	Judgeable
Help Yourself (Gold)Sum the number of connected regions in the union of segments over all 2^N subsets, modulo 1e9+7.	Hard8	CombinatoricsSorting+2	No attempts yet	2s	512 MB	Judgeable
Delegation (Gold)Given a tree with N pastures, decide for each K from 1 to N-1 whether its edges can be split into paths that each have exactly K edges.	Hard8	TreeDynamic programming+2	No attempts yet	2s	512 MB	Judgeable
Bridge ConstructionCount unlabeled connected graphs on N vertices with maximum degree at most 4, modulo a prime X.	Hard8	CombinatoricsDynamic programming+2	No attempts yet	2s	256 MB	Judgeable
Fabulous PhotosGiven the set of balls in each photo, find for each ball the smallest-numbered ball that must share its colour in every consistent colouring.	Hard8	Union-findBit manipulation+1	No attempts yet	6s	512 MB	Judgeable
Solving a Problem (Park Seungwon)Count the ways to tile an n×m grid (n, m up to 10) with 1×1, 2×2, and 4×4 tiles, where each size comes in several kinds, modulo 1e9+7.	Hard8	Dynamic programmingCombinatorics+1	No attempts yet	1s	512 MB	Judgeable
Longest Increasing Subsequence KGiven a sequence of N integers and K, find the K-th longest increasing subsequence in lexicographic order of index sequences, or print -1 if fewer than K exist.	Hard8	Dynamic programmingBinary search+1	No attempts yet	0.25s	512 MB	Judgeable
Hamburg SteakPlace K points on the grid so that every given rectangle contains at least one point, then output the K coordinates.	Hard8	BacktrackingGeometry+1	No attempts yet	3s	1024 MB	Judgeable
Lingering RegretFor each valley, the task counts how many valleys Uk-je can reach by jumping down the source-rooted tree under the bounce rule, starting from that valley.	Hard8	TreeDFS+1	No attempts yet	3s	1024 MB	Judgeable
Everything Is NewGiven a shuffled Ukdimensional sliding puzzle on an a x b x c x d x e x f grid, decide whether the pieces can be returned to the solved order.	Hard8	MathGraph+1	No attempts yet	1s	1024 MB	Judgeable
O Life of My YouthGiven N pairs of happiness and fatigue with some values missing (0), find the largest K < N such that all young-day pairs can exceed all old-day pairs in happiness and stay below them in fatigue.	Hard8	SortingGreedy+2	No attempts yet	2s	1024 MB	Judgeable
CircusFor each K, count the equivalence classes of starting states of K labeled cows on a tree, where cows move to adjacent empty vertices.	Hard8	TreeDivide and conquer+1	No attempts yet	1s	512 MB	Judgeable
HaircutFor each threshold j from 0 to N-1, clip every value above j down to j and count the resulting inversions.	Hard8	SortingPrefix sum+2	No attempts yet	1s	512 MB	Judgeable
New Year and Castle ConstructionGiven n points with no three collinear, count over all points p the number of 4-point subsets whose convex quadrilateral strictly contains p, and sum these counts.	Hard8	GeometryCombinatorics+2	No attempts yet	3s	512 MB	Judgeable
Longest Increasing Subsequence ksGiven a permutation-like sequence, find the K-th longest increasing subsequence when all LISs are sorted lexicographically by index, or -1 if fewer than K exist.	Hard8	Dynamic programmingGreedy+2	No attempts yet	0.25s	512 MB	Judgeable
Nam Hyeon-ukGiven n and m (0 to 3), sum the inversion counts of all length-n permutations with exactly m increasing subsequences of length 3, mod 998244353.	Hard8	CombinatoricsMath+1	No attempts yet	2s	1024 MB	Judgeable
Daycare ChildrenAssign each of n children at least k toy kinds from floor(3k^2/2) available kinds so that every pair shares exactly one kind and no two sets are equal.	Hard8	CombinatoricsGreedy+2	No attempts yet	2s	64 MB	Judgeable
Encryption FunctionGiven the output of a digit-subset-sum encryption, find any positive integer that encrypts to it or report that none exists.	Hard8	MathDynamic programming+2	No attempts yet	1s	64 MB	Judgeable
Minimal Variance TreeGiven a connected multigraph, find the spanning tree whose edge weights have the smallest variance, and print that minimal variance.	Hard8	Minimum spanning treeSorting+1	No attempts yet	1s	256 MB	Judgeable
