Math and counting

Number theory, combinatorics, and geometry

Under construction

Still being built. Things may change

Total results13,153 problems

Prime Tree - 6
Hard9
Graph, Greedy+2
No attempts yet
Time limit
10s
Memory limit
512 MB
Judgeable
Prime Tree - 7
Hard9
Greedy, Number theory+2
No attempts yet
Time limit
10s
Memory limit
512 MB
Judgeable
Prime Tree - 9
Hard9
Graph, Greedy+2
No attempts yet
Time limit
10s
Memory limit
512 MB
Judgeable
Prime Tree - 10
Hard9
Number theory, Greedy+2
No attempts yet
Time limit
10s
Memory limit
512 MB
Judgeable
Game
Hard9
Dynamic programming, Stack+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Crypto
Hard9
Combinatorics, Number theory+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Odd Colouring
Hard9
Math, Combinatorics+2
No attempts yet
Time limit
1s
Memory limit
256 MB
Judgeable
Awesome Numbers
Hard9
Number theory, Math
No attempts yet
Time limit
0.5s
Memory limit
512 MB
Judgeable
Decorator Cubelover
Hard9
Combinatorics, Math+2
No attempts yet
Time limit
1s
Memory limit
512 MB
Judgeable
SquareFree
Hard9
Math, Number theory+2
No attempts yet
Time limit
5s
Memory limit
512 MB
Judgeable
Forgotten Land
Hard9
Dynamic programming, Tree+2
No attempts yet
Time limit
3s
Memory limit
512 MB
Judgeable
Halves Not Equal
Hard9
Math, Greedy+1
No attempts yet
Time limit
3s
Memory limit
512 MB
Judgeable
Interval-Free Permutations
Hard9
Combinatorics, Dynamic programming+1
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Congruence Equation
Hard9
Number theory, Math+1
No attempts yet
Time limit
1s
Memory limit
256 MB
Judgeable
Youngkwail Club Room
Hard9
Graph, DFS+2
No attempts yet
Time limit
1s
Memory limit
256 MB
Judgeable
Removing Magical Tiles
Hard9
Greedy, Geometry+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Black Company
Hard9
Graph, Topological sort+2
No attempts yet
Time limit
5s
Memory limit
512 MB
Judgeable
Magic Triangles
Hard9
Geometry, Divide and conquer+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Snake
Hard9
Geometry, Binary search
No attempts yet
Time limit
1s
Memory limit
512 MB
Judgeable
Rook, Bishop, King, Knight, and Palace Game
Hard9
Game theory, Math+1
No attempts yet
Time limit
0.5s
Memory limit
512 MB
Judgeable
Nim Game Without Repeats
Hard9
Game theory, Dynamic programming+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Quarry Game
Hard9
Game theory, Math+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
XOR Sequences
Hard9
Bit manipulation, Divide and conquer+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Moorio Kart
Hard9
Tree, Dynamic programming+2
No attempts yet
Time limit
3s
Memory limit
512 MB
Judgeable
Mowing Mischief
Hard9
Dynamic programming, Sorting+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Message
Hard9
Dynamic programming, String matching+2
No attempts yet
Time limit
5s
Memory limit
512 MB
Judgeable
Sweet and Sour
Hard9
Probability, Combinatorics+2
No attempts yet
Time limit
1s
Memory limit
512 MB
Judgeable
Sum of Equivalent Resistances Between Every Pair of Vertices Joined by an Edge, Given a Connected Graph with Unit Resistance Edges
Hard9
Graph, Matrix+2
No attempts yet
Time limit
1s
Memory limit
512 MB
Judgeable
Africa 2
Hard9
Implementation, Brute force+2
No attempts yet
Time limit
1.357s
Memory limit
1357 MB
Judgeable
Directing Rainfall
Hard9
Geometry, Graph+2
No attempts yet
Time limit
15s
Memory limit
512 MB
Judgeable
Dijkstra Is Playing At My House
Hard9
Shortest path, Segment tree+2
No attempts yet
Time limit
3s
Memory limit
1024 MB
Judgeable
Overflowing Uncertainty
Hard9
Number theory, Dynamic programming+2
No attempts yet
Time limit
1s
Memory limit
256 MB
Judgeable
Numbers in a Grid
Hard9
Matrix, Prefix sum+2
No attempts yet
Time limit
3s
Memory limit
1024 MB
Judgeable
The Tallest and Widest Castle
Hard9
Geometry, Dynamic programming+2
No attempts yet
Time limit
1s
Memory limit
512 MB
Judgeable
Looks like a sum of GCDs of Fibonacci numbers, but...
