Math and counting

Number theory, combinatorics, and geometry

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Total results13,153 problems

Rotate Sum 3
Hard9
Geometry, Math+1
No attempts yet
Time limit
1s
Memory limit
1024 MB
Judgeable
Great Party
Hard9
Game theory, Bit manipulation+1
No attempts yet
Time limit
1s
Memory limit
1024 MB
Judgeable
DS Team Selection
Hard9
Segment tree, Math+1
No attempts yet
Time limit
18s
Memory limit
1024 MB
Judgeable
Games
Hard9
Tree, Dynamic programming+1
No attempts yet
Time limit
4s
Memory limit
1024 MB
Judgeable
Half Plane
Hard9
Geometry, Segment tree+1
No attempts yet
Time limit
12s
Memory limit
1024 MB
Judgeable
Tree
Hard9
Combinatorics, Dynamic programming+1
No attempts yet
Time limit
3s
Memory limit
1024 MB
Judgeable
Infectious Disease
Hard9
Probability, Math+1
No attempts yet
Time limit
5s
Memory limit
1024 MB
Judgeable
DFS
Hard9
Tree, Union-find+2
No attempts yet
Time limit
8s
Memory limit
1024 MB
Judgeable
Village Planning
Hard9
Graph, Combinatorics+1
No attempts yet
Time limit
3s
Memory limit
1024 MB
Judgeable
Drinking Water
Hard9
Binary search, Greedy+2
No attempts yet
Time limit
2s
Memory limit
1024 MB
Judgeable
Battleship: New Rules
Hard9
Implementation, Greedy+1
No attempts yet
Time limit
3s
Memory limit
1024 MB
Judgeable
Fun with Stones
Hard9
Combinatorics, Bit manipulation+2
No attempts yet
Time limit
1s
Memory limit
1024 MB
Judgeable
Park Trails
Hard9
Geometry, Graph+1
No attempts yet
Time limit
3s
Memory limit
1024 MB
Judgeable
Triangle
Hard9
Geometry, Binary search+1
No attempts yet
Time limit
1s
Memory limit
1024 MB
Judgeable
Roll Call
Hard9
Combinatorics, Math+1
No attempts yet
Time limit
1s
Memory limit
256 MB
Judgeable
Arbitration
Hard9
Dynamic programming, Combinatorics+1
No attempts yet
Time limit
10s
Memory limit
1024 MB
Judgeable
Game
Hard9
Math, Array+1
No attempts yet
Time limit
2s
Memory limit
1024 MB
Judgeable
Just Another Edge
Hard9
Graph, BFS+1
No attempts yet
Time limit
2s
Memory limit
1024 MB
Judgeable
Khalin Graph
Hard9
Dynamic programming, Tree+2
No attempts yet
Time limit
2s
Memory limit
1024 MB
Judgeable
Moving Randomly
Hard9
Array, Greedy+2
No attempts yet
Time limit
2s
Memory limit
1024 MB
Judgeable
Sequence, Intervals, and Queries
Hard9
Binary search, Prefix sum+2
No attempts yet
Time limit
5s
Memory limit
1024 MB
Judgeable
Polygons
Hard9
Number theory, Geometry+2
No attempts yet
Time limit
10s
Memory limit
1024 MB
Judgeable
Landing Raid
Hard9
Divide and conquer, Combinatorics+1
No attempts yet
Time limit
6s
Memory limit
1024 MB
Judgeable
Fibonacci Products
Hard9
Dynamic programming, String+1
No attempts yet
Time limit
20s
Memory limit
1024 MB
Judgeable
Island
Hard9
Graph, Combinatorics+1
No attempts yet
Time limit
6s
Memory limit
1024 MB
Judgeable
A very complicated test
Hard9
Tree, DFS+1
No attempts yet
Time limit
3s
Memory limit
1024 MB
Judgeable
Independent Sets
Hard9
Combinatorics, Tree+2
No attempts yet
Time limit
45s
Memory limit
1024 MB
Judgeable
IQ Game
Hard9
Probability, Combinatorics+2
No attempts yet
Time limit
2s
Memory limit
1024 MB
Judgeable
Indecisive Nikolaj
Hard9
Game theory, Dynamic programming+2
No attempts yet
Time limit
3s
Memory limit
1024 MB
Judgeable
Sequence and Queries 43
Hard9
Segment tree, Math+1
No attempts yet
Time limit
5s
Memory limit
1024 MB
Judgeable
Sports Day
Hard9
Game theory, Dynamic programming+1
No attempts yet
Time limit
1s
Memory limit
1024 MB
Judgeable
Picnic
Hard9
Bit manipulation, Math+1
No attempts yet
Time limit
4s
Memory limit
1024 MB
Judgeable
Typing Contest
Hard9
Dynamic programming, Bit manipulation+1
No attempts yet
Time limit
2.5s
Memory limit
1024 MB
Judgeable
GCD and K-th Query
Hard9
Binary search, Number theory+1
No attempts yet
Time limit
1s
Memory limit
1024 MB
Judgeable
Familiar Couples
Hard9
Union-find, Tree+1
No attempts yet
Time limit
15s
Memory limit
1024 MB
Judgeable
Festivals in JOI Kingdom 2
Hard9
Dynamic programming, Combinatorics+1
No attempts yet
Time limit
6s
Memory limit
1024 MB
Judgeable
LaLa and Magic Circle (LiLi Version)
Hard9
Geometry, Simulation+1
No attempts yet
Time limit
10s
Memory limit
1024 MB
Judgeable
LaLa and Magic Circle (LaLa Version)
Hard9
Geometry, Implementation
No attempts yet
Time limit
2s
Memory limit
1024 MB
Judgeable
LaLa and Monster Hunting (Part 2)
Hard9
Graph, Combinatorics+1
No attempts yet
Time limit
6s
Memory limit
1024 MB
Judgeable
The Answer to the Ultimate Question of Life, the Universe, and Everything
Hard9
Math, Number theory
No attempts yet
Time limit
0.42s
Memory limit
420 MB
Judgeable
Who Watches the Watchmen?
