Problems

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Total results21,553 problems

Scored NimHard8
Game theory, Dynamic programming +2No attempts yetTime limit2sMemory limit512 MB
Judgeable
Expected ValueHard8
Dynamic programming, Probability +2No attempts yetTime limit3sMemory limit16 MB
Judgeable
Game XHard8
Math, Greedy +2No attempts yetTime limit1sMemory limit512 MB
Judgeable
Glad You CameHard8
Segment tree, Implementation +2No attempts yetTime limit4sMemory limit512 MB
Judgeable
Bus StopHard8
Probability, Math +2No attempts yetTime limit2sMemory limit512 MB
Judgeable
Cake DistributionHard8
Math, Number theory +2No attempts yetTime limit1sMemory limit512 MB
Judgeable
Nonsense TimeHard8
Dynamic programming, Binary search +2No attempts yetTime limit12sMemory limit512 MB
Judgeable
Snowy SmileHard8
Dynamic programming, Sorting +2No attempts yetTime limit3sMemory limit512 MB
Judgeable
Game PredictionHard8
Dynamic programming, Game theory +2No attempts yetTime limit1sMemory limit512 MB
Judgeable
Block BreakerHard8
Union-find, Simulation +2No attempts yetTime limit2sMemory limit512 MB
Judgeable
AlakazamHard8
Math, Probability +2No attempts yetTime limit2sMemory limit512 MB
Judgeable
Restoring a PermutationHard8
Greedy, Sorting +2No attempts yetTime limit2sMemory limit512 MB
Judgeable
The Older We Are, The Worse It HurtsHard8
Tree, DFS +2No attempts yetTime limit2sMemory limit512 MB
Judgeable
ChallengeHard8
Tree, Greedy +2No attempts yetTime limit2sMemory limit512 MB
Judgeable
QuicksortHard8
Combinatorics, Probability +2No attempts yetTime limit2sMemory limit512 MB
Judgeable
Find the VertexHard8
Graph, BFS +2No attempts yetTime limit1sMemory limit512 MB
Judgeable
Road NetworkHard8
Tree, DFS +2No attempts yetTime limit2sMemory limit512 MB
Judgeable
Valar MorghulisHard8
Graph, Union-find +2No attempts yetTime limit2sMemory limit512 MB
Judgeable
AndorraHard8
Array, Hash map +2No attempts yetTime limit2sMemory limit512 MB
Judgeable
BaklawaHard8
Game theory, Geometry +2No attempts yetTime limit2sMemory limit512 MB
Judgeable
Crazy LCPHard8
String, Trie +2No attempts yetTime limit2sMemory limit512 MB
Judgeable
Awesome ShawarmaHard8
Tree, DFS +2No attempts yetTime limit14sMemory limit512 MB
Judgeable
Dull ChocolatesHard8
Prefix sum, Sorting +2No attempts yetTime limit9sMemory limit512 MB
Judgeable
Exciting MenusHard8
Trie, String +2No attempts yetTime limit4sMemory limit512 MB
Judgeable
KhoshafHard8
Dynamic programming, Combinatorics +2No attempts yetTime limit12sMemory limit512 MB
Judgeable
Invited SpeakersHard8
Geometry, Greedy +2No attempts yetTime limit2sMemory limit512 MB
Judgeable
BallsHard8
Array, Math +2No attempts yetTime limit1sMemory limit512 MB
Judgeable
ExpHard8
Probability, Dynamic programming +2No attempts yetTime limit5sMemory limit512 MB
Judgeable
Help Yourself (Gold)Hard8
Combinatorics, Sorting +2No attempts yetTime limit2sMemory limit512 MB
Judgeable
Bridge ConstructionHard8
Combinatorics, Dynamic programming +2No attempts yetTime limit2sMemory limit256 MB
Judgeable
Stray CatHard8
Graph, Greedy +2No attempts yetTime limit5sMemory limit512 MB
Judgeable
O Life of My YouthHard8
Sorting, Greedy +2No attempts yetTime limit2sMemory limit1024 MB
Judgeable
HaircutHard8
Sorting, Prefix sum +2No attempts yetTime limit1sMemory limit512 MB
Judgeable
Social DistancingHard8
Binary search, Greedy +2No attempts yetTime limit1sMemory limit512 MB
Judgeable
The Moo ParticleHard8
Sorting, Greedy +2No attempts yetTime limit1sMemory limit512 MB
Judgeable
New Year and ConferenceHard8
Intervals, Sorting +2No attempts yetTime limit2sMemory limit1024 MB
Judgeable
New Year and Castle ConstructionHard8
Geometry, Combinatorics +2No attempts yetTime limit3sMemory limit512 MB
Judgeable
Longest Increasing Subsequence ksHard8
Dynamic programming, Greedy +2No attempts yetTime limit0.25sMemory limit512 MB
Judgeable
CartoonsHard8
Two pointers, Divide and conquer +2No attempts yetTime limit2.5sMemory limit256 MB
Judgeable
Daycare ChildrenHard8
Combinatorics, Greedy +2No attempts yetTime limit2sMemory limit64 MB
Judgeable
Encryption FunctionHard8
Math, Dynamic programming +2No attempts yetTime limit1sMemory limit64 MB