Hard9
Number theory, Math
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Gyojun's Errand Boy, Minje's Trouble ("Circle" Ver.)
Hard9
Tree, Divide and conquer+2
No attempts yet
Time limit
4s
Memory limit
1024 MB
Judgeable
Calculator
Hard9
Binary search, Math+2
No attempts yet
Time limit
1s
Memory limit
256 MB
Judgeable
Gosu 2
Hard9
Divide and conquer, Combinatorics+2
No attempts yet
Time limit
2s
Memory limit
1024 MB
Judgeable
Addition on Convex Polygons
Hard9
Geometry, Number theory+1
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Traveling Merchant
Hard9
Segment tree, Divide and conquer+2
No attempts yet
Time limit
10s
Memory limit
1024 MB
Judgeable
Hanging Rack
Hard9
Math, Recursion+2
No attempts yet
Time limit
1s
Memory limit
512 MB
Judgeable
Ruler
Hard9
Backtracking, Brute force+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Asceticism
Hard9
Dynamic programming, Combinatorics+2
No attempts yet
Time limit
0.6s
Memory limit
256 MB
Judgeable
Airline Route Map
Hard9
Graph, Implementation+1
No attempts yet
Time limit
2s
Memory limit
1024 MB
Judgeable
Long Distance Coach
Hard9
Greedy, Sorting+1
No attempts yet
Time limit
2s
Memory limit
256 MB
Judgeable
Toilets
Hard9
Binary search, Greedy+1
No attempts yet
Time limit
1s
Memory limit
512 MB
Judgeable
Construction Project
Hard9
Minimum spanning tree, Geometry+2
No attempts yet
Time limit
5s
Memory limit
256 MB
Judgeable
Messenger
Hard9
Implementation, Simulation+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Constellation
Hard9
Geometry, Combinatorics+2
No attempts yet
Time limit
1s
Memory limit
512 MB
Judgeable
Graph and Cycles
Hard9
Graph, Greedy+2
No attempts yet
Time limit
2s
Memory limit
256 MB
Judgeable
Quadrilaterals
Hard9
Geometry, Sorting+1
No attempts yet
Time limit
1.7s
Memory limit
512 MB
Judgeable
Ghost
Hard9
Geometry, Sorting+1
No attempts yet
Time limit
10s
Memory limit
512 MB
Judgeable
Nearest Points
Hard9
Geometry, Divide and conquer+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Mining a
Hard9
Math, Bit manipulation+2
No attempts yet
Time limit
2s
Memory limit
1024 MB
Judgeable
DivModulo
Hard9
Math, Number theory+2
No attempts yet
Time limit
3s
Memory limit
1024 MB
Judgeable
Be Geeks!
Hard9
Math, Number theory+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Dance Circle
Hard9
Math, Prefix sum+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Tree Depth
Hard9
Dynamic programming, Combinatorics+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Chessboard Movement
Hard9
Dynamic programming, Matrix+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Gnalcats
Hard9
String, Stack+2
No attempts yet
Time limit
0.3s
Memory limit
512 MB
Judgeable
Pilgrim's Memories and the Impressed God
Hard9
Dynamic programming, String+1
No attempts yet
Time limit
8s
Memory limit
1024 MB
Judgeable
Sorcerers of the Round Table
Hard9
Dynamic programming, Bit manipulation+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Speed Reading Course
Hard9
Number theory, String matching+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Graph Counting
Hard9
Combinatorics, Graph+2
No attempts yet
Time limit
5s
Memory limit
512 MB
Judgeable
Interesting Graph
Hard9
Graph, Dynamic programming+1
No attempts yet
Time limit
5s
Memory limit
512 MB
Judgeable
Knowledge
Hard9
String, Combinatorics+2
No attempts yet
Time limit
1s
Memory limit
512 MB
Judgeable
Airplane Cliques
Hard9
Tree, Divide and conquer+1
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
One Goal
Hard9
Combinatorics, Tree+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Bitwise Xor
Hard9
Bit manipulation, Trie+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Easy Win
Hard9
Game theory, Union-find+2
No attempts yet
Time limit
1.5s
Memory limit
512 MB
Judgeable
Four Elements
Hard9
Math, Combinatorics+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Um_nik's Algorithm
Hard9
Graph, Greedy+2
No attempts yet
Time limit
4s
Memory limit
512 MB
Judgeable
FFT Algorithm
Hard9
Number theory, Math+2
No attempts yet
Time limit
1.5s
Memory limit
512 MB
Judgeable
One Root
Hard9
Math, Number theory+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Another Coin Weighing Puzzle
Hard9
Combinatorics, Math+2
No attempts yet
Time limit
1s
Memory limit
512 MB
Judgeable
Counting Edit Distances