Hard9
Geometry, Graph+1
No attempts yet
Time limit
4s
Memory limit
2048 MB
Judgeable
Range Closest Pair of Points Query
Hard9
Divide and conquer, Geometry+1
No attempts yet
Time limit
9s
Memory limit
1024 MB
Judgeable
Forever Young
Hard9
Dynamic programming, Combinatorics+1
No attempts yet
Time limit
2s
Memory limit
1024 MB
Judgeable
Endless Road
Hard9
Probability, Combinatorics+1
No attempts yet
Time limit
10s
Memory limit
1024 MB
Judgeable
Egor Has a Problem
Hard9
Array, Hash map+1
No attempts yet
Time limit
1s
Memory limit
1024 MB
Judgeable
Nerd Sniping
Hard9
Math, Number theory
No attempts yet
Time limit
1s
Memory limit
1024 MB
Judgeable
Overgrown-Puzzled
Hard9
Simulation, Implementation+1
No attempts yet
Time limit
3s
Memory limit
1024 MB
Judgeable
Colored Points
Hard9
Geometry, Graph+1
No attempts yet
Time limit
1s
Memory limit
1024 MB
Judgeable
Cell Automaton
Hard9
BFS, Math+1
No attempts yet
Time limit
6s
Memory limit
1024 MB
Judgeable
Mental Arithmetic
Hard9
Math, Number theory+1
No attempts yet
Time limit
4s
Memory limit
1024 MB
Judgeable
Conflict of Interest
Hard9
Combinatorics, Math
No attempts yet
Time limit
2s
Memory limit
1024 MB
Judgeable
Help Prapor
Hard9
Combinatorics, Math+1
No attempts yet
Time limit
1s
Memory limit
1024 MB
Judgeable
Decorating Junhyeok's Windows
Hard9
Math, Matrix+1
No attempts yet
Time limit
1s
Memory limit
1024 MB
Judgeable
Black and White
Hard9
Graph, Dynamic programming+2
No attempts yet
Time limit
5s
Memory limit
1024 MB
Judgeable
Random Tree
Hard9
Tree, Probability+1
No attempts yet
Time limit
2s
Memory limit
1024 MB
Judgeable
Card Game
Hard9
Math, Implementation+1
No attempts yet
Time limit
2s
Memory limit
1024 MB
Judgeable
In Search of the Unknown
Hard9
Graph, Combinatorics+1
No attempts yet
Time limit
2s
Memory limit
1024 MB
Judgeable
Fraction paradox
Hard9
Geometry, Greedy+2
No attempts yet
Time limit
1s
Memory limit
1024 MB
Judgeable
Very Strange String
Hard9
String matching, Math+1
No attempts yet
Time limit
2s
Memory limit
1024 MB
Judgeable
Triangular Number of a Polygon
Hard9
Math, Number theory+1
No attempts yet
Time limit
3s
Memory limit
1024 MB
Judgeable
Jenga
Hard9
Game theory, Dynamic programming+1
No attempts yet
Time limit
2s
Memory limit
1024 MB
Judgeable
Fibonacci Digit Count
Hard9
Math, Dynamic programming+2
No attempts yet
Time limit
2s
Memory limit
1024 MB
Judgeable
A Light Inconvenience
Hard9
Math, Implementation+1
No attempts yet
Time limit
1s
Memory limit
1024 MB
Judgeable
Segment Union
Hard9
Sorting, Dynamic programming+1
No attempts yet
Time limit
5s
Memory limit
1024 MB
Judgeable
Magical BF 4
Hard9
Implementation, Simulation+1
No attempts yet
Time limit
1s
Memory limit
1024 MB
Judgeable
N-Queen (Special)
Hard9
Math, Implementation
No attempts yet
Time limit
1s
Memory limit
512 MB
Judgeable
Magic
Hard9
Geometry, Divide and conquer+1
No attempts yet
Time limit
3s
Memory limit
1024 MB
Judgeable
Butterfly and Telephone Poles (Hard)
Hard9
Dynamic programming, Segment tree+1
No attempts yet
Time limit
4.5s
Memory limit
1024 MB
Judgeable
Osmanthus Tree
Hard9
Dynamic programming, Tree+1
No attempts yet
Time limit
0.5s
Memory limit
1024 MB
Judgeable
Why Hobanwoo Was Late for School 8
Hard9
Dynamic programming, Geometry+1
No attempts yet
Time limit
2s
Memory limit
1024 MB
Judgeable
Mike Sees The Storm (Large)
Hard9
Math, Combinatorics+1
No attempts yet
Time limit
1s
Memory limit
1024 MB
Judgeable
Impartial Strings
Hard9
String matching, Math
No attempts yet
Time limit
4s
Memory limit
1024 MB
Judgeable
Monkey and Bananas
Hard9
Geometry, Sorting+1
No attempts yet
Time limit
3s
Memory limit
1024 MB
Judgeable
Programmable Snake
Hard9
Math, Number theory+1
No attempts yet
Time limit
3s
Memory limit
1024 MB
Judgeable
Igor and the Toys
Hard9
Geometry, Divide and conquer+1
No attempts yet
Time limit
2.5s
Memory limit
1024 MB
Judgeable
Vault Heist 2
Hard9
Tree, Math+1
No attempts yet
Time limit
2s
Memory limit
1024 MB
Judgeable
Patrol Duty
Hard9
Graph, Implementation+1
No attempts yet
Time limit
3s
Memory limit
1024 MB
Judgeable
Multiplayer Game
Hard9
Array, Math+1
No attempts yet
Time limit
3s
Memory limit
1024 MB
Judgeable
Popcount Words