Judgeable
Printer's HeadHard8
Greedy, Dynamic programming +1No attempts yetTime limit1.5sMemory limit64 MB
Judgeable
PasswordsHard8
Greedy, Sorting +2No attempts yetTime limit1.5sMemory limit64 MB
Judgeable
Alice and BobHard8
Game theory, Dynamic programming +2No attempts yetTime limit1sMemory limit512 MB
Judgeable
Hidden GraphHard8
Graph, Divide and conquer +2No attempts yetTime limit5sMemory limit512 MB
Judgeable
Banned WordsHard8
String matching, Trie +2No attempts yetTime limit2sMemory limit512 MB
Judgeable
Cost Of SubtreeHard8
Tree, Union-find +2No attempts yetTime limit1sMemory limit512 MB
Judgeable
Disk TroublesHard8
Math, Bit manipulation +2No attempts yetTime limit2sMemory limit512 MB
Judgeable
Non-Decreasing Subarray GameHard8
Game theory, Dynamic programming +2No attempts yetTime limit2sMemory limit256 MB
Judgeable
Tree HullHard8
Tree, DFS +2No attempts yetTime limit3sMemory limit256 MB
Judgeable
KnapsackHard8
Dynamic programming, Greedy +2No attempts yetTime limit3sMemory limit512 MB
Judgeable
Partition into TeamsHard8
Combinatorics, Math +2No attempts yetTime limit1sMemory limit256 MB
Judgeable
Classic QuotationHard8
String matching, Prefix sum +2No attempts yetTime limit1sMemory limit512 MB
Judgeable
Counting DivisorsHard8
Number theory, Math +2No attempts yetTime limit7sMemory limit512 MB
Judgeable
Lazy RunningHard8
Shortest path, Dynamic programming +2No attempts yetTime limit1sMemory limit256 MB
Judgeable
Matching In MultiplicationHard8
Graph, Math +2No attempts yetTime limit1sMemory limit512 MB
Judgeable
QuestionnaireHard8
Math, Number theory +2No attempts yetTime limit1sMemory limit512 MB
Judgeable
Bag of BagsHard8
Intervals, Union-find +2No attempts yetTime limit2sMemory limit256 MB
Judgeable
Balanced SequenceHard8
Greedy, Sorting +2No attempts yetTime limit1sMemory limit256 MB
Judgeable
Rikka with LinkerHard8
Bit manipulation, Dynamic programming +2No attempts yetTime limit2sMemory limit512 MB
Judgeable
Remove the TreeHard8
Tree, Greedy +2No attempts yetTime limit2sMemory limit256 MB
Judgeable
Exact ArithmeticHard8
Implementation, Math +2No attempts yetTime limit1sMemory limit512 MB
Judgeable
Hokusai ArtworksHard8
Graph, Dynamic programming +2No attempts yetTime limit1sMemory limit512 MB
Judgeable
Wavel SequenceHard8
Dynamic programming, Combinatorics +2No attempts yetTime limit1sMemory limit512 MB
Judgeable
Nutella's LifeHard8
Dynamic programming, Segment tree +1No attempts yetTime limit2sMemory limit512 MB
Judgeable
Oleg and Data ScienceHard8
Number theory, Math +2No attempts yetTime limit2sMemory limit256 MB
Judgeable
Christmas GarlandHard8
Array, Implementation +2No attempts yetTime limit2sMemory limit256 MB
Judgeable
Anna and Lucky TicketsHard8
Combinatorics, Dynamic programming +2No attempts yetTime limit2sMemory limit256 MB
Judgeable
Build the GraphHard8
Graph, Greedy +2No attempts yetTime limit1sMemory limit512 MB
Judgeable
Subsequence SumsHard8
Dynamic programming, Greedy +2No attempts yetTime limit1sMemory limit512 MB
Judgeable
Lying From YouHard8
Math, Geometry +2No attempts yetTime limit10sMemory limit512 MB
Judgeable
Leave Out All The RestHard8
Dynamic programming, Greedy +2No attempts yetTime limit2sMemory limit512 MB
Judgeable
FaintHard8
Combinatorics, Math +2No attempts yetTime limit1sMemory limit512 MB
Judgeable
Biggest NumberHard8
Segment tree, Sorting +2No attempts yetTime limit0.5sMemory limit256 MB
Judgeable
Hotter-colderHard8
Binary search, Implementation +2No attempts yetTime limit1sMemory limit256 MB
Judgeable
OnesHard8
Dynamic programming, Math +2No attempts yetTime limit1sMemory limit512 MB
Judgeable
SeatsHard8
Probability, Math +2No attempts yetTime limit1.5sMemory limit256 MB
Judgeable
PrimesHard8
Number theory, Prefix sum +2No attempts yetTime limit8sMemory limit256 MB
Judgeable
SchedulingHard8
Greedy, Sorting +2No attempts yetTime limit1sMemory limit256 MB
Judgeable
Boring GameHard8
Game theory, Combinatorics +2No attempts yetTime limit4sMemory limit512 MB
Judgeable
Brother and SisterHard8
Graph, Math +2No attempts yetTime limit1.5sMemory limit512 MB
Judgeable
MonkeysHard8
