Math and counting

Number theory, combinatorics, and geometry

Under construction

Still being built. Things may change

Total results13,153 problems

Island
Hard9
Tree, DFS+2
No attempts yet
Time limit
1s
Memory limit
512 MB
Judgeable
Fermat's Last Theorem
Hard9
Math, Combinatorics+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Right Expansion Of The Mind
Hard9
String, String matching+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Robogolf
Hard9
Dynamic programming, Sorting+1
No attempts yet
Time limit
3s
Memory limit
512 MB
Judgeable
Oleg and Binary Sequences
Hard9
String matching, Dynamic programming+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Sewing Graph
Hard9
Geometry, Sorting+2
No attempts yet
Time limit
2s
Memory limit
1024 MB
Judgeable
Unscrambling a Messy Bug
Hard9
Bit manipulation, Implementation+1
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Why the Cow Crossed Yonsei-ro
Hard9
Divide and conquer, Combinatorics+2
No attempts yet
Time limit
5s
Memory limit
1024 MB
Judgeable
Vista 6
Hard9
Geometry, Sorting+2
No attempts yet
Time limit
0.1s
Memory limit
128 MB
Judgeable
Vista 8
Hard9
Geometry, Greedy+2
No attempts yet
Time limit
0.1s
Memory limit
128 MB
Judgeable
Vista 9
Hard9
Geometry, Greedy+2
No attempts yet
Time limit
0.1s
Memory limit
128 MB
Judgeable
814 - 3
Hard9
Geometry, Greedy+2
No attempts yet
Time limit
4.814s
Memory limit
814 MB
Judgeable
Homework
Hard9
Segment tree, Math+2
No attempts yet
Time limit
3s
Memory limit
1024 MB
Judgeable
Imperial Civilization
Hard9
Dynamic programming, Divide and conquer+1
No attempts yet
Time limit
1.5s
Memory limit
512 MB
Judgeable
Random Walk on a Tree: Expected Time
Hard9
Tree, Dynamic programming+2
No attempts yet
Time limit
2.5s
Memory limit
512 MB
Judgeable
Sail Shreds - 5
Hard9
Geometry, Implementation+1
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Sail Shreds - 9
Hard9
Geometry, Greedy+1
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Meandian
Hard9
Sorting, Math+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
MVP Diamond (Hard)
Hard9
Dynamic programming, Math+2
No attempts yet
Time limit
1s
Memory limit
512 MB
Judgeable
Dart Game
Hard9
Dynamic programming, Geometry+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Cactus Shoppe
Hard9
Graph, DFS+2
No attempts yet
Time limit
5s
Memory limit
1024 MB
Judgeable
Pop music
Hard9
Dynamic programming, Bit manipulation+1
No attempts yet
Time limit
5s
Memory limit
256 MB
Judgeable
Even rain
Hard9
Dynamic programming, Prefix sum+1
No attempts yet
Time limit
3s
Memory limit
512 MB
Judgeable
Biggest Set Ever
Hard9
Combinatorics, Number theory
No attempts yet
Time limit
3s
Memory limit
512 MB
Judgeable
Justice For Everyone
Hard9
Combinatorics, Dynamic programming+1
No attempts yet
Time limit
10s
Memory limit
512 MB
Judgeable
Dynamic Convex Hull
Hard9
Geometry, Segment tree+1
No attempts yet
Time limit
4s
Memory limit
512 MB
Judgeable
It's All Squares
Hard9
Geometry, Segment tree+1
No attempts yet
Time limit
4s
Memory limit
512 MB
Judgeable
Fibonacci Partition
Hard9
Math, Number theory+1
No attempts yet
Time limit
10s
Memory limit
256 MB
Judgeable
Anti-hash Test
Hard9
String matching, Recursion+1
No attempts yet
Time limit
1s
Memory limit
256 MB
Judgeable
Stabbing Number
Hard9
Dynamic programming, Bit manipulation+1
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Tree Beauty
Hard9
Tree, Segment tree+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Find a Square
Hard9
Number theory, Math
No attempts yet
Time limit
6s
Memory limit
512 MB
Judgeable
Geometrical Combinatorics
Hard9
Combinatorics, Geometry+1
No attempts yet
Time limit
3s
Memory limit
512 MB
Judgeable
Partitions
Hard9
Number theory, Combinatorics+1
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Game with stones
Hard9
Game theory, Bit manipulation+2
No attempts yet
Time limit
1s
Memory limit
256 MB
Judgeable
Hotels
Hard9
Tree, Dynamic programming+2
No attempts yet
Time limit
2s
Memory limit
256 MB
Judgeable
Fibonacci Suffix Array
Hard9
String, Recursion+1
No attempts yet
Time limit
5s
Memory limit
512 MB
Judgeable
Greatest Square
Hard9
Geometry, Segment tree+1
No attempts yet
Time limit
8s
Memory limit
512 MB
Judgeable
Hamming Distance
Hard9
Divide and conquer, String matching+1