Hard9
String matching, Bit manipulation+1
No attempts yet
Time limit
1s
Memory limit
1024 MB
Judgeable
LIS Counting
Hard9
Dynamic programming, Combinatorics+2
No attempts yet
Time limit
2s
Memory limit
1024 MB
Judgeable
Paimon Segment Tree
Hard9
Segment tree, Prefix sum+1
No attempts yet
Time limit
2s
Memory limit
1024 MB
Judgeable
Paimon Polygon
Hard9
Geometry, Sorting+1
No attempts yet
Time limit
2s
Memory limit
1024 MB
Judgeable
Tree Embedding
Hard9
Tree, Divide and conquer+1
No attempts yet
Time limit
1s
Memory limit
1024 MB
Judgeable
Biology
Hard9
Geometry, Graph+1
No attempts yet
Time limit
1s
Memory limit
1024 MB
Judgeable
Land Sale
Hard9
Math, Number theory+1
No attempts yet
Time limit
5s
Memory limit
1024 MB
Judgeable
Sorted Fractal Sequence
Hard9
Dynamic programming, Combinatorics+1
No attempts yet
Time limit
1s
Memory limit
1024 MB
Judgeable
1D Stone Game 1
Hard9
Game theory, Math
No attempts yet
Time limit
1s
Memory limit
1024 MB
Judgeable
Minimum Spanning Tree Redrawing Game
Hard9
Minimum spanning tree, Combinatorics+2
No attempts yet
Time limit
2s
Memory limit
1024 MB
Judgeable
Good Luck in Your Service, Haneul
Hard9
Math, Combinatorics+1
No attempts yet
Time limit
0.5s
Memory limit
1024 MB
Judgeable
Bit Counting Sequence
Hard9
Bit manipulation, Math+1
No attempts yet
Time limit
2s
Memory limit
1024 MB
Judgeable
Highway Tolls
Hard9
Graph, Shortest path+1
No attempts yet
Time limit
4s
Memory limit
1024 MB
Judgeable
Lepeze
Hard9
Combinatorics, Tree+1
No attempts yet
Time limit
2s
Memory limit
1024 MB
Judgeable
Sandpile on Clique
Hard9
Math, Sorting+1
No attempts yet
Time limit
1s
Memory limit
1024 MB
Judgeable
Permutation Group
Hard9
Combinatorics, Math
No attempts yet
Time limit
15s
Memory limit
1024 MB
Judgeable
Interleaving Sequences
Hard9
Array, Two pointers+1
No attempts yet
Time limit
9s
Memory limit
1024 MB
Judgeable
Desant 3
Hard9
Bit manipulation, Combinatorics+1
No attempts yet
Time limit
4s
Memory limit
1024 MB
Judgeable
Schedule
Hard9
Combinatorics, Bit manipulation+1
No attempts yet
Time limit
2s
Memory limit
1024 MB
Judgeable
A Recurring Problem
Hard9
Math, Binary search+1
No attempts yet
Time limit
20s
Memory limit
1024 MB
Judgeable
A guide for Seongjae traveling the multiverse
Hard9
Math, Divide and conquer+1
No attempts yet
Time limit
3s
Memory limit
1024 MB
Judgeable
House Deconstruction
Hard9
Combinatorics, Greedy+1
No attempts yet
Time limit
1s
Memory limit
2048 MB
Judgeable

Title	Level	Topics	Solved	Time limit	Memory limit	Judge
Rotate Sum 3Given a convex polygon, find the volume swept when it is repeatedly rotated in 3D about its symmetry axes, which move with it.	Hard9	GeometryMath+1	No attempts yet	1s	1024 MB	Judgeable
Great PartyFor each query range [l, r], count the sub-segments whose stone piles give the first player a win in the merge-and-remove game.	Hard9	Game theoryBit manipulation+1	No attempts yet	1s	1024 MB	Judgeable
DS Team SelectionEach update adds a square pyramid of weights centered at (x, y), and each query asks for the weight sum over a rectangle modulo 2^30.	Hard9	Segment treeMath+1	No attempts yet	18s	1024 MB	Judgeable
GamesCount the labelings of a tree's vertices with values 0 to m that keep the uncolored vertices connected at every stage, after each single-label update.	Hard9	TreeDynamic programming+1	No attempts yet	4s	1024 MB	Judgeable
Half PlaneEach query sums the vectors of points strictly below the line ax+by=c, then multiplies those vectors by a 3x3 matrix in place.	Hard9	GeometrySegment tree+1	No attempts yet	12s	1024 MB	Judgeable
TreeFor each n up to N, count pairs of the two specified rooted trees whose leaf sets are complementary, modulo M.	Hard9	CombinatoricsDynamic programming+1	No attempts yet	3s	1024 MB	Judgeable
Infectious DiseaseFind the expected number of days until a random infection and vaccine-persuasion process ends in a city of n people, modulo 1e9+7.	Hard9	ProbabilityMath+1	No attempts yet	5s	1024 MB	Judgeable
DFSGiven a rooted tree with vertex values, sum the expected minimum value on the random DFS stack over all legal pairs (x, y), modulo 998244353.	Hard9	TreeUnion-find+2	No attempts yet	8s	1024 MB	Judgeable