Tree, Dynamic programming +2No attempts yetTime limit4sMemory limit512 MB
Judgeable
ScheduleHard8
Intervals, Greedy +2No attempts yetTime limit2sMemory limit512 MB
Judgeable
Master Zhu and Math ProblemHard8
Math, Combinatorics +2No attempts yetTime limit3sMemory limit512 MB
Judgeable
Bipartite Graph ColoringHard8
Math, Dynamic programming +2No attempts yetTime limit12sMemory limit512 MB
Judgeable
Three PointsHard8
Geometry, Math +2No attempts yetTime limit1sMemory limit512 MB
Judgeable
Independent SetHard8
Dynamic programming, Tree +2No attempts yetTime limit2sMemory limit512 MB
Judgeable
Subset SumHard8
Heap, Sorting +2No attempts yetTime limit5sMemory limit512 MB
Judgeable
2x+2Hard8
Math, Greedy +2No attempts yetTime limit1sMemory limit512 MB
Judgeable
Escape SequencesHard8
String, Divide and conquer +2No attempts yetTime limit1sMemory limit512 MB
Judgeable
Balls and HolesHard8
Combinatorics, Bit manipulation +2No attempts yetTime limit0.5sMemory limit512 MB
Judgeable
Simple PolygonHard8
Geometry, Math +2No attempts yetTime limit1sMemory limit512 MB
Judgeable
Saddle PointHard8
Combinatorics, Dynamic programming +2No attempts yetTime limit1sMemory limit512 MB
Judgeable
GaloisHard8
Combinatorics, Math +2No attempts yetTime limit1sMemory limit512 MB
Judgeable
KolmogorovHard8
Graph, Dynamic programming +2No attempts yetTime limit1sMemory limit512 MB
Judgeable
Cleaning RobotsHard8
Tree, Dynamic programming +2No attempts yetTime limit1sMemory limit512 MB
Judgeable
Mission PossibleHard8
Geometry, Graph +1No attempts yetTime limit1sMemory limit512 MB
Judgeable
Addition RobotHard8
Segment tree, Matrix +2No attempts yetTime limit3sMemory limit512 MB
Judgeable
Yet Another Problem About PermutationsHard8
Combinatorics, Greedy +2No attempts yetTime limit3sMemory limit256 MB
Judgeable
Fibonacci's NightmareHard8
Probability, Dynamic programming +2No attempts yetTime limit2sMemory limit256 MB
Judgeable

Title	Level	Topics	Solved	Time limit	Memory limit	Judge
Scored NimPlayers alternately split a heap into two colored heaps until all heaps are size one; find Alice's optimal final white-stone count.	Hard8	Game theoryDynamic programming+2	No attempts yet	2s	512 MB	Judgeable
Expected ValueRepeatedly pick a random adjacent pair, replace the left value by its difference with the right, drop the right. Find the expected final value modulo 1e9+7.	Hard8	Dynamic programmingProbability+2	No attempts yet	3s	16 MB	Judgeable
Game XGiven n and k, decide whether exactly k pairs of nonzero, distinct-magnitude integers can have positive sum, and if so maximize the number of pairs whose product is positive.	Hard8	MathGreedy+2	No attempts yet	1s	512 MB	Judgeable
Glad You CameApply m range-max updates (a_j = max(a_j, v_i)) to a zero array, where each l, r, v comes from a fixed 32-bit RNG, then output the XOR of i*a_i.	Hard8	Segment treeImplementation+2	No attempts yet	4s	512 MB	Judgeable
Bus StopEach of n bus routes has independent waiting time uniform on [0, di]; find the expected minimum, output as a fraction modulo 998244353.	Hard8	ProbabilityMath+2	No attempts yet	2s	512 MB	Judgeable
Cake DistributionChoose up to 5000 positive integer cake pieces so that for each of A, B, C guests they can be split evenly, labeling each piece with its recipient for each case.	Hard8	MathNumber theory+2	No attempts yet	1s	512 MB	Judgeable
Nonsense TimeElements of a random permutation are unfrozen one at a time; after each unfreeze report the longest increasing subsequence length among the currently available elements.	Hard8	Dynamic programmingBinary search+2	No attempts yet	12s	512 MB	Judgeable
Snowy SmileGiven up to 2000 weighted points, find an axis-aligned rectangle maximizing the sum of weights of points inside or on its border, allowing an empty rectangle for zero.	Hard8	Dynamic programmingSorting+2	No attempts yet	3s	512 MB	Judgeable
Game PredictionFor each subarray query, compute both players' final scores when they alternately take the leftmost or rightmost element, playing optimally.	Hard8	Dynamic programmingGame theory+2	No attempts yet	1s	512 MB	Judgeable
