Problems

Pick a problem and write your solution in the built-in editor. The judge runs it against real test cases while you watch, and the wider archive is open to read whenever you like.

This page is still under construction.

Parts of this page are still being built. What you see may change.

Total results21,088 problems

Black and WhiteHard9
Combinatorics, MathNo attempts yetTime limit1sMemory limit256 MB
Judgeable
Dirichlet k-th rootHard9
Number theory, Math +2No attempts yetTime limit1sMemory limit256 MB
Judgeable
KingHard9
Number theory, Math +1No attempts yetTime limit2sMemory limit256 MB
Judgeable
MoonHard9
Geometry, Probability +1No attempts yetTime limit2sMemory limit256 MB
Judgeable
PermutationHard9
Dynamic programming, CombinatoricsNo attempts yetTime limit1sMemory limit256 MB
Judgeable
All Pair Maximum FlowHard9
Graph, Divide and conquer +1No attempts yetTime limit6sMemory limit256 MB
Judgeable
TravelHard9
Graph, Dynamic programming +1No attempts yetTime limit2.5sMemory limit256 MB
Judgeable
Boss of all bossesHard9
Tree, DFS +2No attempts yetTime limit2sMemory limit512 MB
Judgeable
Ternary String RevolutionHard9
String, Math +2No attempts yetTime limit1sMemory limit256 MB
Judgeable
Stone GameHard9
Game theory, Number theory +2No attempts yetTime limit1sMemory limit256 MB
Judgeable
Fraction ReductionHard9
Math, Number theory +2No attempts yetTime limit1sMemory limit256 MB
Judgeable
MST CameraHard9
Minimum spanning tree, Divide and conquer +2No attempts yetTime limit7sMemory limit512 MB
Judgeable
NotebookHard9
Math, Bit manipulation +2No attempts yetTime limit1sMemory limit128 MB
Judgeable
Very Simple SumHard9
Math, Combinatorics +2No attempts yetTime limit3sMemory limit256 MB
Judgeable
An Unsure CatchHard9
Graph, Tree +2No attempts yetTime limit8sMemory limit256 MB
Judgeable
String TheoryHard9
String, String matching +2No attempts yetTime limit4sMemory limit512 MB
Judgeable
Data StructureHard9
Tree, DFS +1No attempts yetTime limit20sMemory limit512 MB
Judgeable
Recursive StringHard9
String, Recursion +2No attempts yetTime limit1sMemory limit256 MB
Judgeable
Grid TriangleHard9
Math, Number theory +2No attempts yetTime limit0.5sMemory limit1024 MB
Judgeable
Stock Price PredictionHard9
String matching, Sorting +2No attempts yetTime limit1sMemory limit1024 MB
Judgeable
Clique FestivalHard9
Graph, Shortest path +2No attempts yetTime limit2sMemory limit512 MB
Judgeable
Fibonaccis' vouchersHard9
Math, Combinatorics +2No attempts yetTime limit1sMemory limit256 MB
Judgeable
RoadHard9
Segment tree, Math +1No attempts yetTime limit4sMemory limit512 MB
Judgeable
SubsequencesHard9
Dynamic programming, Combinatorics +2No attempts yetTime limit5sMemory limit512 MB
Judgeable
Road InspectionHard9
Graph, Tree +2No attempts yetTime limit1.5sMemory limit512 MB
Judgeable
Modular KnapsackHard9
Dynamic programming, Number theory +1No attempts yetTime limit1.5sMemory limit256 MB
Judgeable
Handsome multisetsHard9
Number theory, Combinatorics +2No attempts yetTime limit15sMemory limit256 MB
Judgeable
PolynomialHard9
Math, Combinatorics +2No attempts yetTime limit3sMemory limit256 MB
Judgeable
Heretical MöbiusHard9
Number theory, String matching +1No attempts yetTime limit1sMemory limit256 MB
Judgeable
Immortal UniverseHard9
Dynamic programming, CombinatoricsNo attempts yetTime limit2sMemory limit512 MB
Judgeable
Philosophical BalanceHard9
String, Game theory +2No attempts yetTime limit1sMemory limit256 MB
Judgeable
Desperate Fire SurviveHard9
Segment tree, Greedy +1No attempts yetTime limit3sMemory limit256 MB
Judgeable
Eventual JourneyHard9
Graph, Shortest path +2No attempts yetTime limit1sMemory limit256 MB
Judgeable
Hat With An IntegerHard9
Array, Intervals +1No attempts yetTime limit2sMemory limit512 MB
Judgeable
Labeled Connected GraphsHard9
Combinatorics, Dynamic programming +2No attempts yetTime limit2sMemory limit512 MB
Judgeable
Number Of VerticesHard9
Graph, Implementation +2No attempts yetTime limit2sMemory limit512 MB
Judgeable
Inner ProductHard9
Tree, Divide and conquer +1No attempts yetTime limit3sMemory limit256 MB
Judgeable
Gleb EvstropovHard9
Segment tree, Array +2No attempts yetTime limit20sMemory limit512 MB
Judgeable
Kunyavskiy PavelHard9