Village PlanningFor each N from 2 to M, sum the product of A[f(i,j)] over all labeled simple graphs on N houses, where f counts simple paths and at most K are allowed.	Hard9	GraphCombinatorics+1	No attempts yet	3s	1024 MB	Judgeable
Drinking WaterGiven n distinct values and up to k averaging operations on chosen subsets, find the maximum value h_1 can reach, printed to p decimal digits.	Hard9	Binary searchGreedy+2	No attempts yet	2s	1024 MB	Judgeable
Battleship: New RulesOn an n by n board packed with ships, the second player must find any empty 2x2 square using at most 6n queries.	Hard9	ImplementationGreedy+1	No attempts yet	3s	1024 MB	Judgeable
Fun with StonesGiven three pile ranges, find the probability Alice wins Nim with random pile sizes, modulo 1e9+7.	Hard9	CombinatoricsBit manipulation+2	No attempts yet	1s	1024 MB	Judgeable
Park TrailsGiven axis-parallel trails and an evacuation point, add the least-length tunnels so every point can reach the point by a path whose distance keeps shrinking.	Hard9	GeometryGraph+1	No attempts yet	3s	1024 MB	Judgeable
TriangleRecover the three integer vertices of a hidden triangle by querying lines and receiving the fraction of area each line cuts off.	Hard9	GeometryBinary search+1	No attempts yet	1s	1024 MB	Judgeable
Roll CallGiven N and Q queries, find the lexicographically smallest valid order of 2N roll calls with type x at position y, and output the weighted sum of positions modulo 1e9+7.	Hard9	CombinatoricsMath+1	No attempts yet	1s	256 MB	Judgeable
ArbitrationCount the ways to assign votes from 1 to k to the n-1 horizontal and m-1 vertical judges so every cell's signed sum matches the target grid, modulo 10^9+7.	Hard9	Dynamic programmingCombinatorics+1	No attempts yet	10s	1024 MB	Judgeable
GameGiven n players with values a_i, find the winner of a sequential mod-n game after each of q updates that set one a_x to y.	Hard9	MathArray+1	No attempts yet	2s	1024 MB	Judgeable
Just Another EdgeGiven a planar simple graph, count the non-adjacent vertex pairs whose new edge keeps the graph tripartite.	Hard9	GraphBFS+1	No attempts yet	2s	1024 MB	Judgeable
Khalin GraphGiven a Halin graph through its base tree, count edge subsets where every connected component is a single vertex or a tree on 3 vertices, modulo 998244353.	Hard9	Dynamic programmingTree+2	No attempts yet	2s	1024 MB	Judgeable
Moving RandomlyFor each prefix, find the best expected score when a pointer starts at a random cell and may step left or right at random before stopping, modulo 998244353.	Hard9	ArrayGreedy+2	No attempts yet	2s	1024 MB	Judgeable
Sequence, Intervals, and QueriesGiven a sequence, each query asks for the truncated maximum average of a subarray that starts in [a, b] and ends in [c, d].	Hard9	Binary searchPrefix sum+2	No attempts yet	5s	1024 MB	Judgeable
PolygonsCount convex polygons on an X by Y lattice grid whose sides have no interior lattice points and integer length at most K, modulo 2^32.	Hard9	Number theoryGeometry+2	No attempts yet	10s	1024 MB	Judgeable
Landing RaidChoose k of n soldiers so the chosen subsequence of permutation a has the fewest inversions, then count the optimal choices for each k.	Hard9	Divide and conquerCombinatorics+1	No attempts yet	6s	1024 MB	Judgeable
Fibonacci ProductsGiven two positive integers in Zeckendorf form, print their product in the same Fibonacci representation. Total input length is up to 10^6 bits.	Hard9	Dynamic programmingString+1	No attempts yet	20s	1024 MB	Judgeable
IslandCount the subsets of sea-side settlements where ports can be built so that every lake-side settlement can reach at least one port, modulo 1e9+7.	Hard9	GraphCombinatorics+1	No attempts yet	6s	1024 MB	Judgeable
A very complicated testGiven two BSTs on keys 1 to n, find the fewest rotations that turn one into the other without dropping a subtree, modulo 1e9+7, or -1.	Hard9	TreeDFS+1	No attempts yet	3s	1024 MB	Judgeable
Independent SetsCount unlabeled c-colored trees whose maximum independent set size is between l and r, modulo 998244353.	Hard9	CombinatoricsTree+2	No attempts yet	45s	1024 MB	Judgeable
