Problems

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Total results29,098 problems

Chiaki Sequence Revisited
Hard9
Math, Combinatorics+2
No attempts yet
Time limit
1s
Memory limit
256 MB
Judgeable
RMQ Similar Sequence
Hard9
Tree, Combinatorics+2
No attempts yet
Time limit
2s
Memory limit
256 MB
Judgeable
Lyndon Substring
Hard9
String, String matching+1
No attempts yet
Time limit
3s
Memory limit
256 MB
Judgeable
Postcards
Hard9
Graph, Divide and conquer+2
No attempts yet
Time limit
8s
Memory limit
256 MB
Judgeable
Addition
Hard9
String matching, Simulation+2
No attempts yet
Time limit
1s
Memory limit
256 MB
Judgeable
Pastry shop
Hard9
Dynamic programming, Divide and conquer+1
No attempts yet
Time limit
2s
Memory limit
128 MB
Judgeable
Rikka with Proper Fractions
Hard9
Number theory, Math+2
No attempts yet
Time limit
10s
Memory limit
512 MB
Judgeable
Rikka with Tree Game
Hard9
Game theory, Tree+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Rikka with Equation
Hard9
Math, Number theory
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Rikka with Mirror
Hard9
Dynamic programming, Bit manipulation+1
No attempts yet
Time limit
14s
Memory limit
512 MB
Judgeable
Rikka with String
Hard9
String, String matching+1
No attempts yet
Time limit
6s
Memory limit
512 MB
Judgeable
Unseen Segments
Hard9
Geometry, Sorting+2
No attempts yet
Time limit
2s
Memory limit
256 MB
Judgeable
Convolution
Hard9
Divide and conquer, Combinatorics+1
No attempts yet
Time limit
3s
Memory limit
512 MB
Judgeable
Good Game
Hard9
Combinatorics, Dynamic programming+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Jump Jump Jump
Hard9
Probability, Dynamic programming+1
No attempts yet
Time limit
5s
Memory limit
512 MB
Judgeable
Doublindromes
Hard9
String, String matching+2
No attempts yet
Time limit
3s
Memory limit
512 MB
Judgeable
Entanglement
Hard9
Combinatorics, Graph+1
No attempts yet
Time limit
3s
Memory limit
256 MB
Judgeable
Salaj
Hard9
Dynamic programming, Combinatorics+1
No attempts yet
Time limit
2s
Memory limit
256 MB
Judgeable
Taxi
Hard9
Tree, Dynamic programming+2
No attempts yet
Time limit
1.5s
Memory limit
256 MB
Judgeable
Candies
Hard9
Number theory, Math+2
No attempts yet
Time limit
1s
Memory limit
512 MB
Judgeable
Nice Numbers
Hard9
Combinatorics, Number theory+2
No attempts yet
Time limit
1s
Memory limit
512 MB
Judgeable
New Divide
Hard9
Bit manipulation, Trie+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
In the End
Hard9
Probability, Dynamic programming+1
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Connectivity
Hard9
Union-find, Graph+2
No attempts yet
Time limit
8s
Memory limit
256 MB
Judgeable
Ants
Hard9
Tree, Segment tree+2
No attempts yet
Time limit
5s
Memory limit
256 MB
Judgeable
Array Challenge
Hard9
Math, Number theory+2
No attempts yet
Time limit
1s
Memory limit
512 MB
Judgeable
Function Counting
Hard9
Combinatorics, Dynamic programming+1
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Master Zhu and Magic Numbers
Hard9
Bit manipulation, Implementation+2
No attempts yet
Time limit
1s
Memory limit
512 MB
Judgeable
Master Zhu and Candies
Hard9
Game theory, Math+2
No attempts yet
Time limit
3s
Memory limit
512 MB
Judgeable
Master Zhu and Rikka
Hard9
Tree, DFS+2
No attempts yet
Time limit
3s
Memory limit
512 MB
Judgeable
Master Zhu and Root
Hard9
Number theory, Math+2
No attempts yet
Time limit
3s
Memory limit
512 MB
Judgeable
Master Zhu and the Leaper
Hard9
Dynamic programming, Combinatorics+2
No attempts yet
Time limit
1s
Memory limit
512 MB
Judgeable
Random Points
Hard9
Geometry, Combinatorics+2
No attempts yet
Time limit
5s