Block BreakerBlocks drop in a grid when a knocked block has a dropped left/right neighbor and a dropped front/back neighbor; after each of q moves, report how many blocks fall.	Hard8	Union-findSimulation+2	No attempts yet	2s	512 MB	Judgeable
AlakazamGiven an array and range shuffle operations that permute a segment uniformly at random, answer point queries for the expected value at a position.	Hard8	MathProbability+2	No attempts yet	2s	512 MB	Judgeable
Restoring a PermutationGiven arrays a and b, construct a permutation p where a[i] is the LIS ending at i and b[i] is the longest decreasing subsequence starting at i.	Hard8	GreedySorting+2	No attempts yet	2s	512 MB	Judgeable
The Older We Are, The Worse It HurtsRoot the tree anywhere and order each node's children so that the weighted sum of DFS discovery times is minimized; output that minimum.	Hard8	TreeDFS+2	No attempts yet	2s	512 MB	Judgeable
ChallengeConstruct a tree with at most n vertices whose recursive center-removal decomposition puts some vertex in at least floor(sqrt(n)) different pieces.	Hard8	TreeGreedy+2	No attempts yet	2s	512 MB	Judgeable
QuicksortGiven a flawed quicksort with recursion depth limit k, find the expected number of inversions after running it on a uniformly random permutation of size n, times n! modulo 998244353.	Hard8	CombinatoricsProbability+2	No attempts yet	2s	512 MB	Judgeable
Find the VertexGiven a connected graph and the shortest-path distances from an unknown vertex s to all vertices modulo 3, find s.	Hard8	GraphBFS+2	No attempts yet	1s	512 MB	Judgeable
Road NetworkGiven a tree, add one edge so that the number of bridges in the resulting graph is minimized, and report that minimum count.	Hard8	TreeDFS+2	No attempts yet	2s	512 MB	Judgeable
Valar MorghulisGiven a graph of rivalries, for each query interval of edges decide whether the graph using only those edges is bipartite, and if so output the maximum possible size of one wing.	Hard8	GraphUnion-find+2	No attempts yet	2s	512 MB	Judgeable
AndorraProcess investors in order; for each, count contiguous intervals containing at least one free block of their type, then remove all free blocks of that type and report the remaining number of intervals.	Hard8	ArrayHash map+2	No attempts yet	2s	512 MB	Judgeable
BaklawaGiven a huge cuboid with up to 100 poisonous unit cells, players alternate cutting off a safe cuboid half; decide who wins under optimal play.	Hard8	Game theoryGeometry+2	No attempts yet	2s	512 MB	Judgeable
Crazy LCPGiven N strings and Q range queries, for each range [L, R] report the maximum longest common prefix over all pairs of distinct strings in that range.	Hard8	StringTrie+2	No attempts yet	2s	512 MB	Judgeable
Awesome ShawarmaGiven a tree, count the unordered pairs of nodes whose added edge leaves the number of bridges in [L, R].	Hard8	TreeDFS+2	No attempts yet	14s	512 MB	Judgeable
Dull ChocolatesCount prefix rectangles of a huge grid whose parity of white cells is odd versus even, given at most 1000 white cells.	Hard8	Prefix sumSorting+2	No attempts yet	9s	512 MB	Judgeable
Exciting MenusGiven N strings with a joy value per position, maximize over all substrings the product of its length, the joy at its end, and the number of strings having it as a prefix.	Hard8	TrieString+2	No attempts yet	4s	512 MB	Judgeable
KhoshafCount arrays of length N with entries in [L, R] that have exactly K contiguous subarrays whose sum is divisible by 3, modulo 1e9+7.	Hard8	Dynamic programmingCombinatorics+2	No attempts yet	12s	512 MB	Judgeable
Invited SpeakersGiven n red and n blue points in the plane with distinct x and y coordinates and no three collinear, draw n disjoint polygonal chains pairing each red point with a blue point.	Hard8	GeometryGreedy+2	No attempts yet	2s	512 MB	Judgeable
BallsGiven a row of colored balls, repeatedly pick a consecutive segment with a strict majority color and delete all other balls in it; count which colors can remain at the end.	Hard8	ArrayMath+2	No attempts yet	1s	512 MB	Judgeable
ExpEach of n independent monsters grants i experience (0 to k) with probability p_i, totals are capped at x, and the expected capped total must be computed modulo 998244353.	Hard8	ProbabilityDynamic programming+2	No attempts yet	5s	512 MB	Judgeable