Hard9
Dynamic programming, String+2
No attempts yet
Time limit
10s
Memory limit
512 MB
Judgeable
Rooted Subtrees
Hard9
Tree, DFS+2
No attempts yet
Time limit
11s
Memory limit
512 MB
Judgeable
Basis Change
Hard9
Math, Implementation+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Nightmare
Hard9
Geometry, Sorting+1
No attempts yet
Time limit
1s
Memory limit
512 MB
Judgeable
Employees
Hard9
Dynamic programming, Combinatorics+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Modulo-magic squares
Hard9
Math, Combinatorics+2
No attempts yet
Time limit
1s
Memory limit
512 MB
Judgeable
Call It What You Want
Hard9
Number theory, Math+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Kaleidoscope
Hard9
Combinatorics, Math+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Expected Cost
Hard9
Combinatorics, Tree+2
No attempts yet
Time limit
3s
Memory limit
512 MB
Judgeable
Humongous String
Hard9
String, Math+1
No attempts yet
Time limit
1s
Memory limit
512 MB
Judgeable
Long Game
Hard9
Game theory, Greedy+2
No attempts yet
Time limit
1s
Memory limit
512 MB
Judgeable
Milk Candy
Hard9
Matrix, Combinatorics+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Faraway
Hard9
Math, Number theory+2
No attempts yet
Time limit
1s
Memory limit
512 MB
Judgeable
TDL
Hard9
Number theory, Bit manipulation+2
No attempts yet
Time limit
1s
Memory limit
512 MB
Judgeable
Line Graphs
Hard9
Graph, Combinatorics+1
No attempts yet
Time limit
5s
Memory limit
512 MB
Judgeable
Domino Covering
Hard9
Matrix, Dynamic programming+2
No attempts yet
Time limit
6s
Memory limit
512 MB
Judgeable
Yet Another Convolution
Hard9
Number theory, Math+1
No attempts yet
Time limit
4s
Memory limit
512 MB
Judgeable
Magic Strings
Hard9
Dynamic programming, Matrix+2
No attempts yet
Time limit
4s
Memory limit
512 MB
Judgeable
Decimal Expansion
Hard9
Math, Number theory+2
No attempts yet
Time limit
1s
Memory limit
512 MB
Judgeable
Eevee
Hard9
Combinatorics, Probability+2
No attempts yet
Time limit
5s
Memory limit
512 MB
Judgeable
Hypno
Hard9
Graph, Shortest path+1
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Lati@s
Hard9
Game theory, Combinatorics+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Somewhere Over the Rainbow
Hard9
Dynamic programming, Math+1
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Linear Congruential Generator
Hard9
Math, Number theory+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Count the Graphs
Hard9
Combinatorics, Dynamic programming+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable

Title	Level	Topics	Solved	Time limit	Memory limit	Judge
Prime Tree - 6Assign labels 1 to n to tree vertices so that edges joining two numbers with a shared factor are as few as possible.	Hard9	GraphGreedy+2	No attempts yet	10s	512 MB	Judgeable
Prime Tree - 7Relabel the vertices of each given tree with 1..n so that the number of edges whose endpoints share a common divisor above 1 is minimized, and submit the answer file.	Hard9	GreedyNumber theory+2	No attempts yet	10s	512 MB	Judgeable
Prime Tree - 9Relabel the vertices of given trees so that the number of edges whose endpoints share a common divisor greater than 1 is as small as possible.	Hard9	GraphGreedy+2	No attempts yet	10s	512 MB	Judgeable
Prime Tree - 10Relabel the vertices of a given tree with 1..n so that as few edges as possible join two labels sharing a common divisor; this is an output-only optimization task.	Hard9	Number theoryGreedy+2	No attempts yet	10s	512 MB	Judgeable
GameChoose the order in which balls are manually removed so chain reactions of merging equal neighbors delete as many other balls as possible; output that maximum count.	Hard9	Dynamic programmingStack+2	No attempts yet	2s	512 MB	Judgeable
CryptoCount permutations of 1..N whose window-product multiset, taken as the K smallest primes, has exactly P distinct values, modulo 1e9+7.	Hard9	CombinatoricsNumber theory+2	No attempts yet	2s	512 MB	Judgeable
Odd ColouringCount black/white ball colorings under cycle-index and Hadamard identities with large R, C, N, returning the count modulo 998244353.	Hard9	MathCombinatorics+2	No attempts yet	1s	256 MB	Judgeable
Awesome NumbersDecide whether n is reachable from 1 by repeatedly applying P (nth prime) or S (nth perfect square), and print the shortest such sequence.	Hard9	Number theoryMath	No attempts yet	0.5s	512 MB	Judgeable