Memory limit
512 MB
Judgeable
Long Binary Sequence
Hard9
String matching, String+1
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
GCD vs LCM
Hard9
Number theory, Math+2
No attempts yet
Time limit
2.5s
Memory limit
512 MB
Judgeable
Power of XOR
Hard9
Bit manipulation, Math+2
No attempts yet
Time limit
6s
Memory limit
512 MB
Judgeable
Aho
Hard9
String, String matching+1
No attempts yet
Time limit
1s
Memory limit
512 MB
Judgeable
Fulkerson
Hard9
Tree, Dynamic programming+1
No attempts yet
Time limit
5s
Memory limit
512 MB
Judgeable
Performance Review
Hard9
Dynamic programming, Binary search+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Joke
Hard9
String matching, Dynamic programming+2
No attempts yet
Time limit
1s
Memory limit
512 MB
Judgeable
Game
Hard9
Game theory, Dynamic programming+1
No attempts yet
Time limit
8s
Memory limit
512 MB
Judgeable
Bermutation
Hard9
Combinatorics, Math+1
No attempts yet
Time limit
2s
Memory limit
256 MB
Judgeable
Strange Sequence
Hard9
Matrix, Math+1
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Catalan Combinatorial Objects
Hard9
Combinatorics, Math+1
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Isomorphism
Hard9
Graph, BFS+1
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Masterpiece
Hard9
Combinatorics, Math+1
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Airport Check-in
Hard9
Probability, Math+1
No attempts yet
Time limit
1s
Memory limit
256 MB
Judgeable
Beyond the Rescue
Hard9
Tree, Shortest path+1
No attempts yet
Time limit
3s
Memory limit
256 MB
Judgeable
Fresh Matrix
Hard9
Dynamic programming, Matrix+1
No attempts yet
Time limit
6s
Memory limit
256 MB
Judgeable
Short Random Problem
Hard9
Tree, Probability+2
No attempts yet
Time limit
6s
Memory limit
512 MB
Judgeable
Earthquake
Hard9
Probability, Dynamic programming+2
No attempts yet
Time limit
1s
Memory limit
512 MB
Judgeable
Window XOR
Hard9
Math, Bit manipulation+2
No attempts yet
Time limit
2s
Memory limit
1024 MB
Judgeable
Conic Section
Hard9
Segment tree, Geometry+1
No attempts yet
Time limit
3s
Memory limit
256 MB
Judgeable
Connected Subgraph
Hard9
Tree, Dynamic programming+1
No attempts yet
Time limit
1s
Memory limit
256 MB
Judgeable
Dogs
Hard9
Graph, Combinatorics+1
No attempts yet
Time limit
2s
Memory limit
256 MB
Judgeable
Compressed Spanning Subtrees
Hard9
Tree, Divide and conquer+1
No attempts yet
Time limit
2s
Memory limit
256 MB
Judgeable
Prefix-free Queries
Hard9
String, Trie+2
No attempts yet
Time limit
2s
Memory limit
256 MB
Judgeable
Flip a Coin
Hard9
Probability, Dynamic programming+2
No attempts yet
Time limit
1s
Memory limit
256 MB
Judgeable
Multi-stage Marathon
Hard9
Matrix, Dynamic programming+1
No attempts yet
Time limit
3s
Memory limit
512 MB
Judgeable
Compressed LCS
Hard9
Dynamic programming, Greedy+1
No attempts yet
Time limit
3s
Memory limit
512 MB
Judgeable
K-th String
Hard9
String, Combinatorics+2
No attempts yet
Time limit
1s
Memory limit
256 MB
Judgeable
Kitamasa's Counterattack
Hard9
Graph, Bit manipulation+1
No attempts yet
Time limit
2s
Memory limit
256 MB
Judgeable
Those Russian Hackers
Hard9
Dynamic programming, Probability+2
No attempts yet
Time limit
3s
Memory limit
256 MB
Judgeable
Defense Tower
Hard9
Tree, Divide and conquer+1
No attempts yet
Time limit
6s
Memory limit
512 MB
Judgeable
Palindrome
Hard9
String, String matching+1
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Territory Game
Hard9
Tree, Game theory+1
No attempts yet
Time limit
3s
Memory limit
512 MB
Judgeable
Ascent Sequences Avoiding Pattern 201
Hard9
Dynamic programming, Combinatorics+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Inversions in Lexicographical Order