Game theory, Dynamic programming +2No attempts yetTime limit3sMemory limit512 MB
Judgeable
Dungeon RelayHard9
Segment tree, Sorting +2No attempts yetTime limit2sMemory limit1024 MB
Judgeable
A Simple Tree ProblemHard9
Tree, DFS +2No attempts yetTime limit8sMemory limit1024 MB
Judgeable
Server ExpansionHard9
Combinatorics, Dynamic programming +2No attempts yetTime limit1sMemory limit512 MB
Judgeable
KućiceHard9
Geometry, Combinatorics +2No attempts yetTime limit1sMemory limit512 MB
Judgeable
Yet Another Minimax ProblemHard9
Geometry, Binary search +1No attempts yetTime limit2sMemory limit512 MB
Judgeable
Rooted MSTHard9
Minimum spanning tree, Divide and conquer +1No attempts yetTime limit3sMemory limit1024 MB
Judgeable
Bracelet CrossingsHard9
Geometry, Implementation +2No attempts yetTime limit2sMemory limit1024 MB
Judgeable
Tearing BarcodesHard9
String, Greedy +2No attempts yetTime limit1sMemory limit1024 MB
Judgeable
Tree ReconstructionHard9
Tree, Graph +2No attempts yetTime limit1sMemory limit512 MB
Judgeable
Regular Meeting 3Hard9
Tree, Greedy +2No attempts yetTime limit1sMemory limit1024 MB
Judgeable
Linear AlgebraHard9
Geometry, Segment tree +1No attempts yetTime limit2sMemory limit1024 MB
Judgeable
SequenceHard9
Bit manipulation, Math +2No attempts yetTime limit1sMemory limit1024 MB
Judgeable
AbductionHard9
Dynamic programming, Combinatorics +1No attempts yetTime limit1sMemory limit1024 MB
Judgeable
RabbitHard9
Game theory, SimulationNo attempts yetTime limitNot setMemory limit1024 MB
Judgeable
Pretty sequencesHard9
Combinatorics, Math +2No attempts yetTime limit0.4sMemory limit1024 MB
Judgeable
SgameHard9
String, Sorting +2No attempts yetTime limit4sMemory limit1024 MB
Judgeable
Game on two heapsHard9
Game theory, Math +2No attempts yetTime limit2sMemory limit1024 MB
Judgeable
Uniform StringHard9
String, Implementation +2No attempts yetTime limit1sMemory limit1024 MB
Judgeable
Avoiding AsteroidsHard9
Geometry, MathNo attempts yetTime limit1sMemory limit1024 MB
Judgeable
Integer GraphHard9
Number theory, Graph +2No attempts yetTime limit1sMemory limit512 MB
Judgeable
King Shipri Station, Exit GHard9
Graph, Shortest path +2No attempts yetTime limit2sMemory limit512 MB
Judgeable
AutobusHard9
Graph, Shortest path +2No attempts yetTime limit1sMemory limit512 MB
Judgeable
IzboriHard9
Divide and conquer, Hash map +2No attempts yetTime limit3sMemory limit512 MB
Judgeable
ParksHard9
Binary search, Greedy +2No attempts yetTime limit3sMemory limit512 MB
Judgeable
Railway Trip 2Hard9
Graph, Greedy +2No attempts yetTime limit2sMemory limit512 MB
Judgeable
Sandcastle 2Hard9
Sorting, Divide and conquer +1No attempts yetTime limit4sMemory limit1024 MB
Judgeable
Land PurchaseHard9
Graph, Minimum spanning tree +2No attempts yetTime limit1sMemory limit1024 MB
Judgeable
Land EqualityHard9
Dynamic programming, Bit manipulation +1No attempts yetTime limit1sMemory limit1024 MB
Judgeable
Even SubstringsHard9
Segment tree, Bit manipulation +2No attempts yetTime limit7sMemory limit1024 MB
Judgeable
Problem Set ConstructionHard9
Probability, Combinatorics +2No attempts yetTime limit1sMemory limit1024 MB
Judgeable
Super NineHard9
Combinatorics, Backtracking +2No attempts yetTime limit1sMemory limit512 MB
Judgeable
Notability IndexHard9
Number theory, Prefix sum +2No attempts yetTime limit2sMemory limit512 MB
Judgeable
First to SolveHard9
Probability, Combinatorics +2No attempts yetTime limit5sMemory limit512 MB
Judgeable
High PowersHard9
Math, Combinatorics +2No attempts yetTime limit2sMemory limit1024 MB
Judgeable
Tarzan JumpsHard9
Tree, Dynamic programming +1No attempts yetTime limit2sMemory limit256 MB
Judgeable
InversionsHard9
Math, CombinatoricsNo attempts yetTime limit3sMemory limit256 MB
Judgeable
MountainsHard9
Dynamic programming, Combinatorics +1No attempts yetTime limit1sMemory limit256 MB
Judgeable
Casual DancersHard9
Probability, Dynamic programming +1No attempts yetTime limit4sMemory limit512 MB
Judgeable
First OccurrenceHard9
String matching, Bit manipulation +2No attempts yetTime limit2sMemory limit512 MB
Judgeable
MismatchHard9
Bit manipulation, Combinatorics +1No attempts yetTime limit4sMemory limit512 MB
Judgeable
Spiral MatrixHard9
Matrix, Prefix sum +1No attempts yetTime limit4sMemory limit512 MB
Judgeable
DCMSFHard9