Alice and BobCount placements of at most one token per vertex on a colored DAG where Alice (white moves) beats Bob (black moves) under optimal play.	Hard8	Game theoryDynamic programming+2	No attempts yet	1s	512 MB	Judgeable
Joining PointsCount the sets of n non-crossing arcs on a circle, each joining two same-colored points with no point of that color inside the arc.	Hard8	Dynamic programmingCombinatorics	No attempts yet	1s	512 MB	Judgeable
Disk TroublesGiven a polynomial remainder Q(x) modulo a fixed degree-32 binary polynomial, find the smallest k with x^k mod P(x) equal to Q(x), inverting a discrete-log-like map.	Hard8	MathBit manipulation+2	No attempts yet	2s	512 MB	Judgeable
Fox LabelingGiven n foxes with their initial colors and a label size k, find the expected minutes until every pair of foxes becomes distinguishable by repeatedly labeling random k-subsets.	Hard8	ProbabilityCombinatorics+1	No attempts yet	3s	512 MB	Judgeable
Lands of InfinistanCount the lands that n straight walls and one quadratic river curve divide the plane into, given all their equations.	Hard8	GeometryMath+1	No attempts yet	1s	512 MB	Judgeable
Non-Decreasing Subarray GameFor each query range, Yuto picks an integer to minimize and Platina then picks one to maximize the count of non-decreasing subarrays inside the interval they bound; output the resulting score.	Hard8	Game theoryDynamic programming+2	No attempts yet	2s	256 MB	Judgeable
KnapsackCount subsets of weights where each of n types has 2 copies and masses grow at least by a factor of 2, so the total equals W.	Hard8	Dynamic programmingGreedy+2	No attempts yet	3s	512 MB	Judgeable
Algebra on SegmentGiven an array modulo a prime p, support range multiplication and report the order of the subgroup generated by the elements of a segment.	Hard8	Segment treeNumber theory+1	No attempts yet	10s	512 MB	Judgeable
Partition into TeamsFor n people each choosing red, blue, or spectator uniformly, compute 3^n times the probability that red wins, modulo a prime p.	Hard8	CombinatoricsMath+2	No attempts yet	1s	256 MB	Judgeable
Classic QuotationGiven strings S and T and queries (L, R), compute the expected number of occurrences of T after deleting a random substring spanning positions L to R, scaled by the number of choices.	Hard8	String matchingPrefix sum+2	No attempts yet	1s	512 MB	Judgeable
Counting DivisorsFor each query with l, r, k, compute the sum of d(i^k) for i from l to r, modulo 998244353, where d counts divisors.	Hard8	Number theoryMath+2	No attempts yet	7s	512 MB	Judgeable
Lazy RunningStarting and ending at checkpoint p2 on a 4-cycle, find the shortest closed walk whose swipe-recorded total distance is at least K, given the four edge lengths.	Hard8	Shortest pathDynamic programming+2	No attempts yet	1s	256 MB	Judgeable
Matching In MultiplicationGiven a bipartite graph where each of the n vertices on one side has degree 2, sum the products of edge weights over all perfect matchings, modulo 998244353.	Hard8	GraphMath+2	No attempts yet	1s	512 MB	Judgeable
QuestionnaireGiven n distinct positive integers, find a modulus m and residue k so that at least half the numbers are congruent to k mod m.	Hard8	MathNumber theory+2	No attempts yet	1s	512 MB	Judgeable
Stable PermutationFind the k-th lexicographically smallest permutation of length n whose inversion count is exactly half of all pairs, or report NO if none exists.	Hard8	CombinatoricsMath+1	No attempts yet	3s	256 MB	Judgeable
Rikka with XORGiven n and m, compute the product of n xor i for i from 0 to m, modulo 1500000001.	Hard8	Bit manipulationNumber theory+1	No attempts yet	1s	512 MB	Judgeable
Road ConnectivityEach day one of the 10 roads is picked at random and its open or closed state is flipped. For each query [l, r], find the probability the country is connected on some day in that range.	Hard8	ProbabilityMatrix+2	No attempts yet	2s	256 MB	Judgeable