Hard9
Combinatorics, Dynamic programming+1
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Connected Spanning Subgraph
Hard9
Graph, Combinatorics+2
No attempts yet
Time limit
1s
Memory limit
512 MB
Judgeable
Power of Power Partition Function
Hard9
Number theory, Divide and conquer+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Line Counting
Hard9
Number theory, Geometry+1
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Maximum Flow
Hard9
Graph, Shortest path+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Born Slippy
Hard9
Tree, Dynamic programming+2
No attempts yet
Time limit
6s
Memory limit
256 MB
Judgeable
Memento Mori
Hard9
Matrix, Dynamic programming+1
No attempts yet
Time limit
2.5s
Memory limit
64 MB
Judgeable
Binary Neural Network
Hard9
Implementation, Greedy+2
No attempts yet
Time limit
2s
Memory limit
256 MB
Judgeable
Bitwise Range Queries
Hard9
Segment tree, Bit manipulation+2
No attempts yet
Time limit
3s
Memory limit
512 MB
Judgeable
Simple Graph
Hard9
Combinatorics, Dynamic programming+2
No attempts yet
Time limit
1s
Memory limit
512 MB
Judgeable
Parentheses
Hard9
Combinatorics, Math+1
No attempts yet
Time limit
1s
Memory limit
512 MB
Judgeable
Values on a Tree
Hard9
Tree, Dynamic programming+2
No attempts yet
Time limit
1s
Memory limit
512 MB
Judgeable
Suffix Array for Thue-Morse
Hard9
Array, String+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Process with Constant Sum
Hard9
Segment tree, Prefix sum+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Generator
Hard9
Probability, String matching+2
No attempts yet
Time limit
3s
Memory limit
256 MB
Judgeable
Honey Tour
Hard9
Dynamic programming, Bit manipulation+2
No attempts yet
Time limit
1s
Memory limit
256 MB
Judgeable
Jong Hyok and String
Hard9
String, Trie+2
No attempts yet
Time limit
1s
Memory limit
1024 MB
Judgeable
Less Time, More Profit
Hard9
Dynamic programming, Graph+2
No attempts yet
Time limit
1s
Memory limit
256 MB
Judgeable
Pet Tree
Hard9
Dynamic programming, Tree+2
No attempts yet
Time limit
8s
Memory limit
1024 MB
Judgeable
Matrix and Queries
Hard9
Math, Matrix+2
No attempts yet
Time limit
5s
Memory limit
512 MB
Judgeable
Rectangle
Hard9
Math, Combinatorics+2
No attempts yet
Time limit
1s
Memory limit
256 MB
Judgeable
Navigation Game
Hard9
Greedy, Implementation+2
No attempts yet
Time limit
1s
Memory limit
256 MB
Judgeable
Fence
Hard9
Geometry, Binary search+2
No attempts yet
Time limit
1s
Memory limit
1024 MB
Judgeable
Shopping Plans
Hard9
Divide and conquer, Heap+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Human Error
Hard9
Game theory, Bit manipulation+2
No attempts yet
Time limit
1s
Memory limit
512 MB
Judgeable
Wrong Answer
Hard9
Greedy, Dynamic programming+2
No attempts yet
Time limit
1s
Memory limit
512 MB
Judgeable
Sequence and Queries 39
Hard9
Segment tree, Math+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Jump
Hard9
Shortest path, Graph+2
No attempts yet
Time limit
1s
Memory limit
512 MB
Judgeable
Landlords
Hard9
Probability, Math+1
No attempts yet
Time limit
1s
Memory limit
512 MB
Judgeable
Explore
Hard9
Graph, Divide and conquer+2
No attempts yet
Time limit
1s
Memory limit
512 MB
Judgeable
Holy cow, Vim! (Easy)
Hard9
Implementation, Simulation+2
No attempts yet
Time limit
1s
Memory limit
512 MB
Judgeable
Holy cow, Vim! (Hard)
Hard9
Implementation, Stack+2
No attempts yet
Time limit
1s
Memory limit
512 MB
Judgeable
Star Trek
Hard9
Game theory, Tree+2
No attempts yet
Time limit
1s
Memory limit
32 MB
Judgeable

Title	Level	Topics	Solved	Time limit	Memory limit	Judge