IQ GameGiven k remaining envelopes on a circle of n sectors, find the expected number of rounds until the Hyperblitz envelope is opened, modulo 998244353.	Hard9	ProbabilityCombinatorics+2	No attempts yet	2s	1024 MB	Judgeable
Indecisive NikolajEach starting cell of an N by M grid is a minimax game between alternating moves, and the task sums the resulting utilities over all cells modulo 998244353.	Hard9	Game theoryDynamic programming+2	No attempts yet	3s	1024 MB	Judgeable
Sequence and Queries 43Given a sequence, answer point queries and apply range operations: conditional subtraction, arithmetic-progression assignment, and integer square root.	Hard9	Segment treeMath+1	No attempts yet	5s	1024 MB	Judgeable
Sports DayGiven four teams of 15 soldiers with skills in three events, decide whether team A has a lineup that wins the overall title against every placement of the other teams.	Hard9	Game theoryDynamic programming+1	No attempts yet	1s	1024 MB	Judgeable
PicnicWizards on a round table write numbers over three rounds with limited visibility so that adjacent final numbers differ and stay below 40.	Hard9	Bit manipulationMath+1	No attempts yet	4s	1024 MB	Judgeable
Typing ContestGiven a 15-letter string and each contestant's press, left, and right costs, find the minimum typing time when the keys can be placed in any order on one row.	Hard9	Dynamic programmingBit manipulation+1	No attempts yet	2.5s	1024 MB	Judgeable
GCD and K-th QueryGiven a sequence of N positive integers, answer queries for the K-th smallest gcd over all subarrays inside a range [L, R].	Hard9	Binary searchNumber theory+1	No attempts yet	1s	1024 MB	Judgeable
Familiar CouplesAfter each of q merge events on men or women, count the couple pairs connected in both DSUs, and output the sum of i times that count modulo 1e9+7.	Hard9	Union-findTree+1	No attempts yet	15s	1024 MB	Judgeable
Festivals in JOI Kingdom 2Count the pairs of sequences a and b of N intervals using each value from 1 to 2N once, where greedy selection by start time is not optimal, modulo prime P.	Hard9	Dynamic programmingCombinatorics+1	No attempts yet	6s	1024 MB	Judgeable
LaLa and Magic Circle (LiLi Version)Output a simple polygon of at most 1000 segments that needs between 120000 and 1000000 path reflections to become convex.	Hard9	GeometrySimulation+1	No attempts yet	10s	1024 MB	Judgeable
LaLa and Magic Circle (LaLa Version)Repeatedly reflect non-convex chains of a simple polygon until it is convex, then print its vertices counterclockwise from the lexicographically smallest one.	Hard9	GeometryImplementation	No attempts yet	2s	1024 MB	Judgeable
LaLa and Monster Hunting (Part 2)Count the subgraphs of a graph with up to 100,000 vertices and edges that are isomorphic to a fixed 6-vertex graph, modulo 998244353.	Hard9	GraphCombinatorics+1	No attempts yet	6s	1024 MB	Judgeable
The Answer to the Ultimate Question of Life, the Universe, and EverythingGiven n, k, and the leading digit x of 2^n, count the powers of 2 up to 2^n whose leading digit is 4.	Hard9	MathNumber theory	No attempts yet	0.42s	420 MB	Judgeable
Who Watches the Watchmen?Reposition sentries so each one watches a different sentry and is watched by exactly one other, minimizing energy (1 per rotation, 1000 per move).	Hard9	GeometryGraph+1	No attempts yet	4s	2048 MB	Judgeable
Range Closest Pair of Points QueryGiven n points and q index ranges [l, r], find the squared distance of the closest pair of points inside each range.	Hard9	Divide and conquerGeometry+1	No attempts yet	9s	1024 MB	Judgeable
Forever YoungCount the ways to turn non-increasing array A into B in exactly k unit steps, where every intermediate array must also stay non-increasing.	Hard9	Dynamic programmingCombinatorics+1	No attempts yet	2s	1024 MB	Judgeable
Endless RoadThree chips start at a, b, c, and a random chip steps right each second. For each t up to n, print the expected maximum position modulo 998244353.	Hard9	ProbabilityCombinatorics+1	No attempts yet	10s	1024 MB	Judgeable
Egor Has a ProblemGiven a sorted array of distinct positive integers up to 1e18, find indices i<j<p<q with a_i * a_q = a_j * a_p, or report NO.	Hard9	ArrayHash map+1	No attempts yet	1s	1024 MB	Judgeable