Decorator CubeloverArrange n decorations on an n^3-cycle so each window of three labels is unique and the positional-value sum is minimal; report the nth digit of p-1.	Hard9	CombinatoricsMath+2	No attempts yet	1s	512 MB	Judgeable
SquareFreeGiven n up to 10^18, find the n-th squarefree positive integer using Mobius inversion and binary search.	Hard9	MathNumber theory+2	No attempts yet	5s	512 MB	Judgeable
Forgotten LandSum over all partitions of a tree's vertices into arbitrary sets of the total language difficulty, where a set's difficulty depends on the union of languages on its vertices and on paths between them.	Hard9	Dynamic programmingTree+2	No attempts yet	3s	512 MB	Judgeable
Halves Not EqualDivide s dinars among n wives so that every pair's shares match the given two-person fair split rule and the total equals s.	Hard9	MathGreedy+1	No attempts yet	3s	512 MB	Judgeable
Interval-Free PermutationsCount permutations of length n with no contiguous block of length 2 to n-1 whose values form consecutive integers, modulo a prime p.	Hard9	CombinatoricsDynamic programming+1	No attempts yet	2s	512 MB	Judgeable
Congruence EquationCount ordered pairs (a, b) within 1 to p(p-1) whose residues satisfy a^b = b^a mod p, reducing to counting solutions of a discrete-log exponential congruence.	Hard9	Number theoryMath+1	No attempts yet	1s	256 MB	Judgeable
Youngkwail Club RoomCover all '.' cells of a grid with 1x1 and 1x2 tiles, avoiding 'X' pillars, using the fewest tiles possible.	Hard9	GraphDFS+2	No attempts yet	1s	256 MB	Judgeable
Removing Magical TilesGiven trapezoid tiles above the x-axis, find the minimum number of groups where each group is a set of tiles that pairwise overlap.	Hard9	GreedyGeometry+2	No attempts yet	2s	512 MB	Judgeable
Black CompanyAssign positive salaries minimizing their sum so that every edge and every two edges sharing an endpoint order their endpoints consistently with contribution degrees.	Hard9	GraphTopological sort+2	No attempts yet	5s	512 MB	Judgeable
Magic TrianglesGiven up to 100000 counter-clockwise triangles, compute the area of their common intersection.	Hard9	GeometryDivide and conquer+2	No attempts yet	2s	512 MB	Judgeable
SnakeGiven a polyline above the wall y = 0, decide whether rigid translations and rotations can move the whole snake entirely below the wall through the hole at the origin.	Hard9	GeometryBinary search	No attempts yet	1s	512 MB	Judgeable
Rook, Bishop, King, Knight, and Palace GameTwo players take turns moving chess pieces toward the lower left on a huge board, and the task is to find who wins with optimal play.	Hard9	Game theoryMath+1	No attempts yet	0.5s	512 MB	Judgeable
Nim Game Without RepeatsNim with piles of size up to 60, but each specific removal size can be used at most once per pile; decide the winner under optimal play.	Hard9	Game theoryDynamic programming+2	No attempts yet	2s	512 MB	Judgeable
Quarry GameEach of N piles is a run of M consecutive pile sizes starting at X; a move takes at least one stone from one pile. Decide the winner under optimal play.	Hard9	Game theoryMath+2	No attempts yet	2s	512 MB	Judgeable
XOR SequencesCount, modulo 1e9+7, the ordered sequences of n distinct m-bit integers consistent with a given nearest-XOR-label map over all 2^m query values.	Hard9	Bit manipulationDivide and conquer+2	No attempts yet	2s	512 MB	Judgeable
Moorio KartCount and sum the lengths of simple cycles (at least Y) formed by joining every tree in a forest with one X-length edge between consecutive trees and a chosen path inside each tree.	Hard9	TreeDynamic programming+2	No attempts yet	3s	512 MB	Judgeable
Mowing MischiefGiven flowers on a grid, pick a longest chain of flowers both paths must visit, then find the minimum area the two monotone paths can sweep.	Hard9	Dynamic programmingSorting+2	No attempts yet	2s	512 MB	Judgeable
MessageCount length-n lowercase strings that contain a given pattern p as a substring, modulo m, where n can reach 10^12 and p has length at most 50.	Hard9	Dynamic programmingString matching+2	No attempts yet	5s	512 MB	Judgeable
Sweet and SourChoose which Candy Country players drink a potion that randomizes their sweetness and sourness, maximizing Candy's expected match points under all random player orders and event coin flips.	Hard9	ProbabilityCombinatorics+2	No attempts yet	1s	512 MB	Judgeable