Help Yourself (Gold)Sum the number of connected regions in the union of segments over all 2^N subsets, modulo 1e9+7.	Hard8	CombinatoricsSorting+2	No attempts yet	2s	512 MB	Judgeable
Bridge ConstructionCount unlabeled connected graphs on N vertices with maximum degree at most 4, modulo a prime X.	Hard8	CombinatoricsDynamic programming+2	No attempts yet	2s	256 MB	Judgeable
Stray CatMark the edges of a connected graph so that a cat walking from any town can reach town 0 in at most d+B steps, knowing only the mark types of edges at its current town and the last edge used.	Hard8	GraphGreedy+2	No attempts yet	5s	512 MB	Judgeable
O Life of My YouthGiven N pairs of happiness and fatigue with some values missing (0), find the largest K < N such that all young-day pairs can exceed all old-day pairs in happiness and stay below them in fatigue.	Hard8	SortingGreedy+2	No attempts yet	2s	1024 MB	Judgeable
HaircutFor each threshold j from 0 to N-1, clip every value above j down to j and count the resulting inversions.	Hard8	SortingPrefix sum+2	No attempts yet	1s	512 MB	Judgeable
Social DistancingPlace N cows on distinct integer grass points across M disjoint intervals on a line so that the minimum pairwise distance D is as large as possible, and output the largest achievable D.	Hard8	Binary searchGreedy+2	No attempts yet	1s	512 MB	Judgeable
The Moo ParticleGiven N points with distinct coordinates, one of two points may vanish when one dominates the other; find the minimum number of points that can remain.	Hard8	SortingGreedy+2	No attempts yet	1s	512 MB	Judgeable
New Year and ConferenceGiven n lectures, each with one time interval at venue a and another at venue b, decide whether every subset that is conflict-free at one venue is also conflict-free at the other.	Hard8	IntervalsSorting+2	No attempts yet	2s	1024 MB	Judgeable
New Year and Castle ConstructionGiven n points with no three collinear, count over all points p the number of 4-point subsets whose convex quadrilateral strictly contains p, and sum these counts.	Hard8	GeometryCombinatorics+2	No attempts yet	3s	512 MB	Judgeable
Longest Increasing Subsequence ksGiven a permutation-like sequence, find the K-th longest increasing subsequence when all LISs are sorted lexicographically by index, or -1 if fewer than K exist.	Hard8	Dynamic programmingGreedy+2	No attempts yet	0.25s	512 MB	Judgeable
CartoonsCount subarrays in which every sub-subarray contains at least one value that appears exactly once, over a sequence of up to 500,000 values.	Hard8	Two pointersDivide and conquer+2	No attempts yet	2.5s	256 MB	Judgeable
Daycare ChildrenAssign each of n children at least k toy kinds from floor(3k^2/2) available kinds so that every pair shares exactly one kind and no two sets are equal.	Hard8	CombinatoricsGreedy+2	No attempts yet	2s	64 MB	Judgeable
Encryption FunctionGiven the output of a digit-subset-sum encryption, find any positive integer that encrypts to it or report that none exists.	Hard8	MathDynamic programming+2	No attempts yet	1s	64 MB	Judgeable
Printer's HeadGiven a permutation of heights 1..n to print in order, find the minimum number of left-to-right or right-to-left sweeps, where each sweep prints positions in order with heights dropping by 1.	Hard8	GreedyDynamic programming+1	No attempts yet	1.5s	64 MB	Judgeable
PasswordsGiven n rows of m letters, permute the columns so the rows become lexicographically nondecreasing, choosing the smallest such permutation or reporting NIE.	Hard8	GreedySorting+2	No attempts yet	1.5s	64 MB	Judgeable
Alice and BobCount placements of at most one token per vertex on a colored DAG where Alice (white moves) beats Bob (black moves) under optimal play.	Hard8	Game theoryDynamic programming+2	No attempts yet	1s	512 MB	Judgeable
Hidden GraphFind a hidden undirected graph on n vertices, where every induced subgraph has a vertex of degree at most k, using at most 2nk+n independence queries that return an edge when the set is not independent.	Hard8	GraphDivide and conquer+2	No attempts yet	5s	512 MB	Judgeable