Chiaki Sequence RevisitedSum the first n terms of the self-referential Chiaki sequence, where each term depends on earlier terms via a_{n-a_{n-1}} + a_{n-1-a_{n-2}}, modulo 1e9+7.	Hard9	MathCombinatorics+2	No attempts yet	1s	256 MB	Judgeable
RMQ Similar SequenceGiven sequence A, count the expected sum of a random real sequence B in [0,1] that has identical RMQ answers to A for every subarray, modulo 1e9+7.	Hard9	TreeCombinatorics+2	No attempts yet	2s	256 MB	Judgeable
Lyndon SubstringFor each query (i, j), find the length of the longest Lyndon substring of the concatenation s_i s_j, given n strings and m queries.	Hard9	StringString matching+1	No attempts yet	3s	256 MB	Judgeable
PostcardsFor each shutdown plan, count the cities that can reach every other city when some roads are closed in one direction, with each plan decoded from earlier answers.	Hard9	GraphDivide and conquer+2	No attempts yet	8s	256 MB	Judgeable
AdditionDesign a short string-rewriting script in a custom language that reads two binary numbers joined by + and rewrites them into their binary sum.	Hard9	String matchingSimulation+2	No attempts yet	1s	256 MB	Judgeable
Pastry shopFor each oven baking time d, find the minimum total customer waiting time when pies are baked one at a time, starting at time 0.	Hard9	Dynamic programmingDivide and conquer+1	No attempts yet	2s	128 MB	Judgeable
Rikka with Proper FractionsCount reduced proper fractions e/f with f at most n lying between two given fractions a/b and c/d, answering modulo 998244353.	Hard9	Number theoryMath+2	No attempts yet	10s	512 MB	Judgeable
Rikka with Tree GameOn a rooted tree where players alternately move a token to a child and the score is the final depth, repeatedly attach leaves and find the limit of f(k)/k, where f(k) is the fewest additions making the optimal score exactly k.	Hard9	Game theoryTree+2	No attempts yet	2s	512 MB	Judgeable
Rikka with EquationFor each n, count tuples (a, b, m) with m at most n such that some integers x and y satisfy x^2 + y^2 is congruent to a and xy is congruent to b modulo m.	Hard9	MathNumber theory	No attempts yet	2s	512 MB	Judgeable
Rikka with MirrorGiven an n by m grid with some mirror slots, find for each k from 0 to nm the minimum total light path length over all 2(n+m) entry points when at most k mirrors are placed.	Hard9	Dynamic programmingBit manipulation+1	No attempts yet	14s	512 MB	Judgeable
Rikka with StringGiven a string over the letters a to l, decide for each suffix whether some permutation of the 12 letters can make that suffix the lexicographically largest suffix.	Hard9	StringString matching+1	No attempts yet	6s	512 MB	Judgeable
Unseen SegmentsGiven n vertical segments and queries of (west power, east power), find the total length of parts no observer sees through at most that many segments.	Hard9	GeometrySorting+2	No attempts yet	2s	256 MB	Judgeable
ConvolutionGiven sequences a and b of length n+1, compute c_k as the sum of C(k,i)·a_i·b_(k-i) modulo 2^32 for every k from 0 to n.	Hard9	Divide and conquerCombinatorics+1	No attempts yet	3s	512 MB	Judgeable
Good GameCount monotone lattice paths in n dimensions from the origin to a target, avoiding m forbidden points, modulo 1e9+7.	Hard9	CombinatoricsDynamic programming+2	No attempts yet	2s	512 MB	Judgeable
Jump Jump JumpGiven k jump vectors with coordinates up to 3, find for each x up to n the probability that a random walk from (0, 0) first lands on the diagonal point (x, x).	Hard9	ProbabilityDynamic programming+1	No attempts yet	5s	512 MB	Judgeable