Sum of Equivalent Resistances Between Every Pair of Vertices Joined by an Edge, Given a Connected Graph with Unit Resistance EdgesGiven a connected unit-resistance graph, compute the sum of effective resistances over all m edges, using the fact that each equals the probability a random walk crosses that edge in the commute.	Hard9	GraphMatrix+2	No attempts yet	1s	512 MB	Judgeable
Africa 2Submit code that matches the judge on exactly half its hidden test cases while passing the sample, a problem about exploiting judge behavior rather than a computable answer.	Hard9	ImplementationBrute force+2	No attempts yet	1.357s	1357 MB	Judgeable
Directing RainfallGiven slanted tarps above a vineyard interval, find the fewest tarps to puncture so that rain falling from directly above the vineyard reaches the ground.	Hard9	GeometryGraph+2	No attempts yet	15s	512 MB	Judgeable
Dijkstra Is Playing At My HouseFind the shortest Manhattan path from start to house around up to 250,000 non-overlapping axis-parallel rectangles, without entering any rectangle interior.	Hard9	Shortest pathSegment tree+2	No attempts yet	3s	1024 MB	Judgeable
Overflowing UncertaintyFor each interval [i,j] compute the probability that the gcd of j-i+1 independent uniform values in [1,Y] is coprime with Y, sum over all intervals, and report the numerator modulo 1e9+9 with denominator Y^N.	Hard9	Number theoryDynamic programming+2	No attempts yet	1s	256 MB	Judgeable
Numbers in a GridDigits of 1, 2, 3, ... concatenated are written row by row into a grid M wide, and each query asks for the digit sum over a rectangle.	Hard9	MatrixPrefix sum+2	No attempts yet	3s	1024 MB	Judgeable
The Tallest and Widest CastleChoose which signposts serve as vertices of each floor so the castle has the most floors, then the largest total floor area, then the fewest signposts used, and report each signpost's floor number.	Hard9	GeometryDynamic programming+2	No attempts yet	1s	512 MB	Judgeable
Looks like a sum of GCDs of Fibonacci numbers, but...Given n and k, compute the sum over all pairs (i, j) with 1 to n of gcd(i, j) to the power k times gcd(F_i, F_j), modulo 1,000,000,007.	Hard9	Number theoryMath	No attempts yet	2s	512 MB	Judgeable
Gyojun's Errand Boy, Minje's Trouble ("Circle" Ver.)Given disjoint circles and houses with XOR values, each query asks for the XOR of house values within crossing distance L of a point.	Hard9	TreeDivide and conquer+2	No attempts yet	4s	1024 MB	Judgeable
CalculatorStarting from X=0, reach a given N by pressing +2, -2, *2, /2 (floor) at most 99 times while X stays in [0, 2^63-1], or report that it is impossible.	Hard9	Binary searchMath+2	No attempts yet	1s	256 MB	Judgeable
Gosu 2Given a tournament on N players, find a transitive subtournament (chain) of size exactly 1 + floor(log2 N).	Hard9	Divide and conquerCombinatorics+2	No attempts yet	2s	1024 MB	Judgeable
Addition on Convex PolygonsGiven convex polygons R and S, find nonnegative a, b, c, d with ad-bc=1 and integer polygons P and Q with R=aP+bQ, S=cP+dQ, minimizing total area.	Hard9	GeometryNumber theory+1	No attempts yet	2s	512 MB	Judgeable
Traveling MerchantGiven weekly price cycles at n towns, answer q queries for the max profit from buying and later selling during a trip from town s to town t.	Hard9	Segment treeDivide and conquer+2	No attempts yet	10s	1024 MB	Judgeable
Hanging RackGiven a binary hanging rack with 2^n hooks, find the hook number (mod 1e9+7) used on the k-th step when coats are hung to keep every rod balanced within 0 or 1.	Hard9	MathRecursion+2	No attempts yet	1s	512 MB	Judgeable
RulerFind the shortest ruler with N marks (0 to L) where all pairwise distances between marks are distinct, and print the mark positions.	Hard9	BacktrackingBrute force+2	No attempts yet	2s	512 MB	Judgeable
AsceticismCount permutations of 1..N such that an optimal daily reading schedule (reading consecutive sentences within each day's time slots) finishes the sutra in exactly K days.	Hard9	Dynamic programmingCombinatorics+2	No attempts yet	0.6s	256 MB	Judgeable
Airline Route MapEncode an arbitrary simple graph with up to 1000 vertices as a graph with the fewest vertices, where vertex and edge labels are shuffled, so that the original map can be recovered.	Hard9	GraphImplementation+1	No attempts yet	2s	1024 MB	Judgeable