Nerd SnipingGiven integer point (x,y) on an infinite grid of 1-ohm resistors, output the modular parts of the equivalent resistance from the origin to that point.	Hard9	MathNumber theory	No attempts yet	1s	1024 MB	Judgeable
Overgrown-PuzzledFind the starting cell on a ring of N cells with unknown icing types, using at most M moves and only a same-cell check after each move.	Hard9	SimulationImplementation+1	No attempts yet	3s	1024 MB	Judgeable
Colored PointsGiven n points and t, classify each point as G, B, or R by whether the angular t-th successor process starts from it infinitely often, at least once, or never.	Hard9	GeometryGraph+1	No attempts yet	1s	1024 MB	Judgeable
Cell AutomatonBlack cells spread to adjacent white cells, then fade to gray and white over time. For each query time T, report how many cells are black.	Hard9	BFSMath+1	No attempts yet	6s	1024 MB	Judgeable
Mental ArithmeticGiven a sum-product expression and its claimed value modulo 10^9+7, find at most two changed digits that make it correct, or report NO.	Hard9	MathNumber theory+1	No attempts yet	4s	1024 MB	Judgeable
Conflict of InterestCount ordered pairs of non-overlapping sub-rectangles in an H by W grid, each at most h tall and w wide, modulo 10^9+7.	Hard9	CombinatoricsMath	No attempts yet	2s	1024 MB	Judgeable
Help PraporGiven an odd-length array of distinct integers, sum the maximum-weight perfect matching cost over all permutations, modulo 998244353.	Hard9	CombinatoricsMath+1	No attempts yet	1s	1024 MB	Judgeable
Decorating Junhyeok's WindowsCount the ways to pick a worker for each day so that N windows, each a tensor product of M vectors, end at the given light levels up to sign.	Hard9	MathMatrix+1	No attempts yet	1s	1024 MB	Judgeable
Black and WhiteCount the spanning trees of a wheel-shaped graph for each k, where k is the number of trees' roads controlled by the White gang.	Hard9	GraphDynamic programming+2	No attempts yet	5s	1024 MB	Judgeable
Random TreeFor each prefix of a randomly grown tree, print the sum over all vertex subsets A of the number of vertices in the minimal subtree connecting A, modulo 998244353.	Hard9	TreeProbability+1	No attempts yet	2s	1024 MB	Judgeable
Card GameSplit a shuffled deck of n cards, k of them face down, into two piles with equal face-down counts using Reverse, Move, and Up actions.	Hard9	MathImplementation+1	No attempts yet	2s	1024 MB	Judgeable
In Search of the UnknownCount the routes that visit every house exactly once in an undirected street graph with up to 1000 houses, and print the count modulo 2.	Hard9	GraphCombinatorics+1	No attempts yet	2s	1024 MB	Judgeable
Fraction paradoxGiven k irreducible fractions, pick four distinct ones forming two pairs with a at most b and c at most d, maximizing (a+c)/(b+d) minus (...) of the other pair.	Hard9	GeometryGreedy+2	No attempts yet	1s	1024 MB	Judgeable
Very Strange StringGiven k and m, the task is to build a lowercase string of length at most m whose strangeness (the sum of G_i times F_i) equals k.	Hard9	String matchingMath+1	No attempts yet	2s	1024 MB	Judgeable
Triangular Number of a PolygonGiven a regular n-gon with vertices colored W or B, print the count of same-colored isosceles triangles after each of m single-vertex color flips.	Hard9	MathNumber theory+1	No attempts yet	3s	1024 MB	Judgeable
JengaTwo players take turns moving blocks in a Jenga tower, and whoever leaves an unstable layer below the top one loses. The task asks who wins with optimal play.	Hard9	Game theoryDynamic programming+1	No attempts yet	2s	1024 MB	Judgeable
Fibonacci Digit CountCount occurrences of the substring "11" within the first N characters of the infinite string formed by writing 1, 2, 3, ... in Fibonacci (Zeckendorf) representation.	Hard9	MathDynamic programming+2	No attempts yet	2s	1024 MB	Judgeable
A Light InconveniencePerformers join or leave a line over Q acts, and you must pick a fire-spread value t_a up to 5p_a while keeping the lit torches at 150 or fewer.	Hard9	MathImplementation+1	No attempts yet	1s	1024 MB	Judgeable
Segment UnionGiven centers x_i and radii a_i, sum the union length of the intervals [x_i - r, x_i + r] over all ways to assign the radii to the centers, modulo 1e9+7.	Hard9	SortingDynamic programming+1	No attempts yet	5s	1024 MB	Judgeable