DoublindromesCount distinct substrings of s that are palindromes and split into two non-empty palindromes, with length at least k.	Hard9	StringString matching+2	No attempts yet	3s	512 MB	Judgeable
EntanglementCount pairs of arrays A (length N) and B (length M) with values from 1 to K such that every cell C[i][j] equals A[i] or B[j].	Hard9	CombinatoricsGraph+1	No attempts yet	3s	256 MB	Judgeable
SalajFor each edge count j up to MAX, count the valid connectivity history arrays on V vertices with j edges, modulo MOD.	Hard9	Dynamic programmingCombinatorics+1	No attempts yet	2s	256 MB	Judgeable
TaxiSum over all ways to place M taxis and M customers on a weighted tree of the maximum-weight perfect matching cost, modulo 1e9+7.	Hard9	TreeDynamic programming+2	No attempts yet	1.5s	256 MB	Judgeable
CandiesFor each query k, count modulo 2 the pairs (child, candy kind) where buying only her favorite candy at that price leaves exactly k dollars.	Hard9	Number theoryMath+2	No attempts yet	1s	512 MB	Judgeable
Nice NumbersCount numbers in [L, R] that are pandigital (a permutation of all digits) in some base d, modulo 998244353, with L and R up to 5000-digit integers.	Hard9	CombinatoricsNumber theory+2	No attempts yet	1s	512 MB	Judgeable
New DivideFor every prefix of the array, split it into two contiguous parts maximizing the sum of the two parts' XOR values.	Hard9	Bit manipulationTrie+2	No attempts yet	2s	512 MB	Judgeable
In the EndEach column holds one cake at a random row, and the robot moves right with a row change of at most 1; find the limit of f(m)/m modulo 1e9+7.	Hard9	ProbabilityDynamic programming+1	No attempts yet	2s	512 MB	Judgeable
ConnectivityAfter each of m highways is added, count ordered city pairs (a,b) such that for every one of d types, a and b are connected using only that type's edges.	Hard9	Union-findGraph+2	No attempts yet	8s	256 MB	Judgeable
AntsOn a weighted tree, for each ant, find the largest number of other ants it meets at one point in time, either inside a tunnel or at an anthill.	Hard9	TreeSegment tree+2	No attempts yet	5s	256 MB	Judgeable
Array ChallengeGiven a linear recurrence h and closed-form arrays b and a, compute floor(sqrt(a_n)) modulo 1e9+7 for n up to 1e15.	Hard9	MathNumber theory+2	No attempts yet	1s	512 MB	Judgeable
Function CountingCount maps f on integers in [-n, n] where k applications of f send every x to -x and \| \|f(x)\| - \|x\| \| is at most 2. Print the count modulo 1e9+7.	Hard9	CombinatoricsDynamic programming+1	No attempts yet	2s	512 MB	Judgeable
Master Zhu and Magic NumbersGiven sparse positions of ones in a triangular binary layout, simulate a bitwise dependency program to get values b_j, then answer queries asking for the popcount of ORs of selected b_j.	Hard9	Bit manipulationImplementation+2	No attempts yet	1s	512 MB	Judgeable
Master Zhu and CandiesGiven n candy heaps, players may remove any positive number from one heap or split one heap into three non-empty heaps; decide the winner under optimal play.	Hard9	Game theoryMath+2	No attempts yet	3s	512 MB	Judgeable
Master Zhu and RikkaGiven a rooted tree with values on vertices, answer queries that ask for the GCD of sums of values occurring exactly a times and exactly b times in a subtree or on a path.	Hard9	TreeDFS+2	No attempts yet	3s	512 MB	Judgeable
Master Zhu and RootFor each query (x, y), find the smallest k >= 0 with x^k congruent to y modulo some prime divisor p of n, or report -1.	Hard9	Number theoryMath+2	No attempts yet	3s	512 MB	Judgeable
Master Zhu and the LeaperCount monotone leaper paths from (1,1) to (n,m) on a huge board with at most 100 blocked cells, modulo 110119.	Hard9	Dynamic programmingCombinatorics+2	No attempts yet	1s	512 MB	Judgeable