No attempts yet
Time limit
3s
Memory limit
512 MB
Judgeable
Rikka with Storehouse
Hard9
Tree, Dynamic programming+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Rikka with Composite Number
Hard9
Math, Probability+2
No attempts yet
Time limit
1s
Memory limit
512 MB
Judgeable
House Building
Hard9
Greedy, Brute force+2
No attempts yet
Time limit
4s
Memory limit
1024 MB
Judgeable
Snow Wall
Hard9
Implementation, Greedy+1
No attempts yet
Time limit
1s
Memory limit
1024 MB
Judgeable
Counting Good Arrays
Hard9
Combinatorics, Dynamic programming+2
No attempts yet
Time limit
1s
Memory limit
512 MB
Judgeable
Parity Constraint Perfect Matching
Hard9
Graph, Matrix+1
No attempts yet
Time limit
1s
Memory limit
1024 MB
Judgeable
Civilizations
Hard9
Geometry, Hash map+1
No attempts yet
Time limit
15s
Memory limit
512 MB
Judgeable
Instruction Anagram
Hard9
Combinatorics, Math+2
No attempts yet
Time limit
4s
Memory limit
512 MB
Judgeable
All Subsequences
Hard9
Dynamic programming, Math+2
No attempts yet
Time limit
1s
Memory limit
512 MB
Judgeable
Cartesian MST
Hard9
Graph, Minimum spanning tree+2
No attempts yet
Time limit
1s
Memory limit
512 MB
Judgeable
Game on a Tree
Hard9
Tree, Bit manipulation+2
No attempts yet
Time limit
5s
Memory limit
512 MB
Judgeable
Joyful Numbers
Hard9
Number theory, Math+2
No attempts yet
Time limit
1s
Memory limit
512 MB
Judgeable
Revenue
Hard9
Probability, Sorting+1
No attempts yet
Time limit
1s
Memory limit
256 MB
Judgeable
Multiple?
Hard9
Combinatorics, Number theory+2
No attempts yet
Time limit
6s
Memory limit
256 MB
Judgeable
The Hash Table
Hard9
Number theory, Math+1
No attempts yet
Time limit
1s
Memory limit
512 MB
Judgeable
Colorful Components
Hard9
Combinatorics, Dynamic programming+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Belarusian State University
Hard9
Bit manipulation, Math+1
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Brave Seekers of Unicorns
Hard9
Dynamic programming, Bit manipulation+2
No attempts yet
Time limit
1s
Memory limit
512 MB
Judgeable
Bytelandia States Union
Hard9
Math, Implementation
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Binary Supersonic Utahraptors
Hard9
Game theory, Greedy+2
No attempts yet
Time limit
1s
Memory limit
512 MB
Judgeable
Derangement Rotations
Hard9
Combinatorics, Math+2
No attempts yet
Time limit
1s
Memory limit
512 MB
Judgeable
Counting Graphs
Hard9
Graph, BFS+2
No attempts yet
Time limit
1s
Memory limit
512 MB
Judgeable
Stone Game
Hard9
Game theory, Number theory+2
No attempts yet
Time limit
1s
Memory limit
512 MB
Judgeable
Games
Hard9
Game theory, Combinatorics+2
No attempts yet
Time limit
4s
Memory limit
1024 MB
Judgeable
Japanese Knowledge
Hard9
Dynamic programming, Divide and conquer+2
No attempts yet
Time limit
10s
Memory limit
512 MB
Judgeable
Graph Game
Hard9
Combinatorics, Dynamic programming+2
No attempts yet
Time limit
2s
Memory limit
1024 MB
Judgeable
Matches Are Not a Toy for Children
Hard9
Geometry, Hash map+2
No attempts yet
Time limit
2s
Memory limit
1024 MB
Judgeable
Puzzle
Hard9
Graph, Number theory+2
No attempts yet
Time limit
2s
Memory limit
1024 MB
Judgeable
Waging War Peacefully
Hard9
Math, Number theory+2
No attempts yet
Time limit
5s
Memory limit
256 MB
Judgeable
Polynomial and Easy Queries
Hard9
Math, Segment tree+2
No attempts yet
Time limit
2s
Memory limit
256 MB
Judgeable
Back to Space
Hard9
String matching, Hash map+1
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Road Construction
Hard9
Divide and conquer, Sorting+2
No attempts yet
Time limit
10s
Memory limit
2048 MB
Judgeable
Routing Schemes
Hard9
Graph, Combinatorics+1
No attempts yet
Time limit
1s
Memory limit
512 MB
Judgeable
Vote-Value Disparity 2
Hard9
Graph, BFS+2
No attempts yet
Time limit
1s
Memory limit
512 MB
Judgeable
Binary Subsequences
Hard9
Dynamic programming, Combinatorics+2
No attempts yet
Time limit
1s
Memory limit
512 MB
Judgeable
Deque Game
Hard9
Dynamic programming, Combinatorics+2
No attempts yet
Time limit
1s
Memory limit
1024 MB
Judgeable
The Grade
Hard9
Dynamic programming, Combinatorics+2
No attempts yet
Time limit
1s
Memory limit
512 MB
Judgeable
Football
Hard9
Game theory, Dynamic programming+1
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Crossing
Hard9
Segment tree, Math+2
No attempts yet