Banned WordsCount length-L strings over 26 letters avoiding a given set of banned substrings, modulo 998244353, with L up to 1e9.	Hard8	String matchingTrie+2	No attempts yet	2s	512 MB	Judgeable
Cost Of SubtreeGiven a tree with weighted edges, find a non-empty connected edge set maximizing its edge count times the minimum edge weight in it.	Hard8	TreeUnion-find+2	No attempts yet	1s	512 MB	Judgeable
Disk TroublesGiven a polynomial remainder Q(x) modulo a fixed degree-32 binary polynomial, find the smallest k with x^k mod P(x) equal to Q(x), inverting a discrete-log-like map.	Hard8	MathBit manipulation+2	No attempts yet	2s	512 MB	Judgeable
Non-Decreasing Subarray GameFor each query range, Yuto picks an integer to minimize and Platina then picks one to maximize the count of non-decreasing subarrays inside the interval they bound; output the resulting score.	Hard8	Game theoryDynamic programming+2	No attempts yet	2s	256 MB	Judgeable
Tree HullMaintain a set of tree vertices under insertions and deletions, and after each query report the total edge weight of the minimal subtree spanning the current set.	Hard8	TreeDFS+2	No attempts yet	3s	256 MB	Judgeable
KnapsackCount subsets of weights where each of n types has 2 copies and masses grow at least by a factor of 2, so the total equals W.	Hard8	Dynamic programmingGreedy+2	No attempts yet	3s	512 MB	Judgeable
Partition into TeamsFor n people each choosing red, blue, or spectator uniformly, compute 3^n times the probability that red wins, modulo a prime p.	Hard8	CombinatoricsMath+2	No attempts yet	1s	256 MB	Judgeable
Classic QuotationGiven strings S and T and queries (L, R), compute the expected number of occurrences of T after deleting a random substring spanning positions L to R, scaled by the number of choices.	Hard8	String matchingPrefix sum+2	No attempts yet	1s	512 MB	Judgeable
Counting DivisorsFor each query with l, r, k, compute the sum of d(i^k) for i from l to r, modulo 998244353, where d counts divisors.	Hard8	Number theoryMath+2	No attempts yet	7s	512 MB	Judgeable
Lazy RunningStarting and ending at checkpoint p2 on a 4-cycle, find the shortest closed walk whose swipe-recorded total distance is at least K, given the four edge lengths.	Hard8	Shortest pathDynamic programming+2	No attempts yet	1s	256 MB	Judgeable
Matching In MultiplicationGiven a bipartite graph where each of the n vertices on one side has degree 2, sum the products of edge weights over all perfect matchings, modulo 998244353.	Hard8	GraphMath+2	No attempts yet	1s	512 MB	Judgeable
QuestionnaireGiven n distinct positive integers, find a modulus m and residue k so that at least half the numbers are congruent to k mod m.	Hard8	MathNumber theory+2	No attempts yet	1s	512 MB	Judgeable
Bag of BagsProcess bags one by one; keep a bag unless its equality class merges two classes that were already equal, and report the decision for each.	Hard8	IntervalsUnion-find+2	No attempts yet	2s	256 MB	Judgeable
Balanced SequenceReorder n bracket strings to maximize the length of the longest balanced subsequence of their concatenation.	Hard8	GreedySorting+2	No attempts yet	1s	256 MB	Judgeable
Rikka with LinkerGiven a directed dependency graph on n libraries, find the shortest sequence of library names in which every edge (a,b) has some occurrence of a before some occurrence of b.	Hard8	Bit manipulationDynamic programming+2	No attempts yet	2s	512 MB	Judgeable
Remove the TreeGiven a tree, repeatedly delete the vertices of any chosen path (and incident edges); find the minimum number of path-deletions needed to remove every edge.	Hard8	TreeGreedy+2	No attempts yet	2s	256 MB	Judgeable
Exact ArithmeticSimulate a stack calculator whose values are sums of rationals and rational multiples of square roots, and print each result in a canonical exact form.	Hard8	ImplementationMath+2	No attempts yet	1s	512 MB	Judgeable
Hokusai ArtworksOn a directed graph, each city has a museum open only on even days; find the maximum total weight of distinct museums visitable starting at city 0 on an even day.	Hard8	GraphDynamic programming+2	No attempts yet	1s	512 MB	Judgeable