Long Distance CoachGiven refill stops, passenger deadlines modulo T, and a driver needing water every T, find the minimum total of water cost and refunds for the trip to city O.	Hard9	GreedySorting+1	No attempts yet	2s	256 MB	Judgeable
ToiletsGiven a line of 2N men and women (in run-length form), rearrange it so everyone finishes within N minutes and minimize the largest discontent, or report -1.	Hard9	Binary searchGreedy+1	No attempts yet	1s	512 MB	Judgeable
Construction ProjectPlace at most H airports among N towns and connect all towns with axis-parallel roads that avoid M rectangular obstacles, minimizing airport cost times count plus total road length.	Hard9	Minimum spanning treeGeometry+2	No attempts yet	5s	256 MB	Judgeable
MessengerDesign strategies for two players who alternately move a piece on a 4x4 grid, knowing neither the call order nor its timing, so B can deduce the secret value X within 10000 moves.	Hard9	ImplementationSimulation+2	No attempts yet	2s	512 MB	Judgeable
ConstellationCount the ways to assign each unlabeled point to constellation A or B so that the two vertex sets can be drawn connected with mutually non-crossing segments.	Hard9	GeometryCombinatorics+2	No attempts yet	1s	512 MB	Judgeable
Graph and CyclesGiven a weighted complete graph on an odd number of vertices, partition all edges into edge-disjoint cycles and minimize the sum over each cycle of the max weight on consecutive edge pairs.	Hard9	GraphGreedy+2	No attempts yet	2s	256 MB	Judgeable
QuadrilateralsGiven n points with no three collinear, find the maximum total credit from all quadrilaterals, where convex and minimum-area shapes score more.	Hard9	GeometrySorting+1	No attempts yet	1.7s	512 MB	Judgeable
GhostGiven axis-aligned rectangles that move at constant speeds, answer each query by reporting the maximum area common to all rectangles during a time interval [l, r].	Hard9	GeometrySorting+1	No attempts yet	10s	512 MB	Judgeable
Nearest PointsCount the integer lattice points in an axis-aligned rectangle whose Euclidean distance to p1 is the minimum among K marked points.	Hard9	GeometryDivide and conquer+2	No attempts yet	2s	512 MB	Judgeable
Mining aFor each n, find the largest a such that 1/n = 1/(a xor b) + 1/b for some positive integer b.	Hard9	MathBit manipulation+2	No attempts yet	2s	1024 MB	Judgeable
DivModuloCompute C(M,N) after removing every factor of D, and report the remainder modulo D, for M up to 4e18 and D up to 1.6e7.	Hard9	MathNumber theory+2	No attempts yet	3s	1024 MB	Judgeable
Be Geeks!Sum gcd(a_i..a_j) * max(a_i..a_j) over all subarrays, modulo 1e9+7, with N up to 2e5.	Hard9	MathNumber theory+2	No attempts yet	2s	512 MB	Judgeable
Dance CircleCount, modulo 1e9+7, the binary assignments to n children around a circle matching n parity constraints, each covering a contiguous arc centered at some child.	Hard9	MathPrefix sum+2	No attempts yet	2s	512 MB	Judgeable
Tree DepthFor each node i, sum its depth over all permutations of 1..N with exactly K inversions, using the Cartesian-tree BST built by recursively taking the minimum. Output each sum mod a large prime.	Hard9	Dynamic programmingCombinatorics+2	No attempts yet	2s	512 MB	Judgeable
Chessboard MovementCount paths from row 1 to row N on an N x M chessboard where odd rows restrict moves to same-colored adjacent cells and even rows allow any adjacent move, modulo 1e9+7.	Hard9	Dynamic programmingMatrix+2	No attempts yet	2s	512 MB	Judgeable
GnalcatsDecide whether two genes, each a sequence of seven possible base transformations on proteins, produce identical results or both fail on every sufficiently long input protein.	Hard9	StringStack+2	No attempts yet	0.3s	512 MB	Judgeable
Pilgrim's Memories and the Impressed GodGiven an N by N grid of 0 and 1 trials, sum X^2+1 over every distinct color string formed by monotone chains of sites, where X counts how often that string occurs.	Hard9	Dynamic programmingString+1	No attempts yet	8s	1024 MB	Judgeable
Sorcerers of the Round TableCount the circular seatings of the other sorcerers, with the chairman fixed at height n, where neighbors' hat heights differ by at most p and no disliked pair sits adjacent.	Hard9	Dynamic programmingBit manipulation+2	No attempts yet	2s	512 MB	Judgeable