Time limit
3s
Memory limit
512 MB
Judgeable
Broken Clocks
Hard9
Number theory, Math+2
No attempts yet
Time limit
3s
Memory limit
512 MB
Judgeable
Double Move
Hard9
Game theory, Combinatorics+1
No attempts yet
Time limit
5s
Memory limit
512 MB
Judgeable
Forgotten Homework
Hard9
Matrix, Dynamic programming+2
No attempts yet
Time limit
1s
Memory limit
512 MB
Judgeable
Mezhdurechye Bombs
Hard9
Geometry, Combinatorics+1
No attempts yet
Time limit
2s
Memory limit
256 MB
Judgeable
Fibonacci Numbers
Hard9
Math, Number theory+1
No attempts yet
Time limit
5s
Memory limit
256 MB
Judgeable
Table
Hard9
Combinatorics, Math+2
No attempts yet
Time limit
2s
Memory limit
256 MB
Judgeable
Trisolarians
Hard9
Combinatorics, Dynamic programming+2
No attempts yet
Time limit
2s
Memory limit
256 MB
Judgeable
Jawaian Weapon Set
Hard9
Number theory, Math+2
No attempts yet
Time limit
3s
Memory limit
256 MB
Judgeable
Parade
Hard9
Geometry, Brute force+2
No attempts yet
Time limit
2s
Memory limit
256 MB
Judgeable
Table 5
Hard9
Backtracking, Math+2
No attempts yet
Time limit
1s
Memory limit
512 MB
Judgeable
Table 7
Hard9
Backtracking, Brute force+2
No attempts yet
Time limit
1s
Memory limit
512 MB
Judgeable
Departure
Hard9
Shortest path, Sorting+1
No attempts yet
Time limit
4s
Memory limit
512 MB
Judgeable
Truck
Hard9
Tree, Dynamic programming+2
No attempts yet
Time limit
1s
Memory limit
512 MB
Judgeable
Tiles
Hard9
Dynamic programming, Segment tree+2
No attempts yet
Time limit
4s
Memory limit
1024 MB
Judgeable
Paper, Pen, Triangle
Hard9
Combinatorics, Math+2
No attempts yet
Time limit
3s
Memory limit
1024 MB
Judgeable
Edge First or Vertex First
Hard9
Game theory, Graph+2
No attempts yet
Time limit
8s
Memory limit
512 MB
Judgeable
Feed candies
Hard9
Number theory, Math+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Watching Baseball
Hard9
Combinatorics, Math+2
No attempts yet
Time limit
8s
Memory limit
512 MB
Judgeable
Air Pollution
Hard9
Math, Greedy+1
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Entangled with Lottery
Hard9
Dynamic programming, Probability+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Double Magic Made Clear
Hard9
Graph, Topological sort+2
No attempts yet
Time limit
8s
Memory limit
512 MB
Judgeable
Lapin Noir
Hard9
Game theory, Geometry+1
No attempts yet
Time limit
1s
Memory limit
512 MB
Judgeable

Title	Level	Topics	Solved	Time limit	Memory limit	Judge
IslandGiven the edge list of a tree whose N leaves are towns and whose internal nodes all have degree at least 3, count the distinct circular orderings of the leaves realizable as the outer face, and print the count as a product of prime powers.	Hard9	TreeDFS+2	No attempts yet	1s	512 MB	Judgeable
Fermat's Last TheoremOrder all positive quadruples (a,b,c,n) with n>=3 by max element then lexicographically, and print the sign of a^n+b^n compared to c^n for positions l through r.	Hard9	MathCombinatorics+2	No attempts yet	2s	512 MB	Judgeable
Right Expansion Of The MindGroup n infinite strings, each formed by a finite prefix s followed by repeats of t, so that within each group every pair is mutually a subsequence of the other; minimize the number of groups.	Hard9	StringString matching+2	No attempts yet	2s	512 MB	Judgeable
RobogolfTwo robots alternately move a chip right or down across an n by m grid with priced traps, and the task is to sum the game value over every starting square.	Hard9	Dynamic programmingSorting+1	No attempts yet	3s	512 MB	Judgeable
Oleg and Binary SequencesCount binary sequences of length n whose Z-function matches the given entries, with -1 marking unknown values, modulo 1e9+7.	Hard9	String matchingDynamic programming+2	No attempts yet	2s	512 MB	Judgeable
Sewing GraphFind the shortest alternating front/back sequence of edges that connects all N points on both sides with no crossings on either side.	Hard9	GeometrySorting+2	No attempts yet	2s	1024 MB	Judgeable
Unscrambling a Messy BugFind a hidden bit permutation of n-bit integers (n a power of two) using at most w insertions and r membership queries after a single compile step.	Hard9	Bit manipulationImplementation+1	No attempts yet	2s	512 MB	Judgeable