Graph, Minimum spanning tree +1No attempts yetTime limit2sMemory limit1024 MB
Judgeable
multiple edgesHard9
Graph, Union-find +1No attempts yetTime limit0.5sMemory limit1024 MB
Judgeable
Regional TourHard9
Tree, Dynamic programming +1No attempts yetTime limit4sMemory limit512 MB
Judgeable
JailHard9
Tree, Graph +2No attempts yetTime limit4sMemory limit1024 MB
Judgeable
Ants and SugarHard9
Segment tree, Greedy +1No attempts yetTime limit4sMemory limit1024 MB
Judgeable
EvolutionHard9
Tree, Dynamic programming +1No attempts yetTime limit2sMemory limit1024 MB
Judgeable
Find the Magic BeadHard9
Dynamic programming, Divide and conquer +1No attempts yetTime limit2sMemory limit1024 MB
Judgeable
Security SystemHard9
Graph, GeometryNo attempts yetTime limit2.5sMemory limit1024 MB
Judgeable
PalindromiHard9
String, String matching +1No attempts yetTime limit1sMemory limit512 MB
Judgeable
FarmHard9
Graph, Sorting +1No attempts yetTime limit1sMemory limit1024 MB
Judgeable
Tree GCDHard9
Tree, Divide and conquer +1No attempts yetTime limit2.5sMemory limit1024 MB
Judgeable
Cruel BordersHard9
Tree, Segment tree +2No attempts yetTime limit1.5sMemory limit1024 MB
Judgeable
Uplifting ExcursionHard9
Dynamic programming, MathNo attempts yetTime limit4sMemory limit512 MB
Judgeable
GameHard9
Graph, Divide and conquer +1No attempts yetTime limit2sMemory limit256 MB
Judgeable
Race for the GalaxyHard9
Dynamic programming, Combinatorics +1No attempts yetTime limit4sMemory limit1024 MB
Judgeable
Gravity HackenbushHard9
Graph, Game theory +1No attempts yetTime limit2sMemory limit1024 MB
Judgeable
Hide-and-Seek with a SpiritHard9
Implementation, Bit manipulation +1No attempts yetTime limit1sMemory limit1024 MB
Judgeable
Nieun Forest ArtistHard9
Combinatorics, Dynamic programming +1No attempts yetTime limit2sMemory limit1024 MB
Judgeable
Trees, Sets, and QueriesHard9
Tree, DFS +2No attempts yetTime limit4sMemory limit512 MB
Judgeable
Thousand IslandsHard9
Graph, DFS +1No attempts yetTime limit1sMemory limit1024 MB
Judgeable

Title	Level	Topics	Solved	Time limit	Memory limit	Judge
Black and WhiteCount monotone lattice paths from (0,0) to (n,m) whose white-minus-black cell score to the left equals k, modulo 998244353.	Hard9	CombinatoricsMath	No attempts yet	1s	256 MB	Judgeable
Dirichlet k-th rootGiven g on 1..n over F_p with g(1)=1, find f with f(1)=1 such that the k-fold Dirichlet convolution of f equals g, or report no solution.	Hard9	Number theoryMath+2	No attempts yet	1s	256 MB	Judgeable
KingGiven a prime p and a sequence B, find the longest subsequence where each term is the previous term times a fixed q mod p, or print -1 if it is under half of n.	Hard9	Number theoryMath+1	No attempts yet	2s	256 MB	Judgeable
MoonGiven n fixed points on a unit sphere, find the probability that a uniformly random extra point lets all points fit inside one hemisphere.	Hard9	GeometryProbability+1	No attempts yet	2s	256 MB	Judgeable
PermutationCount the distinct permutations reachable from a given one by rearranging elements next to an interval's minimum at either end, modulo 998244353.	Hard9	Dynamic programmingCombinatorics	No attempts yet	1s	256 MB	Judgeable
All Pair Maximum FlowGiven an outerplanar graph with edge capacities, compute the sum of maximum flows over all vertex pairs, modulo 998244353.	Hard9	GraphDivide and conquer+1	No attempts yet	6s	256 MB	Judgeable
TravelCount pairs of paths covering every vertex of a directed graph with at most one cycle per vertex, each vertex used at most k times in total, mod 998244353.	Hard9	GraphDynamic programming+1	No attempts yet	2.5s	256 MB	Judgeable
Boss of all bossesGiven a weighted tree, seat all n vertices on integer seats of a table so that every pairwise tree distance is at most the seat gap, and find the minimum possible table width.	Hard9	TreeDFS+2	No attempts yet	2s	512 MB	Judgeable
Ternary String RevolutionGiven a rewrite system on ternary strings, count for each query string the substrings of s that can be transformed into it.	Hard9	StringMath+2	No attempts yet	1s	256 MB	Judgeable
Stone GameFor piles (a,b) with 1<=a<=n and 1<=b<=m, count how many positions are a first-player win, a draw, or a second-player win, modulo 1e9+7, with n and m given as binary strings.	Hard9	Game theoryNumber theory+2	No attempts yet	1s	256 MB	Judgeable