Wavel SequenceCount pairs of increasing index sequences from two arrays whose selected values are equal and form a strictly alternating up-down wave, modulo 998244353.	Hard8	Dynamic programmingCombinatorics+2	No attempts yet	1s	512 MB	Judgeable
Nutella's LifeChoose a subsequence of contests with nondecreasing values, where skipping x contests in a row costs x+1 each, to maximize total fun.	Hard8	Dynamic programmingSegment tree+1	No attempts yet	2s	512 MB	Judgeable
Oleg and Data ScienceCount positive integers X such that ((S mod Q) mod X) equals (S mod X) for every S in [L, R], or report infinity.	Hard8	Number theoryMath+2	No attempts yet	2s	256 MB	Judgeable
Christmas GarlandGiven a garland of n bulbs with colors, each query flips the state of every bulb of one color, and after each flip you report the number of maximal lit segments.	Hard8	ArrayImplementation+2	No attempts yet	2s	256 MB	Judgeable
Anna and Lucky TicketsCount n-digit palindromes that are lucky under neither the alternating-position sum test nor the first-half-versus-second-half sum test, modulo 1e9+7.	Hard8	CombinatoricsDynamic programming+2	No attempts yet	2s	256 MB	Judgeable
Build the GraphGiven n nodes and at most m edges, build an undirected graph minimizing the sum of all-pairs shortest distances, where unreachable pairs count as n.	Hard8	GraphGreedy+2	No attempts yet	1s	512 MB	Judgeable
Subsequence SumsGiven the multiset of all subsequence sums of a hidden positive-integer sequence, reconstruct the sequence, choosing the lexicographically smallest one.	Hard8	Dynamic programmingGreedy+2	No attempts yet	1s	512 MB	Judgeable
Lying From YouGiven n lines y = a_i x + b_i, change coefficients at L1 cost so all lines pass through one point; find the infimum total cost.	Hard8	MathGeometry+2	No attempts yet	10s	512 MB	Judgeable
Leave Out All The RestGiven two arrays with distinct values, interleave them into one sequence so that its longest increasing subsequence is as long as possible, and output that maximum length.	Hard8	Dynamic programmingGreedy+2	No attempts yet	2s	512 MB	Judgeable
FaintSum the absolute differences between consecutive rows of a fixed column in the lexicographically ordered list of k-subsets of {1,...,n}, modulo 1e9+7.	Hard8	CombinatoricsMath+2	No attempts yet	1s	512 MB	Judgeable
Biggest NumberAfter each of Q point updates to the digits on N cards, report the largest base-D number obtainable by rearranging the cards, modulo 1e9+7.	Hard8	Segment treeSorting+2	No attempts yet	0.5s	256 MB	Judgeable
Hotter-colderAn interactive problem: locate a hidden point in a d-dimensional integer grid using at most 100d queries that only report whether the latest Chebyshev distance got smaller or larger.	Hard8	Binary searchImplementation+2	No attempts yet	1s	256 MB	Judgeable
OnesFor each k up to 1e9, output a 1-expression using only ones, +, *, and parentheses that evaluates to k with at most 100 ones, or NO.	Hard8	Dynamic programmingMath+2	No attempts yet	1s	512 MB	Judgeable
SeatsGiven n prize values, choose one probability distribution over seats so that a player's expected prize, accounting for random contests at each seat, is maximized.	Hard8	ProbabilityMath+2	No attempts yet	1.5s	256 MB	Judgeable
PrimesAnswer online queries that ask for the sum of shared distinct prime counts over all pairs in a range [a, b] up to 10^6.	Hard8	Number theoryPrefix sum+2	No attempts yet	8s	256 MB	Judgeable
SchedulingDecide whether n preemptible tasks with release times, deadlines, and processing times can be scheduled on m identical processors within their windows.	Hard8	GreedySorting+2	No attempts yet	1s	256 MB	Judgeable
Boring GameDecide the winner of a coin-flipping game on a huge N by N board where each move flips a rectangle whose bottom-right corner is heads, with heads cells given as a union of M rectangles.	Hard8	Game theoryCombinatorics+2	No attempts yet	4s	512 MB	Judgeable
Brother and SisterGiven a functional graph on n labeled girls plus node 0, compute the expected number of queries before reaching 0 under a randomized probing process, modulo 1e9+7.	Hard8	GraphMath+2	No attempts yet	1.5s	512 MB	Judgeable