Why the Cow Crossed Yonsei-roGiven two permutations of 1..N, sum over all cyclic rotations of each side the number of crossing pairs (inversions) between the two orders, modulo 1,000,000,009.	Hard9	Divide and conquerCombinatorics+2	No attempts yet	5s	1024 MB	Judgeable
Vista 6Given up to a million distinct points in the plane, output a cyclic order visiting all of them that is short enough under the Euclidean metric.	Hard9	GeometrySorting+2	No attempts yet	0.1s	128 MB	Judgeable
Vista 8Given up to a million distinct points in the plane, output a cyclic tour that visits every point and returns to the start, under the Euclidean metric.	Hard9	GeometryGreedy+2	No attempts yet	0.1s	128 MB	Judgeable
Vista 9Given up to a million points in the plane, output a cyclic tour that visits each point once and returns to the start.	Hard9	GeometryGreedy+2	No attempts yet	0.1s	128 MB	Judgeable
814 - 3Partition 8000 random points among 140 salesmen and give each a closed tour so the longest tour is as short as possible.	Hard9	GeometryGreedy+2	No attempts yet	4.814s	814 MB	Judgeable
HomeworkEach child builds an expression from range-assigned operators and integers; output the sum of all expression values modulo 1e9+7 under PEMDAS.	Hard9	Segment treeMath+2	No attempts yet	3s	1024 MB	Judgeable
Imperial CivilizationChoose a subset of stops that must include the first and last positions to maximize total resident satisfaction minus stop dissatisfaction, where each consecutive gap of length d scores the sum of \|d - d_i\|.	Hard9	Dynamic programmingDivide and conquer+1	No attempts yet	1.5s	512 MB	Judgeable
Random Walk on a Tree: Expected TimeGiven a tree, answer queries giving the expected hitting time of a random walk from one vertex to another, modulo 1e9+7.	Hard9	TreeDynamic programming+2	No attempts yet	2.5s	512 MB	Judgeable
Sail Shreds - 5Translate N triangles without rotating them so they tile an X by Y rectangle exactly, with no overlaps and nothing outside the sail.	Hard9	GeometryImplementation+1	No attempts yet	2s	512 MB	Judgeable
Sail Shreds - 9Place N triangles without rotating them so they tile an X by Y rectangle exactly, then print the new position of each triangle's vertex A.	Hard9	GeometryGreedy+1	No attempts yet	2s	512 MB	Judgeable
MeandianUsing at most 1000 queries to a library that returns the mean of the two middle salaries among any four distinct employees, recover every salary that is uniquely determined by the answers.	Hard9	SortingMath+2	No attempts yet	2s	512 MB	Judgeable
MVP Diamond (Hard)Given N monthly MVP tiers and four thresholds, find the maximum total spending that could produce that tier sequence, with each month capped at d and spend in units of 10,000.	Hard9	Dynamic programmingMath+2	No attempts yet	1s	512 MB	Judgeable
Dart GameGiven K rounds of weighted Seunggyu darts and movable Uiseok darts, compute the original score and the max and min achievable scores after relocating at most L Uiseok darts, all modulo 1e9+7.	Hard9	Dynamic programmingGeometry+2	No attempts yet	2s	512 MB	Judgeable
Cactus ShoppeGiven a cactus whose vertices carry values, and divisibility queries, count the connected components left after deleting every vertex not divisible by the query.	Hard9	GraphDFS+2	No attempts yet	5s	1024 MB	Judgeable
Pop musicPick strictly increasing integers b_1 to b_n in the range 0 to m to maximize the sum of a_i times the number of ones in each b_i.	Hard9	Dynamic programmingBit manipulation+1	No attempts yet	5s	256 MB	Judgeable
Even rainCount the ways to zero out k of n columns so that the trapped rain area is even, modulo 10^9+7, with n up to 25,000 and k up to 25.	Hard9	Dynamic programmingPrefix sum+1	No attempts yet	3s	512 MB	Judgeable
Biggest Set EverCount subsets of {0, ..., T-1} whose element sum is congruent to rem modulo n, for a huge T, modulo 998244353.	Hard9	CombinatoricsNumber theory	No attempts yet	3s	512 MB	Judgeable
Justice For EveryoneCount the orders of pair increments that turn distinct starting numbers a into distinct targets b, keeping all numbers distinct at every step, modulo 998244353.	Hard9	CombinatoricsDynamic programming+1	No attempts yet	10s	512 MB	Judgeable
Dynamic Convex HullMaintain a set of functions (x-a)^4+b under insertions and deletions, and report the minimum value at each queried point x.	Hard9	GeometrySegment tree+1	No attempts yet	4s	512 MB	Judgeable