Fraction ReductionFor each fraction a/b, find the minimum number of steps (negate-and-reciprocal, or add 1) to reach 0, modulo 1e9+7, or -1 if impossible.	Hard9	MathNumber theory+2	No attempts yet	1s	256 MB	Judgeable
MST CameraFor each query submatrix of an R by C grid of weighted edges, print the MST weight over N nodes, or -1 if those edges do not connect the graph.	Hard9	Minimum spanning treeDivide and conquer+2	No attempts yet	7s	512 MB	Judgeable
NotebookGiven a set of integers closed under doubling, halving when even, and xor, find the smallest reachable value; answer range queries with point updates.	Hard9	MathBit manipulation+2	No attempts yet	1s	128 MB	Judgeable
Very Simple SumSum (a_x+a_y+a_z+a_w)^(b_x xor b_y xor b_z xor b_w) over all n^4 index quadruples, modulo 998244353, with a_i, b_i at most 500.	Hard9	MathCombinatorics+2	No attempts yet	3s	256 MB	Judgeable
An Unsure CatchGiven a functional graph of prisoner moves a_i, find the fewest a_i to change so every prisoner can be caught, and the most arrests possible for each change budget j.	Hard9	GraphTree+2	No attempts yet	8s	256 MB	Judgeable
String TheoryCount substrings of S that equal some nonempty string repeated exactly k times, counting each occurrence position separately.	Hard9	StringString matching+2	No attempts yet	4s	512 MB	Judgeable
Data StructureGiven a tree rooted at node 1, add z to the nodes at distance y mod x below node a, and answer queries for a node's current weight.	Hard9	TreeDFS+1	No attempts yet	20s	512 MB	Judgeable
Recursive StringGiven a string T built by recursively wrapping characters around previous blocks, recover the original string S and repetition counts A.	Hard9	StringRecursion+2	No attempts yet	1s	256 MB	Judgeable
Grid TriangleCount triangles with integer vertices, one at the origin, inside a box, where each pair is a diagonal of an X by Y by Z cuboid for three distinct positive integers X, Y, Z.	Hard9	MathNumber theory+2	No attempts yet	0.5s	1024 MB	Judgeable
Stock Price PredictionFind every start position in y where the length-m window has the same relative-rank pattern (order-isomorphic) as the pattern sequence x.	Hard9	String matchingSorting+2	No attempts yet	1s	1024 MB	Judgeable
Clique FestivalGiven up to 18 weighted cliques added to a graph on n vertices, compute the sum of shortest-path distances over all vertex pairs.	Hard9	GraphShortest path+2	No attempts yet	2s	512 MB	Judgeable
Fibonaccis' vouchersGiven k and n, find the n-th smallest number expressible as a sum of exactly k Fibonacci values, or report that it exceeds 10^18.	Hard9	MathCombinatorics+2	No attempts yet	1s	256 MB	Judgeable
RoadProcess plow, salt, and blizzard events on a road of n segments and report the maximum snow depth on a range at a given minute, modulo 1e9+7.	Hard9	Segment treeMath+1	No attempts yet	4s	512 MB	Judgeable
SubsequencesGiven up to 20 short strings, count the permutations whose concatenation has an even number of distinct subsequences.	Hard9	Dynamic programmingCombinatorics+2	No attempts yet	5s	512 MB	Judgeable
Road InspectionThe graph is a unicyclic connected graph (one cycle plus trees). A road can be inspected only if removing it keeps the graph connected, so only cycle edges qualify. For each cycle edge, removing it turns the graph into a tree; the inconvenience equals the tree's diameter. We must count cycle edges and find the maximum resulting diameter over all single cycle-edge removals, with N up to 200,000.	Hard9	GraphTree+2	No attempts yet	1.5s	512 MB	Judgeable
Modular KnapsackGiven n items with weights and costs and a prime p, find for each remainder mod p the maximum total cost of a subset whose weight sum has that remainder.	Hard9	Dynamic programmingNumber theory+1	No attempts yet	1.5s	256 MB	Judgeable
Handsome multisetsCount, over all multisets of positive integers summing to n that uniquely represent every value 1 to n as a subset sum, the total number of elements, modulo a prime near 1e9.	Hard9	Number theoryCombinatorics+2	No attempts yet	15s	256 MB	Judgeable
PolynomialGiven a 0/1 polynomial of degree at most 20 and a huge n up to 1e16, count the odd coefficients in P(x)^n.	Hard9	MathCombinatorics+2	No attempts yet	3s	256 MB	Judgeable