Speed Reading CourseCount how many positions i where c contains the given m-bit word w, with c defined by an arithmetic progression modulo n against threshold p.	Hard9	Number theoryString matching+2	No attempts yet	2s	512 MB	Judgeable
Graph CountingCount, modulo 998244353, the non-isomorphic undirected graphs on 2n vertices that have no perfect matching but lose that property when any missing edge is added.	Hard9	CombinatoricsGraph+2	No attempts yet	5s	512 MB	Judgeable
Interesting GraphGiven a graph where every 7-vertex subset has a pair separated by a outside vertex, output the chromatic polynomial values for 1 to n colors modulo 998244353.	Hard9	GraphDynamic programming+1	No attempts yet	5s	512 MB	Judgeable
KnowledgeCount strings of length x reachable from s by inserting or deleting the blocks aa, bbb, and ababab, modulo 998244353.	Hard9	StringCombinatorics+2	No attempts yet	1s	512 MB	Judgeable
Airplane CliquesGiven a tree of n cities and a distance limit x, count the sets of k cities whose pairwise distances are all at most x, for every k from 1 to n.	Hard9	TreeDivide and conquer+1	No attempts yet	2s	512 MB	Judgeable
One GoalGiven a tree of n cities and k friends, sum the smallest optimal meeting city over all n^k placements of the friends, modulo 998244353.	Hard9	CombinatoricsTree+2	No attempts yet	2s	512 MB	Judgeable
Bitwise XorCount non-empty subsequences in which the pairwise xor of every two chosen elements is at least x, modulo 998244353.	Hard9	Bit manipulationTrie+2	No attempts yet	2s	512 MB	Judgeable
Easy WinAfter each edge insertion, find the maximum total weight of a subset of edges such that no non-empty edge-disjoint union of cycles in it has Nim value (xor of stone counts) equal to zero.	Hard9	Game theoryUnion-find+2	No attempts yet	1.5s	512 MB	Judgeable
Four ElementsCount the 4-element subsets of a union of n disjoint integer ranges whose sum equals s, modulo 998244353.	Hard9	MathCombinatorics+2	No attempts yet	2s	512 MB	Judgeable
Um_nik's AlgorithmGiven an undirected bipartite graph with up to 2e6 vertices and edges per side, output a matching whose size is at least 0.95 times the maximum matching size, with heavy constant-factor optimization required.	Hard9	GraphGreedy+2	No attempts yet	4s	512 MB	Judgeable
FFT AlgorithmGiven m and k, find a primitive 2^k-th root of unity modulo m, or report that none exists.	Hard9	Number theoryMath+2	No attempts yet	1.5s	512 MB	Judgeable
One RootCount pairs (p, q) with \|p\|, \|q\| <= m for which x^n + px + q has exactly one real root.	Hard9	MathNumber theory+2	No attempts yet	2s	512 MB	Judgeable
Another Coin Weighing PuzzleGiven m weighings and k coins per bag, find the maximum number of bags whose unique heavy bag can be identified, modulo 998244353.	Hard9	CombinatoricsMath+2	No attempts yet	1s	512 MB	Judgeable
Counting Edit DistancesCount the number of distinct strings over 'A' to 'Z' whose Levenshtein distance from a given string s is exactly d, modulo 998244353.	Hard9	Dynamic programmingString+2	No attempts yet	10s	512 MB	Judgeable
Rooted SubtreesFor each query with two roots r and p, count the distinct non-empty sets that are the intersection of a subtree of the tree rooted at r and a subtree of the tree rooted at p.	Hard9	TreeDFS+2	No attempts yet	11s	512 MB	Judgeable
Basis ChangeGiven one linear recurrence with coefficients a_i, find the unique recurrence with prescribed lags b_i that every sequence satisfying the first also satisfies.	Hard9	MathImplementation+2	No attempts yet	2s	512 MB	Judgeable
NightmareFind how far a rectangular car can drive along its normal before it hits one more pothole than it can withstand, among n pothole polyhedra.	Hard9	GeometrySorting+1	No attempts yet	1s	512 MB	Judgeable
EmployeesGiven n employees with distinct workloads and hall size k, output for each employee the product of two permutation-based scores, modulo 1e9+7.	Hard9	Dynamic programmingCombinatorics+2	No attempts yet	2s	512 MB	Judgeable
Modulo-magic squaresCount n x n matrices over Z_m whose row, column, and two diagonal sums are all congruent to one constant, for n and m up to 1e9.	Hard9	MathCombinatorics+2	No attempts yet	1s	512 MB	Judgeable