It's All SquaresGiven a grid of cell values and a closed simple route for each query, count the distinct values of the cells enclosed by that route.	Hard9	GeometrySegment tree+1	No attempts yet	4s	512 MB	Judgeable
Fibonacci PartitionAfter each update X += a_i * F_{b_i}, the task asks for partition(X), the largest number of distinct Fibonacci numbers that sum to X.	Hard9	MathNumber theory+1	No attempts yet	10s	256 MB	Judgeable
Anti-hash TestCount occurrences of u in the popcount-parity string s(n) of length 2^n, and how many strings v share that occurrence count.	Hard9	String matchingRecursion+1	No attempts yet	1s	256 MB	Judgeable
Stabbing NumberGiven a histogram polygon drawn in ASCII, find a rectangle decomposition that minimizes the maximum number of rectangles an axis-parallel segment crosses.	Hard9	Dynamic programmingBit manipulation+1	No attempts yet	2s	512 MB	Judgeable
Tree BeautyGiven a rooted tree, apply updates that add floor(Y/K^depth) to a subtree and answer subtree sum queries. N and Q are up to 100,000.	Hard9	TreeSegment tree+2	No attempts yet	2s	512 MB	Judgeable
Find a SquareGiven p(x) = a·x^2 + b·x + c, find the largest square dividing the product of p(0) through p(n-1), modulo 10^9+7.	Hard9	Number theoryMath	No attempts yet	6s	512 MB	Judgeable
Geometrical CombinatoricsGiven three integer vertices of a triangle, sum the Pascal's triangle values at lattice points inside or on it, modulo 10^9+7, for up to 5 tests.	Hard9	CombinatoricsGeometry+1	No attempts yet	3s	512 MB	Judgeable
PartitionsFind the smallest set of distinct positive integers with exactly k splits where one part's LCM equals the other part's GCD, given as prime factorizations.	Hard9	Number theoryCombinatorics+1	No attempts yet	2s	512 MB	Judgeable
Game with stonesCount the ways to color each of n piles black or white so that Bob wins the Steins;Game under optimal play, modulo 1000000007.	Hard9	Game theoryBit manipulation+2	No attempts yet	1s	256 MB	Judgeable
HotelsGiven a weighted tree and three independent uniform choices of vertices from three candidate sets, find the expected total distance from the three chosen vertices to their median (the vertex minimizing the sum of distances).	Hard9	TreeDynamic programming+2	No attempts yet	2s	256 MB	Judgeable
Fibonacci Suffix ArrayGiven n, q, and m, the task finds the suffix array of the Fibonacci word fib_n at q query positions and prints each value modulo m.	Hard9	StringRecursion+1	No attempts yet	5s	512 MB	Judgeable
Greatest SquareGiven a rectilinear simple polygon and query points, find the largest axis-parallel square inside it with each point as its lower left corner.	Hard9	GeometrySegment tree+1	No attempts yet	8s	512 MB	Judgeable
Hamming DistanceGiven a sequence a of length n and m, find the minimum and the sum mod 1e9+7 of Hamming distances to every length-n window of S^m.	Hard9	Divide and conquerString matching+1	No attempts yet	3s	512 MB	Judgeable
Rikka with StorehouseOn a complete binary tree of 2^n-1 nodes, the last half of node values are given and updated; minimize the sum of squared edge differences over the free nodes after each update, modulo 998244353.	Hard9	TreeDynamic programming+2	No attempts yet	2s	512 MB	Judgeable
Rikka with Composite NumberGiven a set of digits, find the expected number of random digits drawn before the growing decimal number first becomes composite, modulo 998244353.	Hard9	MathProbability+2	No attempts yet	1s	512 MB	Judgeable
House BuildingPlace K houses on an N by M grid so that the total happiness, each house's value times its Manhattan distance to the nearest other house, is as large as possible.	Hard9	GreedyBrute force+2	No attempts yet	4s	1024 MB	Judgeable
Snow WallStack blocks of given widths into a wall of width W as tall as possible, with no two consecutive rows sharing a gap position and every block endpoint supported below.	Hard9	ImplementationGreedy+1	No attempts yet	1s	1024 MB	Judgeable
Counting Good ArraysCount permutations of 1..n with one value duplicated, whose inversion-like score falls in [a,b], modulo 1e9+7.	Hard9	CombinatoricsDynamic programming+2	No attempts yet	1s	512 MB	Judgeable
Parity Constraint Perfect MatchingGiven a weighted bipartite graph, find one perfect matching with an even weight sum and one with an odd weight sum, or print -1 when none exists.	Hard9	GraphMatrix+1	No attempts yet	1s	1024 MB	Judgeable