Heretical MöbiusGiven a 200-character binary string t, find the first position p where t appears in the sequence \|mu(1)\|, \|mu(2)\|, ... up to 10^9, or report -1.	Hard9	Number theoryString matching+1	No attempts yet	1s	256 MB	Judgeable
Immortal UniverseCount the ways to fill the '?' characters in two P/V strings so the boy never goes bankrupt, modulo 998244353.	Hard9	Dynamic programmingCombinatorics	No attempts yet	2s	512 MB	Judgeable
Philosophical BalanceGiven a string, choose a probability distribution over its suffixes to maximize the minimum expected LCP against any suffix the guard picks.	Hard9	StringGame theory+2	No attempts yet	1s	256 MB	Judgeable
Desperate Fire SurviveFor each query [l, r, k], count the sub-segments that can be merged and trimmed into one node of level exactly k.	Hard9	Segment treeGreedy+1	No attempts yet	3s	256 MB	Judgeable
Eventual JourneyIn a connected graph whose vertices are colored 0 or 1, moving inside one color costs nothing and each edge costs one ticket; for every vertex, sum the ticket distances to all other vertices.	Hard9	GraphShortest path+2	No attempts yet	1s	256 MB	Judgeable
Hat With An IntegerGiven an array a and bounds b and c on consecutive differences, find the day on which some wise one first deduces a value not on his hat, or report -1.	Hard9	ArrayIntervals+1	No attempts yet	2s	512 MB	Judgeable
Labeled Connected GraphsSum the distance between vertices 1 and 2 over every labeled connected graph on n vertices, modulo a prime m.	Hard9	CombinatoricsDynamic programming+2	No attempts yet	2s	512 MB	Judgeable
Number Of VerticesMaintain a graph under edge insertions and deletions, and after each query report whether its edges can be partitioned into zigzag cycles (locally alternating around each vertex).	Hard9	GraphImplementation+2	No attempts yet	2s	512 MB	Judgeable
Inner ProductGiven two trees on n labeled vertices, compute the sum over all ordered pairs (i, j) of the first-tree distance times the second-tree distance, modulo 10^9+7.	Hard9	TreeDivide and conquer+1	No attempts yet	3s	256 MB	Judgeable
Gleb EvstropovWith point updates on an array, for each query find the largest m such that k, k+1, ..., m is a subsequence of the half-open range a[l:r).	Hard9	Segment treeArray+2	No attempts yet	20s	512 MB	Judgeable
Kunyavskiy PavelCount, over all assignments of integer pairs to the leaves of a binary tree, the total number of pure-strategy Nash equilibria of a two-player game where Carol picks children at even depth and David at odd depth.	Hard9	Game theoryDynamic programming+2	No attempts yet	3s	512 MB	Judgeable
Dungeon RelayGiven dungeons with difficulty, fee, and reward, and point updates to fee or reward, answer range queries asking whether a relay over a difficulty interval can be completed with starting cash c, and the final cash if so.	Hard9	Segment treeSorting+2	No attempts yet	2s	1024 MB	Judgeable
A Simple Tree ProblemMaintain a weighted tree under point updates to vertex and edge weights, and after each update report the sum over all paths of (vertex-weight sum) times (edge-weight sum).	Hard9	TreeDFS+2	No attempts yet	8s	1024 MB	Judgeable
Server ExpansionCount the ways to choose some of a distinguishable disks of each size 2^0..2^(k-1) so the chosen capacities sum to exactly n, modulo 1048573.	Hard9	CombinatoricsDynamic programming+2	No attempts yet	1s	512 MB	Judgeable
KućiceGiven n points in general position, each chosen independently with probability 1/2, find the expected number of points inside the convex hull of the chosen subset, output as the numerator over 2^n modulo 1e9+7.	Hard9	GeometryCombinatorics+2	No attempts yet	1s	512 MB	Judgeable
Yet Another Minimax ProblemGiven n integer points, pick a line with points on both sides so that the smallest distance from any point to the line is as large as possible, and print that distance.	Hard9	GeometryBinary search+1	No attempts yet	2s	512 MB	Judgeable
Rooted MSTEach query changes the weight of edge 0-i to w, and the task is to print the minimum spanning tree weight after every change.	Hard9	Minimum spanning treeDivide and conquer+1	No attempts yet	3s	1024 MB	Judgeable