Magical BF 4Write an N by N grid of BF code that computes F_k into cell M0 whether the grid is read by rows or by columns, for k from 3 to 10.	Hard9	ImplementationSimulation+1	No attempts yet	1s	1024 MB	Judgeable
N-Queen (Special)Given an N x N board with Q queens already fixed, place the remaining queens so that no two attack each other, or print -1 if that is impossible.	Hard9	MathImplementation	No attempts yet	1s	512 MB	Judgeable
MagicEach round deletes some points (indices decoded from the previous answer). Print twice the convex hull area of the remaining points each round.	Hard9	GeometryDivide and conquer+1	No attempts yet	3s	1024 MB	Judgeable
Butterfly and Telephone Poles (Hard)Pole heights change over time. For each query at start pole p, find the valid wire chain with the largest total length and print its squared cost.	Hard9	Dynamic programmingSegment tree+1	No attempts yet	4.5s	1024 MB	Judgeable
Osmanthus TreeCount trees on n+m vertices that keep the LCAs of the given tree T on vertices 1 to n and keep each pairwise LCA label within max(i, j) + k, modulo 1e9+7.	Hard9	Dynamic programmingTree+1	No attempts yet	0.5s	1024 MB	Judgeable
Why Hobanwoo Was Late for School 8Find the minimum total time to reach planet N from the origin, where a move to planet e costs a_e if the start lies on the hull of planets 0 to e, otherwise b_e.	Hard9	Dynamic programmingGeometry+1	No attempts yet	2s	1024 MB	Judgeable
Mike Sees The Storm (Large)Sum the K-th power of the maximum prefix value over all balanced +1/-1 walks of length 2N from 0, modulo 1e9+7.	Hard9	MathCombinatorics+1	No attempts yet	1s	1024 MB	Judgeable
Impartial StringsFor each case, decide whether a finite automaton can generate exactly the strings where S and T occur equally often as substrings.	Hard9	String matchingMath	No attempts yet	4s	1024 MB	Judgeable
Monkey and BananasGiven n rotating triangles with a marked winning vertex each, find the largest number of winning vertices that can be lowest at the same rotation angle.	Hard9	GeometrySorting+1	No attempts yet	3s	1024 MB	Judgeable
Programmable SnakeFind the longest snake that can be placed on an H by W torus and keep moving forever under a repeating K-command program without hitting itself.	Hard9	MathNumber theory+1	No attempts yet	3s	1024 MB	Judgeable
Igor and the ToysGiven N convex polygons resting on the x-axis, answer Q queries: for two toys, find the minimum width of the box after pushing them together side by side in either order.	Hard9	GeometryDivide and conquer+1	No attempts yet	2.5s	1024 MB	Judgeable
Vault Heist 2Jeonghu builds a tree of at most 100 vertices, each with at most 3 edges, that encodes a number up to 10^18 so Yeongu can recover it after one edge is cut.	Hard9	TreeMath+1	No attempts yet	2s	1024 MB	Judgeable
Patrol DutyFind a walk on a hexagonal grid of cells that visits every cell exactly once in each period of K steps, starting from a given cell.	Hard9	GraphImplementation+1	No attempts yet	3s	1024 MB	Judgeable
Multiplayer GameBrue submits a permutation of length N so that Mingyu can recover a bit string of length L from its pivot-partitioned shuffle.	Hard9	ArrayMath+1	No attempts yet	3s	1024 MB	Judgeable
Popcount WordsEach interval contributes the parity of popcount over its range, the parts are concatenated, and each query counts how often its 0/1 pattern appears in the result.	Hard9	String matchingBit manipulation+1	No attempts yet	1s	1024 MB	Judgeable
LIS CountingGiven N, M, and a prime P, count permutations of length N*M with LIS N and LDS M, broken down by the value at each position, modulo P.	Hard9	Dynamic programmingCombinatorics+2	No attempts yet	2s	1024 MB	Judgeable
Paimon Segment TreeGiven an array changed by m range additions, answer q queries for the sum of squared values over an index range and a version range, modulo 1e9+7.	Hard9	Segment treePrefix sum+1	No attempts yet	2s	1024 MB	Judgeable
Paimon PolygonSplit the points besides O into two groups, each forming a strict convex polygon with O whose edges meet only at O, and maximize the total perimeter.	Hard9	GeometrySorting+1	No attempts yet	2s	1024 MB	Judgeable