CivilizationsAfter each ownership change, report the largest power Aw+Bl+Cwl among civilizations that own at least one field, where w is wealth and l is border length.	Hard9	GeometryHash map+1	No attempts yet	15s	512 MB	Judgeable
Instruction AnagramCount strings S consistent with observations, given that P is an anagram of S and the robot's positions at certain times are known.	Hard9	CombinatoricsMath+2	No attempts yet	4s	512 MB	Judgeable
All SubsequencesSum the absolute product of consecutive differences over every subsequence of A, modulo 998244353.	Hard9	Dynamic programmingMath+2	No attempts yet	1s	512 MB	Judgeable
Cartesian MSTGiven two connected weighted graphs G and H, compute the total weight of the minimum spanning tree of their Cartesian product G square H.	Hard9	GraphMinimum spanning tree+2	No attempts yet	1s	512 MB	Judgeable
Game on a TreeFriends draw colored cards along tree paths, score each deck by GCD, then replace one card per round. Output each friend's points modulo 1e9+7.	Hard9	TreeBit manipulation+2	No attempts yet	5s	512 MB	Judgeable
Joyful NumbersA number n is joyful when appending 25 to its digits gives a square; for the k-th joyful number, report how many distinct primes divide it.	Hard9	Number theoryMath+2	No attempts yet	1s	512 MB	Judgeable
RevenueGiven item prices and each item's value distribution, find the lowest expected revenue over all joint distributions of buyer values that share those marginals.	Hard9	ProbabilitySorting+1	No attempts yet	1s	256 MB	Judgeable
Multiple?Count sequences of length n-k with entries in [1,n] such that no non-empty subsequence sums to a multiple of n, modulo 998244353.	Hard9	CombinatoricsNumber theory+2	No attempts yet	6s	256 MB	Judgeable
The Hash TableGiven n and m, find the total insertion cost when elements 0 to n-1 go into m slots at i^2 mod m, where each insert costs the slot's current size.	Hard9	Number theoryMath+1	No attempts yet	1s	512 MB	Judgeable
Colorful ComponentsCount labeled trees on n colored vertices such that the monochromatic components left after deleting bichromatic edges each have size at most k, modulo 1e9+7.	Hard9	CombinatoricsDynamic programming+2	No attempts yet	2s	512 MB	Judgeable
Belarusian State UniversityGiven a lookup table c(i, x_i, y_i) for each bit, count how often each value of f(a, b) appears over all pairs a in A and b in B, with n up to 18.	Hard9	Bit manipulationMath+1	No attempts yet	2s	512 MB	Judgeable
Brave Seekers of UnicornsCount strictly increasing sequences of distinct integers from 1 to n with no three consecutive elements XORing to zero, modulo 998244353.	Hard9	Dynamic programmingBit manipulation+2	No attempts yet	1s	512 MB	Judgeable
Bytelandia States UnionFind the minimum total time to walk from a start square to a portal on a huge grid with position-dependent move costs, modulo 998244353.	Hard9	MathImplementation	No attempts yet	2s	512 MB	Judgeable
Binary Supersonic UtahraptorsAlexey and Boris repeatedly exchange fixed-size groups of yellow or red utahraptors; find the game value \|a_y - b_r\| under optimal play.	Hard9	Game theoryGreedy+2	No attempts yet	1s	512 MB	Judgeable
Derangement RotationsCount derangements of size n whose set of derangement rotations has exactly n-2 distinct rotations, modulo a prime p.	Hard9	CombinatoricsMath+2	No attempts yet	1s	512 MB	Judgeable
Counting GraphsGiven a connected undirected graph, count the graphs whose walk lengths from vertex 1 to every vertex match the original, modulo 1000000007.	Hard9	GraphBFS+2	No attempts yet	1s	512 MB	Judgeable
Stone GameCount the opening moves (pile and stone count) that let Bessie force a win in a game where each removed amount must be a multiple of the previous one.	Hard9	Game theoryNumber theory+2	No attempts yet	1s	512 MB	Judgeable
GamesCount the distinguishable piles of K stones drawn from the N given sizes where the first player loses in a Nim variant that removes from at most 6 piles.	Hard9	Game theoryCombinatorics+2	No attempts yet	4s	1024 MB	Judgeable
Japanese KnowledgeFor each k from 0 to N, count non-decreasing sequences x with x_i at most A_i in which exactly k positions have x_i equal to A_i, modulo 998244353.	Hard9	Dynamic programmingDivide and conquer+2	No attempts yet	10s	512 MB	Judgeable