Random PointsGiven n points in general position, output 2^n times the expected number of vertices of the convex hull of a uniformly random subset, modulo 1e9+7.	Hard9	GeometryCombinatorics+2	No attempts yet	5s	512 MB	Judgeable
Long Binary SequenceCount the distinct consecutive substrings of a binary string of length up to 1e9, where the 1s are given at m up to 1000 positions.	Hard9	String matchingString+1	No attempts yet	2s	512 MB	Judgeable
GCD vs LCMFor each of q queries with n, m, a up to 1e5, sum lcm(i,j) over all i<=n, j<=m with gcd(i,j)<=a, modulo 1e9+7.	Hard9	Number theoryMath+2	No attempts yet	2.5s	512 MB	Judgeable
Power of XORGiven n integers, compute the sum over all 2^n subsets of the k-th power of the popcount of the XOR of the subset, modulo 1e9+7.	Hard9	Bit manipulationMath+2	No attempts yet	6s	512 MB	Judgeable
AhoAfter each character appended to hidden T, ask at most five equality queries, then report how many substrings of T equal hidden S.	Hard9	StringString matching+1	No attempts yet	1s	512 MB	Judgeable
FulkersonGiven a tree with N nodes, find for each K from 1 to N the smallest possible maximum distance from any node to its nearest of K chosen nodes.	Hard9	TreeDynamic programming+1	No attempts yet	5s	512 MB	Judgeable
Performance ReviewGiven yearly rounds where the Ri worst employees are replaced by given new hires, answer Q point-update queries asking whether employee 1 survives all M years.	Hard9	Dynamic programmingBinary search+2	No attempts yet	2s	512 MB	Judgeable
JokeGiven a text and up to ten patterns with per-letter erasure costs, delete letters so that no pattern occurs, minimizing total cost.	Hard9	String matchingDynamic programming+2	No attempts yet	1s	512 MB	Judgeable
GamePlayers alternately remove an end element from a sequence, and the mover who reaches a terminal sequence wins. Decide whether the first player, the second, or neither wins.	Hard9	Game theoryDynamic programming+1	No attempts yet	8s	512 MB	Judgeable
BermutationGiven a permutation and b, find the lexicographic rank of p among all permutations reachable by swapping the two halves of any 2b-length segment.	Hard9	CombinatoricsMath+1	No attempts yet	2s	256 MB	Judgeable
Strange SequenceGiven n up to 10^18, find the length of the n-th term of the look-and-say sequence starting from "2", modulo 7340033.	Hard9	MatrixMath+1	No attempts yet	2s	512 MB	Judgeable
Catalan Combinatorial ObjectsGiven k from 120 to 139, print a construction from lists, multisets, cycles, and pairs over one unit object that has exactly k objects of weight 6.	Hard9	CombinatoricsMath+1	No attempts yet	2s	512 MB	Judgeable
IsomorphismGiven n, output two non-isomorphic connected graphs on n vertices that share one degree profile and give every vertex a distinct profile, or print NO.	Hard9	GraphBFS+1	No attempts yet	2s	512 MB	Judgeable
MasterpieceCount the brush paths (a right/down route and a return left/up route) on an n by n grid whose painted cells match the given row and column counts, modulo 1e9+7.	Hard9	CombinatoricsMath+1	No attempts yet	2s	512 MB	Judgeable
Airport Check-inEach counter has a random per-passenger time and a random remaining time for the current passenger; find the probability that the counter finishing first is also the one with the smallest per-passenger time.	Hard9	ProbabilityMath+1	No attempts yet	1s	256 MB	Judgeable
Beyond the RescueFind the fastest path from s to t in a weighted tree that avoids every street the guards walk on their cyclic route, printed modulo 998244353 or -1.	Hard9	TreeShortest path+1	No attempts yet	3s	256 MB	Judgeable