Tree EmbeddingGiven a weighted tree, assign each vertex a vector of at most 16 integers so the max coordinate gap between two vectors equals their tree distance.	Hard9	TreeDivide and conquer+1	No attempts yet	1s	1024 MB	Judgeable
BiologyConstruct 16 points and a planar straight-line graph on them with more than 300000 simple polygons formed by its edges.	Hard9	GeometryGraph+1	No attempts yet	1s	1024 MB	Judgeable
Land SaleEach grid cell is (pi+q) added to (rj+s) without carry in base B, and each query asks for the carry-free sum of all cells in its rectangle, written in base B.	Hard9	MathNumber theory+1	No attempts yet	5s	1024 MB	Judgeable
Sorted Fractal SequenceCount non-decreasing sequences of length N where a[a[i]] equals a[i] for every i, with K fixed entries, modulo M.	Hard9	Dynamic programmingCombinatorics+1	No attempts yet	1s	1024 MB	Judgeable
1D Stone Game 1Given n stones in a row, two players alternately take runs of stones whose length is one more than the opponent's last take, with discarding rules; output who wins for each n.	Hard9	Game theoryMath	No attempts yet	1s	1024 MB	Judgeable
Minimum Spanning Tree Redrawing GameGiven a connected weighted graph, find the expected number of MSTs that can be redrawn after each weight class is randomly erased with probability 1/x.	Hard9	Minimum spanning treeCombinatorics+2	No attempts yet	2s	1024 MB	Judgeable
Good Luck in Your Service, HaneulCount the length-K sequences of member assignments that return all N bulbs to off, where each member's switches act as a fixed vector over the three bulb states.	Hard9	MathCombinatorics+1	No attempts yet	0.5s	1024 MB	Judgeable
Bit Counting SequenceGiven a sequence a of n values, find the smallest x >= 0 whose popcounts for x, x+1, ..., x+n-1 match a, or report -1 if none exists.	Hard9	Bit manipulationMath+1	No attempts yet	2s	1024 MB	Judgeable
Highway TollsFind the minimum total toll from city 1 to city N on one-way highways, where each toll adds K times the absolute value of the departure time.	Hard9	GraphShortest path+1	No attempts yet	4s	1024 MB	Judgeable
LepezeUnder flip operations on a polygon triangulation, report the fewest flips needed to reach the fan at vertex x and how many shortest flip sequences exist.	Hard9	CombinatoricsTree+1	No attempts yet	2s	1024 MB	Judgeable
Sandpile on CliqueGiven a clique with chip counts on each vertex, determine whether toppling never stops; if it stops, output the final chip count of every vertex.	Hard9	MathSorting+1	No attempts yet	1s	1024 MB	Judgeable
Permutation GroupGiven k permutations, find the average number of inversions over all permutations in the group they generate, modulo 1e9+7.	Hard9	CombinatoricsMath	No attempts yet	15s	1024 MB	Judgeable
Interleaving SequencesGiven sequences A and B, count for each x the pairs of intervals A' and B' whose minimum interleaving stability equals x.	Hard9	ArrayTwo pointers+1	No attempts yet	9s	1024 MB	Judgeable
Desant 3For each k, count the initial ready/unready rows with k ready soldiers that end with all ready soldiers contiguous after the conditional swaps, modulo 2.	Hard9	Bit manipulationCombinatorics+1	No attempts yet	4s	1024 MB	Judgeable
ScheduleSchedule one member per team each week so every pair of people from different teams meets, minimizing the longest gap between their meetings.	Hard9	CombinatoricsBit manipulation+1	No attempts yet	2s	1024 MB	Judgeable
A Recurring ProblemGiven n, find the n-th positive linear recurrence by generated terms (ties by coefficients) and print its coefficients, start values, and next 10 terms.	Hard9	MathBinary search+1	No attempts yet	20s	1024 MB	Judgeable
A guide for Seongjae traveling the multiverseGiven N points and a disk of radius R, find the mean over the disk of the product of squared distances from a random point to all N points, modulo 998244353.	Hard9	MathDivide and conquer+1	No attempts yet	3s	1024 MB	Judgeable
House DeconstructionGiven people and houses on a circle, find the minimum total walking distance after destroying some houses, and count the sets of destroyed houses that reach it.	Hard9	CombinatoricsGreedy+1	No attempts yet	1s	2048 MB	Judgeable