Graph GameCount the number of distinct directed graphs on n labeled vertices that can arise as positions in a game where each move adds an edge without creating a cycle.	Hard9	CombinatoricsDynamic programming+2	No attempts yet	2s	1024 MB	Judgeable
Matches Are Not a Toy for ChildrenGiven two figures made of n unit matches, find the minimum number of matches to move so that A coincides with B after a parallel translation.	Hard9	GeometryHash map+2	No attempts yet	2s	1024 MB	Judgeable
PuzzleGiven k undirected graphs with start 1 and end n, find the smallest length T such that some walk of exactly T edges goes from 1 to n in every graph at once.	Hard9	GraphNumber theory+2	No attempts yet	2s	1024 MB	Judgeable
Waging War PeacefullyGiven group sizes A1..AN, find the largest rectangle width Y that fits all soldiers in row-major order with at most k row-boundary conflicts, for every k from 0 to N-1.	Hard9	MathNumber theory+2	No attempts yet	5s	256 MB	Judgeable
Polynomial and Easy QueriesMaintain an array under range applications of f(x)=2x^2-1 and g(x)=4x^3-3x, and answer point queries modulo 100003.	Hard9	MathSegment tree+2	No attempts yet	2s	256 MB	Judgeable
Back to SpaceGiven an r by c grid of colored tiles, find a panel size a by b and a row shift s so that the grid is covered by shifted copies of the panel, with minimal panel area.	Hard9	String matchingHash map+1	No attempts yet	2s	512 MB	Judgeable
Road ConstructionGiven N points, output the K smallest Manhattan distances among all pairs, in increasing order, for N and K up to 250000.	Hard9	Divide and conquerSorting+2	No attempts yet	10s	2048 MB	Judgeable
Routing SchemesCount the ways to cover every edge of a graph with K backward edges by S paths, each running from a sender to a distinct receiver, modulo 1e9+7.	Hard9	GraphCombinatorics+1	No attempts yet	1s	512 MB	Judgeable
Vote-Value Disparity 2Partition N voter-weighted provinces on a grid into K connected districts minimizing the ratio of largest to smallest district voter total, outputting one district id per province.	Hard9	GraphBFS+2	No attempts yet	1s	512 MB	Judgeable
Binary SubsequencesFor each K up to 10^6, count binary strings with exactly K distinct non-empty subsequences modulo 1e9+7 and output a shortest such string.	Hard9	Dynamic programmingCombinatorics+2	No attempts yet	1s	512 MB	Judgeable
Deque GameGiven two starting stacks over a K-letter alphabet, count for each how many distinct L-length stacks contain that starting stack as a contiguous block, and compare the counts.	Hard9	Dynamic programmingCombinatorics+2	No attempts yet	1s	1024 MB	Judgeable
The GradeAfter each insert or erase into a set A, count the ways to place all elements of A into a length-P list padded with zeros so that each positive value sits at least that far from the previous positive value, modulo 1e9+7, or print -1.	Hard9	Dynamic programmingCombinatorics+2	No attempts yet	1s	512 MB	Judgeable
FootballPlayers alternately take students from one class per turn, at most K and no more than the previous turn's count; decide who takes the last student.	Hard9	Game theoryDynamic programming+1	No attempts yet	2s	512 MB	Judgeable
CrossingGiven three seed strings over J,O,I and a crossing operation, decide after each of Q range-assignment updates whether the current string can be produced by repeated crossings.	Hard9	Segment treeMath+2	No attempts yet	3s	512 MB	Judgeable
Broken ClocksGiven n clocks with start times and per-second drift rates, count how many times during a 24-hour window all clocks show the same time.	Hard9	Number theoryMath+2	No attempts yet	3s	512 MB	Judgeable
Double MoveGiven n stones and some already declared pairs of candidate stones, count the scenarios in which Alice and Bob each win when both play optimally.	Hard9	Game theoryCombinatorics+1	No attempts yet	5s	512 MB	Judgeable
Forgotten HomeworkGiven a matrix A and the first 2n-1 values of the sequence A^k(i,j), find the missing term A^{2n}(i,j) modulo 1e9+7.	Hard9	MatrixDynamic programming+2	No attempts yet	1s	512 MB	Judgeable
Mezhdurechye BombsFind the fewest translations of a fixed convex polygon that together touch every x-monotone polyline between the lines x=0 and x=T.	Hard9	GeometryCombinatorics+1	No attempts yet	2s	256 MB	Judgeable