Fresh MatrixCount the n-by-m 0/1 matrices with no two side-adjacent 1s whose 0 cells form one connected region, modulo a prime p with m up to 1e9.	Hard9	Dynamic programmingMatrix+1	No attempts yet	6s	256 MB	Judgeable
Short Random ProblemGiven a tree whose edge lengths are independent uniform random reals in [0, 1], find the expected diameter modulo 10^9+7.	Hard9	TreeProbability+2	No attempts yet	6s	512 MB	Judgeable
EarthquakeEach route is usable only if all its bridges survive; pick an adaptive inspection order of bridges to minimize the expected number of inspections before deciding whether any route connects the two lands.	Hard9	ProbabilityDynamic programming+2	No attempts yet	1s	512 MB	Judgeable
Window XORApply the operation that replaces each element with the XOR of K consecutive elements (cyclically) exactly T times, where T can be as large as 10^18.	Hard9	MathBit manipulation+2	No attempts yet	2s	1024 MB	Judgeable
Conic SectionPoints (i, y) receive single-point updates and range reflections of y, and each query asks for the max of ax + by + cxy over an x-range.	Hard9	Segment treeGeometry+1	No attempts yet	3s	256 MB	Judgeable
Connected SubgraphCount the ways to delete some edges from a tree plus k extra edges so the remaining graph stays connected, modulo 998244353.	Hard9	TreeDynamic programming+1	No attempts yet	1s	256 MB	Judgeable
DogsGiven a directed inspection graph on n villagers, sum over all sick-dog configurations the day of the first shooting and the total number of dogs shot, modulo 998244353.	Hard9	GraphCombinatorics+1	No attempts yet	2s	256 MB	Judgeable
Compressed Spanning SubtreesReconstruct a hidden tree with no degree-two vertices by asking how many vertices the compressed spanning subtree of a chosen set contains.	Hard9	TreeDivide and conquer+1	No attempts yet	2s	256 MB	Judgeable
Prefix-free QueriesGiven a string and queries of substring lists, count the prefix-free subsets of the substrings modulo m, for each query.	Hard9	StringTrie+2	No attempts yet	2s	256 MB	Judgeable
Flip a CoinTwo players each pick a heads/tails string of length up to 20; a fair coin is flipped until one or both strings appear, and we must output the probabilities of Alice winning, Bob winning, and a tie.	Hard9	ProbabilityDynamic programming+2	No attempts yet	1s	256 MB	Judgeable
Multi-stage MarathonGiven a directed graph of up to 70 checkpoints and players entering at set times, compute the XOR over all moments 1 to T of the expected number of players at checkpoint n, modulo 1e9+7.	Hard9	MatrixDynamic programming+1	No attempts yet	3s	512 MB	Judgeable
Compressed LCSGiven two run-length encoded sequences with up to 2000 runs each and total lengths up to 1e9, find the length of their LCS.	Hard9	Dynamic programmingGreedy+1	No attempts yet	3s	512 MB	Judgeable
K-th StringCount permutations t of n distinct letters whose k-th smallest non-empty substring equals s, modulo 1e9+7.	Hard9	StringCombinatorics+2	No attempts yet	1s	256 MB	Judgeable
Kitamasa's CounterattackKitamasa raises key prices by paying per-shop costs to maximize the gap between Akiba's purchase cost and his payment, so the answer is a min-cut or max-flow value, or -1 if unbounded.	Hard9	GraphBit manipulation+1	No attempts yet	2s	256 MB	Judgeable
Those Russian HackersGiven check-time and hacking-time distributions over k frames of length n, find the maximum probability of logging in and finishing the hack before any security check hits your session.	Hard9	Dynamic programmingProbability+2	No attempts yet	3s	256 MB	Judgeable
Defense TowerGiven a tree of cities with tower powers, each upgrade makes a tower the newest, and the task is to print the sum of protector labels after every upgrade.	Hard9	TreeDivide and conquer+1	No attempts yet	6s	512 MB	Judgeable