Call It What You WantFor each n, factor x^n - 1 over the integers into cyclotomic polynomials, print the factors in a specified coefficient order and a specific sign and exponent format.	Hard9	Number theoryMath+2	No attempts yet	2s	512 MB	Judgeable
KaleidoscopeCount colorings of the 60 faces of a rhombic hexecontahedron with n colors, each color i used at least c_i times, where colorings are identified under the rotational symmetry group, modulo p.	Hard9	CombinatoricsMath+2	No attempts yet	2s	512 MB	Judgeable
Expected CostPick a labeled tree on n vertices uniformly at random and find the expected value of the minimum sum of distances from any vertex to all others, modulo a prime.	Hard9	CombinatoricsTree+2	No attempts yet	3s	512 MB	Judgeable
Humongous StringGiven n and k, count the distinct non-empty substrings of the length-n prefix of the infinite string S built by concatenating the growing blocks T_i.	Hard9	StringMath+1	No attempts yet	1s	512 MB	Judgeable
Long GamePlayers alternately cut a strip of a permutation while every cut must leave at least one strip containing an inversion; decide the winner with optimal play.	Hard9	Game theoryGreedy+2	No attempts yet	1s	512 MB	Judgeable
Milk CandyGiven hints that reveal range sums with costs, and NPCs that force exactly k_i purchases each, find the minimum total cost to determine all n values, or report -1.	Hard9	MatrixCombinatorics+2	No attempts yet	2s	512 MB	Judgeable
FarawayCount lattice points (xe, ye) in [0, m]^2 such that for each of up to 10 constraints, (\|xi - xe\| + \|yi - ye\|) mod ki equals ti, with ki at most 5 and m up to 1e9.	Hard9	MathNumber theory+2	No attempts yet	1s	512 MB	Judgeable
TDLGiven m and k, find the smallest n such that the m-th integer above n coprime to n differs from n by a value whose XOR with n equals k.	Hard9	Number theoryBit manipulation+2	No attempts yet	1s	512 MB	Judgeable
Line GraphsGiven a simple graph G and k, find the size of a maximum clique in the k-th iterated line graph L_k(G) and count such cliques modulo 1000000007.	Hard9	GraphCombinatorics+1	No attempts yet	5s	512 MB	Judgeable
Domino CoveringCount the domino tilings of an n by m grid for up to 20000 queries, with n at most 35, m up to 10^18, and a prime modulus p given per query.	Hard9	MatrixDynamic programming+2	No attempts yet	6s	512 MB	Judgeable
Yet Another ConvolutionGiven arrays a and b of length n, compute for each k the maximum of \|a_i - b_j\| over all pairs (i, j) with gcd(i, j) equal to k.	Hard9	Number theoryMath+1	No attempts yet	4s	512 MB	Judgeable
Magic StringsGiven n up to 10^18, count the distinct subsequences of the recursively doubled string F_n modulo 10^9+7 for up to 10 test cases.	Hard9	Dynamic programmingMatrix+2	No attempts yet	4s	512 MB	Judgeable
Decimal ExpansionFor each query n up to 10^18, find the n-th digit after the decimal point of the infinite product (9/10)(99/100)(999/1000)...	Hard9	MathNumber theory+2	No attempts yet	1s	512 MB	Judgeable
EeveeGiven k random stacks of n fragments, find the expected sum over all ranges of 2 or more stacks of interleavings with no k equal-stone fragments in a row.	Hard9	CombinatoricsProbability+2	No attempts yet	5s	512 MB	Judgeable
HypnoFind the minimum expected time to walk from intersection 1 to intersection n when each road may put you to sleep with a Hypno you are susceptible to, and you learn each road's result after trying it.	Hard9	GraphShortest path+1	No attempts yet	2s	512 MB	Judgeable
Lati@sDetermine the winner of a finite impartial game whose starting multiset is built from all permutation diagonals of an n by n matrix.	Hard9	Game theoryCombinatorics+2	No attempts yet	2s	512 MB	Judgeable
Somewhere Over the RainbowGiven lower bounds a_x at n points, find the minimum sum of a strictly convex integer sequence with a_0 = a_m = 0, modulo 998244353.	Hard9	Dynamic programmingMath+1	No attempts yet	2s	512 MB	Judgeable
Linear Congruential GeneratorGiven a linear congruential generator and two index ranges, sum X_i mod (X_j+1) over all pairs i in the first range and j in the second.	Hard9	MathNumber theory+2	No attempts yet	2s	512 MB	Judgeable
Count the GraphsCount labeled connected undirected graphs on N nodes with exactly K bridges, modulo a possibly composite M, for up to 100 test cases.	Hard9	CombinatoricsDynamic programming+2	No attempts yet	2s	512 MB	Judgeable