Fibonacci NumbersFor each test, compute the sum of the k-th powers of the first n Fibonacci numbers modulo 10^9+23, with n up to 1e9 and k up to 1e18.	Hard9	MathNumber theory+1	No attempts yet	5s	256 MB	Judgeable
TableCount 2-colorings of an n by m grid with no monochromatic axis-parallel rectangle, modulo a given r, for huge n, m, r.	Hard9	CombinatoricsMath+2	No attempts yet	2s	256 MB	Judgeable
TrisolariansCount the maximum number of distinct life histories (strictly increasing chains of k-vectors with all-positive yearly increments) that end at a vector with coordinate sum n, modulo 7340033.	Hard9	CombinatoricsDynamic programming+2	No attempts yet	2s	256 MB	Judgeable
Jawaian Weapon SetFind the k-th triple of primes (d1<=d2<=d3) in lexicographic order satisfying three divisibility conditions involving squares minus one.	Hard9	Number theoryMath+2	No attempts yet	3s	256 MB	Judgeable
ParadeGiven a convex polygon, an interior center, and k fixed garland directions, rotate the whole system to minimize the total distance from the center to the polygon boundary along those directions.	Hard9	GeometryBrute force+2	No attempts yet	2s	256 MB	Judgeable
Table 5Build an N by N digit table (2 <= N <= 10) whose rows, columns, and two main diagonals all read as distinct multiples of M, with no leading zeros.	Hard9	BacktrackingMath+2	No attempts yet	1s	512 MB	Judgeable
Table 7Build an N by N digit table (2 <= N <= 10) where every row, column, and main diagonal forms an N-digit multiple of M with no leading zero and all numbers distinct.	Hard9	BacktrackingBrute force+2	No attempts yet	1s	512 MB	Judgeable
DepartureGiven bus routes whose speed depends on distance, find for each home the earliest arrival time from the stadium at 0, as an exact fraction of days.	Hard9	Shortest pathSorting+1	No attempts yet	4s	512 MB	Judgeable
TruckGiven a weighted tree with per-edge tolls, handle toll updates and queries asking the minimum fuel to move G gold along a path, modulo 1e9+7.	Hard9	TreeDynamic programming+2	No attempts yet	1s	512 MB	Judgeable
TilesCount tilings of a 3 by N grid with 1 by 2 dominoes restricted to white squares, under point color flips and subrectangle queries, modulo 1e9+7.	Hard9	Dynamic programmingSegment tree+2	No attempts yet	4s	1024 MB	Judgeable
Paper, Pen, TriangleGiven a big equilateral triangle of side m and q lines drawn inside it parallel to its sides, count every equilateral triangle fully contained in the figure.	Hard9	CombinatoricsMath+2	No attempts yet	3s	1024 MB	Judgeable
Edge First or Vertex FirstGiven a directed graph, Edgeo picks a probability distribution over edges, then Vertexko picks a distribution over vertices to minimize the expected score; find the game value.	Hard9	Game theoryGraph+2	No attempts yet	8s	512 MB	Judgeable
Feed candiesCandy i has effect (s_i, t_i) generated by a complex recurrence; decide whether a subset sums to (X, Y) and print the chosen indices.	Hard9	Number theoryMath+2	No attempts yet	2s	512 MB	Judgeable
Watching BaseballCount ordered sequences of A+B+C games with A X-wins, B Y-wins, C draws, total runs SX and SY, modulo 1e9+7.	Hard9	CombinatoricsMath+2	No attempts yet	8s	512 MB	Judgeable
Air PollutionEach operation at shop i adds p_i to its two neighbors and subtracts 2p_i from it; find the minimum number of operations so every p_i reaches at least l_i, or -1.	Hard9	MathGreedy+1	No attempts yet	2s	512 MB	Judgeable
Entangled with LotteryGiven an amidakuji with some horizontal bars already placed, the cat adds K more bars at uniformly random distinct valid heights, and we must compute the maximum over starting bars of the probability that the path ends at the labeled winning bar.	Hard9	Dynamic programmingProbability+2	No attempts yet	2s	512 MB	Judgeable
Double Magic Made ClearGiven a graph of N elements with compatible pairs, orient each edge to define a spell logic, and maximize the number of ordered pairs (u,v) reachable as a first and last keyword of a valid spell.	Hard9	GraphTopological sort+2	No attempts yet	8s	512 MB	Judgeable
Lapin NoirFor each starting cell on a hex grid, decide whether a cat can always reach (0, 0) while a rabbit blocks cells, except inside the cat's hexagonal territory.	Hard9	Game theoryGeometry+1	No attempts yet	1s	512 MB	Judgeable