MonkeysChoose K vertices of a tree and delete edges so every chosen monkey can reach another, minimizing the number of surviving edges.	Hard8	TreeDynamic programming+2	No attempts yet	4s	512 MB	Judgeable
ScheduleAssign interval tasks to machines so no two overlapping tasks share a machine; minimize the number of machines, then the total working time (earliest start to latest finish) across those machines.	Hard8	IntervalsGreedy+2	No attempts yet	2s	512 MB	Judgeable
Master Zhu and Math ProblemCount quadruples (a,b,c,d) within given bounds that satisfy two linear inequalities, modulo 1e9+7, with bounds up to 1e18.	Hard8	MathCombinatorics+2	No attempts yet	3s	512 MB	Judgeable
Bipartite Graph ColoringSum, over all 2^n black/white colorings of a bipartite graph, the product of per-edge weights that depend on the colors of each edge's endpoints, modulo 1e9+7.	Hard8	MathDynamic programming+2	No attempts yet	12s	512 MB	Judgeable
Three PointsGiven three points A, B, C, find a point P minimizing \|PA\| + 2\|PB\| + 3\|PC\| and output that minimum distance.	Hard8	GeometryMath+2	No attempts yet	1s	512 MB	Judgeable
Independent SetCount vectors of n nonnegative integers summing to m where positions flagged by a and parent-child pairs in the implicit binary heap cannot both be positive, modulo 1e9+7.	Hard8	Dynamic programmingTree+2	No attempts yet	2s	512 MB	Judgeable
Subset SumGiven n integers, output the k smallest sums over all non-empty subsets, in ascending order.	Hard8	HeapSorting+2	No attempts yet	5s	512 MB	Judgeable
2x+2Given n up to 10^100, choose the largest subset of {1,...,n} with no x and 2x+2 both present.	Hard8	MathGreedy+2	No attempts yet	1s	512 MB	Judgeable
Escape SequencesFor a morphism f that replaces a with aa and b with ab, find the smallest k such that t is a substring of the k-fold iterate f^k(s).	Hard8	StringDivide and conquer+2	No attempts yet	1s	512 MB	Judgeable
Balls and HolesGiven n small sets of integers, count pairs (i<j) where pushing balls at S_i into holes at half-integers of S_j leaves an odd number of occupied holes.	Hard8	CombinatoricsBit manipulation+2	No attempts yet	0.5s	512 MB	Judgeable
Simple PolygonGiven a perimeter l and area s, construct a simple rectilinear polygon with exactly that perimeter and area, or report that none exists.	Hard8	GeometryMath+2	No attempts yet	1s	512 MB	Judgeable
Saddle PointCount the n by m matrices with entries in 1..k that contain at least one position that is a strict maximum of both its row and its column, modulo 1e9+7.	Hard8	CombinatoricsDynamic programming+2	No attempts yet	1s	512 MB	Judgeable
GaloisGiven a permutation p, count permutations q with p(q(i)) = q(p(i)) for all i, that have an even number of inversions, modulo 1e9+7.	Hard8	CombinatoricsMath+2	No attempts yet	1s	512 MB	Judgeable
KolmogorovIn a connected undirected graph where each minute one random edge lights up, find the minimum expected time for an optimal walker to travel from node 1 to node N.	Hard8	GraphDynamic programming+2	No attempts yet	1s	512 MB	Judgeable
Cleaning RobotsCount the ways to partition all vertices of a tree into vertex-disjoint paths such that no two paths can be merged into a longer path.	Hard8	TreeDynamic programming+2	No attempts yet	1s	512 MB	Judgeable
Mission PossibleGiven up to 50 disjoint circular sensors inside a rectangle, output at most 1000 waypoints for a polyline from start to target that stays inside the rectangle and never enters any sensor disk.	Hard8	GeometryGraph+1	No attempts yet	1s	512 MB	Judgeable
Addition RobotMaintain a binary string under range flips and answer queries that apply the range's A/B operations to a pair of numbers, modulo 1e9+7.	Hard8	Segment treeMatrix+2	No attempts yet	3s	512 MB	Judgeable
Yet Another Problem About PermutationsGiven a permutation, write it as a product of the fewest simple permutations, where each simple permutation has only cycles of length one or two, and output one optimal factorization.	Hard8	CombinatoricsGreedy+2	No attempts yet	3s	256 MB	Judgeable
Fibonacci's NightmareFor a random sequence built by summing two earlier terms, find the variance of the n-th term modulo 10^9+7.	Hard8	ProbabilityDynamic programming+2	No attempts yet	2s	256 MB	Judgeable