Bracelet CrossingsGiven vertical sweep readings of colors along M lines, decide whether the closed non-crossing polygonal chains could still exist.	Hard9	GeometryImplementation+2	No attempts yet	2s	1024 MB	Judgeable
Tearing BarcodesGiven a long bracket string (a pattern repeated many times) and a second string attached to each purchased drink, find the maximum number of drinks you can buy, where each drink costs K valid-barcode fragments and each purchase yields a new string to tear.	Hard9	StringGreedy+2	No attempts yet	1s	1024 MB	Judgeable
Tree ReconstructionGiven a weighted tree, each query adds an edge and removes the heaviest edge on the resulting cycle except the new one, then reports the distance between two vertices in the new tree.	Hard9	TreeGraph+2	No attempts yet	1s	512 MB	Judgeable
Regular Meeting 3For each distance X from 1 to N, find the maximum number of vertices in a tree such that every pair is at distance exactly X.	Hard9	TreeGreedy+2	No attempts yet	1s	1024 MB	Judgeable
Linear AlgebraToggle 2D vectors in and out of a set, and report whether (a, b) is a sum of chosen vectors scaled by coefficients between 0 and 1.	Hard9	GeometrySegment tree+1	No attempts yet	2s	1024 MB	Judgeable
SequenceGiven the first m terms of a linear recurrence A_i = A_{i-1} + A_{i-m}, count how many of A_p through A_q are odd, with q up to 2^60.	Hard9	Bit manipulationMath+2	No attempts yet	1s	1024 MB	Judgeable
AbductionCount grid paths from the southwest corner to the northeast corner of a W by H street grid whose sequence of left and right turns matches a given string, with no U-turns and possible revisits, modulo 10^7.	Hard9	Dynamic programmingCombinatorics+1	No attempts yet	1s	1024 MB	Judgeable
RabbitGiven N cells and a rabbit that alternates S scared seconds and C curious seconds, output a fixed check sequence that finds the rabbit from any start.	Hard9	Game theorySimulation	No attempts yet	Not set	1024 MB	Judgeable
Pretty sequencesCount permutations of 1..N that contain at least one adjacent pair (x, x+1), modulo M, where N can reach 10^18 and M is up to 10^7 (not necessarily prime).	Hard9	CombinatoricsMath+2	No attempts yet	0.4s	1024 MB	Judgeable
SgameGiven a string and many queries (m, k), find the maximum occurrence count of a substring with length between m and k that cannot be extended to a longer string with the same count.	Hard9	StringSorting+2	No attempts yet	4s	1024 MB	Judgeable
Game on two heapsCount the first-player moves that win a subtraction game on two heaps, where a move taking x and y balls is illegal exactly when the ratio x:y equals the fixed starting ratio A:B.	Hard9	Game theoryMath+2	No attempts yet	2s	1024 MB	Judgeable
Uniform StringRepeatedly apply a reduction that maps zero-runs to 1 or 0 based on their lengths and count, and report when the string stops being uniform.	Hard9	StringImplementation+2	No attempts yet	1s	1024 MB	Judgeable
Avoiding AsteroidsDecide whether a ship with unknown speed can reach the base without hitting asteroids that move and tumble at unknown rates, printing Go or Surrender.	Hard9	GeometryMath	No attempts yet	1s	1024 MB	Judgeable
Integer GraphGiven n integers, find the minimum over removals of one value of the sum of pairwise shortest-path distances in a graph where each number connects to its smallest-prime-factor quotient.	Hard9	Number theoryGraph+2	No attempts yet	1s	512 MB	Judgeable
King Shipri Station, Exit GA graph with fixed edge lengths and a global offset added to edges outside a chosen path; queries walk from a node to G picking a lexicographically minimized path under a four-level rule, and updates add v to all edges off that path.	Hard9	GraphShortest path+2	No attempts yet	2s	512 MB	Judgeable
AutobusGiven a weighted directed graph with n up to 70 and m up to 10^6 edges, answer queries for the minimum travel time using at most k routes, where k can be as large as 10^9.	Hard9	GraphShortest path+2	No attempts yet	1s	512 MB	Judgeable
IzboriGiven a sequence of n dish values, count the subarrays whose most frequent value occurs strictly more times than every other value combined in that subarray.	Hard9	Divide and conquerHash map+2	No attempts yet	3s	512 MB	Judgeable
ParksOn a weighted tree, choose exactly k vertices as parks so the largest distance from any vertex to its nearest park is minimized, and output that distance plus one optimal choice.	Hard9	Binary searchGreedy+2	No attempts yet	3s	512 MB	Judgeable
Railway Trip 2Given lines as station intervals and a boarding rule that only allows the first K stops, find the minimum number of trains needed for each of Q trips, or -1 if impossible.	Hard9	GraphGreedy+2	No attempts yet	2s	512 MB	Judgeable
Sandcastle 2Count the rectangles whose cells can be visited by a path that steps only to adjacent cells with strictly lower heights.	Hard9	SortingDivide and conquer+1	No attempts yet	4s	1024 MB	Judgeable
Land PurchaseAssign every cell of an N by M grid to one of two owners to maximize per-cell profits plus bonuses for same-owner adjacent pairs, and output the assignment.	Hard9	GraphMinimum spanning tree+2	No attempts yet	1s	1024 MB	Judgeable
Land EqualitySplit an r by c grid of 0, 1, and 2 values into two connected pieces and find the smallest possible difference between the products of their cells.	Hard9	Dynamic programmingBit manipulation+1	No attempts yet	1s	1024 MB	Judgeable
Even SubstringsGiven a string over six letters and point updates, count for each range query the substrings in which every distinct letter occurs an even number of times.	Hard9	Segment treeBit manipulation+2	No attempts yet	7s	1024 MB	Judgeable
Problem Set ConstructionFor each problem, compute the probability that a randomly chosen k-problem set contains it and the team solves it, given teams maximize count then minimize total time under limit t.	Hard9	ProbabilityCombinatorics+2	No attempts yet	1s	1024 MB	Judgeable
Super NineGiven some triples of players from 1 to 9, extend them to a Steiner triple system on 9 points, or report that none exists.	Hard9	CombinatoricsBacktracking+2	No attempts yet	1s	512 MB	Judgeable
Notability IndexGiven a prime P and a digit string T, answer queries that ask how many substrings of T[l..r] form numbers divisible by P.	Hard9	Number theoryPrefix sum+2	No attempts yet	2s	512 MB	Judgeable
First to SolveFor each contestant in a contest with random problem orderings, compute the expected number of problems where they are among the earliest solvers, modulo 998244353.	Hard9	ProbabilityCombinatorics+2	No attempts yet	5s	512 MB	Judgeable
High PowersGiven symmetric sums s, t, u of three distinct complex numbers, compute a symmetric alternating expression in a, b, c raised to huge powers n and m, modulo 998244353.	Hard9	MathCombinatorics+2	No attempts yet	2s	1024 MB	Judgeable
Tarzan JumpsGiven tree heights, find for each k the fewest height changes needed so Tarzan can reach the last tree in at most k jumps.	Hard9	TreeDynamic programming+1	No attempts yet	2s	256 MB	Judgeable
InversionsFor length-n permutations, the task is to sum inv(p)^k over all permutations modulo 998244353, with n up to 10^18 and k up to 1000.	Hard9	MathCombinatorics	No attempts yet	3s	256 MB	Judgeable
MountainsCount n by m grids of non-negative heights, each at most k, whose maximum-weight monotone path from (1,1) to (n,m) has total sum at most k.	Hard9	Dynamic programmingCombinatorics+1	No attempts yet	1s	256 MB	Judgeable
Casual DancersThree friends random-walk on a number line, one random friend moves each second (+1 with p percent); output the expected final span modulo 998244353.	Hard9	ProbabilityDynamic programming+1	No attempts yet	4s	512 MB	Judgeable
First OccurrenceGiven l and r up to 10^18, find the smallest index where the Thue-Morse substring t[l..r] first appears in the sequence.	Hard9	String matchingBit manipulation+2	No attempts yet	2s	512 MB	Judgeable
MismatchFor each k from 1 to n, count the size-k subsequences whose bitwise AND is zero, modulo 998244353.	Hard9	Bit manipulationCombinatorics+1	No attempts yet	4s	512 MB	Judgeable
Spiral MatrixFor each query submatrix, decide whether some neighbour-connected path through all its cells visits a contiguous range of values.	Hard9	MatrixPrefix sum+1	No attempts yet	4s	512 MB	Judgeable
DCMSFFor each edge count from 1 to N-1, find the minimum weight spanning forest where special vertices meet degree caps and nice vertices have degree at most 1.	Hard9	GraphMinimum spanning tree+1	No attempts yet	2s	1024 MB	Judgeable
multiple edgesEdges are added and removed one query at a time in an online interactive stream, and after each query the program prints the number of connected components.	Hard9	GraphUnion-find+1	No attempts yet	0.5s	1024 MB	Judgeable
Regional TourFind a tree path with promotions in at least one of every M consecutive regions, maximizing total support and the ratio of support to time.	Hard9	TreeDynamic programming+1	No attempts yet	4s	512 MB	Judgeable
JailGiven a tree and M prisoner routes from bedroom to workroom, decide whether every prisoner can walk a shortest path without entering a room that is occupied.	Hard9	TreeGraph+2	No attempts yet	4s	1024 MB	Judgeable
Ants and SugarGiven Q online insertions of ants and sugar cubes on a line, after each operation report the maximum number of sugar cubes one ant can eat within distance L.	Hard9	Segment treeGreedy+1	No attempts yet	4s	1024 MB	Judgeable
EvolutionGiven a rooted tree that grows one leaf at a time, each query picks a subtree and finds the smallest possible maximum count of additional edges on any path after choosing main children.	Hard9	TreeDynamic programming+1	No attempts yet	2s	1024 MB	Judgeable
Find the Magic BeadSplit k+1 beads into M pouches to minimize the worst-case cleanup cost of finding the magic bead, for every k from 0 to N-1.	Hard9	Dynamic programmingDivide and conquer+1	No attempts yet	2s	1024 MB	Judgeable
Security SystemChoose which laser sensors to activate so that their beams to the walls never meet, maximizing the total importance of the chosen sensors.	Hard9	GraphGeometry	No attempts yet	2.5s	1024 MB	Judgeable
PalindromiEach concatenation joins two binary strings in a given order, and the task asks for the number of distinct palindromic substrings after each join.	Hard9	StringString matching+1	No attempts yet	1s	512 MB	Judgeable
FarmFind a longest route of trees Mr. P can visit by driving straight left, right, up, or diagonally up, and the fewest road rollers that cover the non-horizontal ruts.	Hard9	GraphSorting+1	No attempts yet	1s	1024 MB	Judgeable
Tree GCDGiven a tree with N vertices labeled 1 to N, compute the sum of gcd(i, j, dist(i, j)) over all pairs i less than j.	Hard9	TreeDivide and conquer+1	No attempts yet	2.5s	1024 MB	Judgeable
Cruel BordersGiven a tree rooted at state 1 with duties, handle online duty changes and new leaf states, and report what each representative pays while traveling to state 1.	Hard9	TreeSegment tree+2	No attempts yet	1.5s	1024 MB	Judgeable
Uplifting ExcursionGiven how many art pieces have each uplift from -M to M, find the maximum number you can pick so their uplifts sum to exactly L, or report impossible.	Hard9	Dynamic programmingMath	No attempts yet	4s	512 MB	Judgeable
GameAfter each added teleporter, report whether a cycle passes through a special planet 0 to k-1, which lets a tourist collect infinitely many stamps.	Hard9	GraphDivide and conquer+1	No attempts yet	2s	256 MB	Judgeable
Race for the GalaxyCount non-intersecting monotone grid paths for N runners with puddles and mud rows, grouped by how many runners cross the mud row S to S+1.	Hard9	Dynamic programmingCombinatorics+1	No attempts yet	4s	1024 MB	Judgeable
Gravity HackenbushGiven a graph of points grounded at y=0 with red, blue, and green segments, determine the winner when both players cut optimally.	Hard9	GraphGame theory+1	No attempts yet	2s	1024 MB	Judgeable
Hide-and-Seek with a SpiritThe spirit fills a 200x200 grid with values 1 to 24 so the seeker can find each of nine hiders' quadrants using one Find call and four Get calls.	Hard9	ImplementationBit manipulation+1	No attempts yet	1s	1024 MB	Judgeable
Nieun Forest ArtistCount the ways to tile an N by N square with L-shaped pieces of sizes 1 to N, where equal-town pieces never share an edge, up to rotation, modulo 998244353.	Hard9	CombinatoricsDynamic programming+1	No attempts yet	2s	1024 MB	Judgeable
Trees, Sets, and QueriesFor a tree, after each query adds u to U and v to V, decide whether the stones on U can slide one move at a time into V while staying independent, and sum the answers.	Hard9	TreeDFS+2	No attempts yet	4s	512 MB	Judgeable
Thousand IslandsFind a closed trip from island 0 that visits another island and leaves every canoe at its starting island U[i], using at most 2,000,000 sailings, or report that none exists.	Hard9	GraphDFS+1	No attempts yet	1s	1024 MB	Judgeable