PalindromeGiven a string s, each query concatenates the length-l substrings starting at the listed positions and asks for the number of palindromic substrings of the result.	Hard9	StringString matching+1	No attempts yet	2s	512 MB	Judgeable
Territory GameGiven a tree and several games where Alice and Bob start at two vertices and color k moves each, find the optimal final value of A minus B.	Hard9	TreeGame theory+1	No attempts yet	3s	512 MB	Judgeable
Ascent Sequences Avoiding Pattern 201Count ascent sequences of length n that avoid the pattern 201, modulo a prime p, with n up to 500.	Hard9	Dynamic programmingCombinatorics+2	No attempts yet	2s	512 MB	Judgeable
Inversions in Lexicographical OrderGiven n with up to 250000 digits, count the inversions in the permutation formed by sorting 1 to n as strings.	Hard9	CombinatoricsDynamic programming+1	No attempts yet	2s	512 MB	Judgeable
Connected Spanning SubgraphGiven a connected undirected graph, count the non-empty edge subsets whose chosen edges form a connected spanning subgraph, and print the count modulo 2.	Hard9	GraphCombinatorics+2	No attempts yet	1s	512 MB	Judgeable
Power of Power Partition FunctionGiven n up to 1e18, m up to 1e18, and k up to 10, compute the sum of the k-th convolution power of the m-ary partition function up to n, modulo 1e9+7.	Hard9	Number theoryDivide and conquer+2	No attempts yet	2s	512 MB	Judgeable
Line CountingFor each n, counts the distinct lines through at least two points of the triangular lattice {(x, y): 1 <= x <= y <= n}, modulo 1000000007.	Hard9	Number theoryGeometry+1	No attempts yet	2s	512 MB	Judgeable
Maximum FlowGiven two paths of n vertices each plus 2n+1 cross edges with huge capacities, find the max flow from (0,0) to (1,n).	Hard9	GraphShortest path+2	No attempts yet	2s	512 MB	Judgeable
Born SlippyFor each vertex of a rooted tree, find the maximum weight of a walk up to an ancestor where consecutive weights combine by AND, OR, or XOR, then output a weighted sum.	Hard9	TreeDynamic programming+2	No attempts yet	6s	256 MB	Judgeable
Memento MoriCount submatrices with exactly four marked cells whose rows increase and whose columns follow the order given by permutation p, with no smaller qualifying submatrix inside.	Hard9	MatrixDynamic programming+1	No attempts yet	2.5s	64 MB	Judgeable
Binary Neural NetworkGiven a truth table of an n-input Boolean function (n up to 10), build a layered sigmoid network with at most 25 layers, 10^4 neurons, and 3*10^4 edges whose single output neuron approximates f.	Hard9	ImplementationGreedy+2	No attempts yet	2s	256 MB	Judgeable
Bitwise Range QueriesMaintain an array under range AND and OR updates and answer range minimum queries, all with n up to 5*10^5 and values below 2^30.	Hard9	Segment treeBit manipulation+2	No attempts yet	3s	512 MB	Judgeable
Simple GraphSum x^k over all simple graphs on n labeled vertices, where x counts the tree components, modulo 998244353.	Hard9	CombinatoricsDynamic programming+2	No attempts yet	1s	512 MB	Judgeable
ParenthesesCount parentheses strings of length n by their reversal-and-flip operation distance, then output the weighted sum of those counts modulo m.	Hard9	CombinatoricsMath+1	No attempts yet	1s	512 MB	Judgeable
Values on a TreeFor every K from 0 to n-1, count the non-empty vertex subsets of a tree whose maximum pairwise distance equals K, modulo 998244353.	Hard9	TreeDynamic programming+2	No attempts yet	1s	512 MB	Judgeable
Suffix Array for Thue-MorseGiven the order k of a Thue-Morse string of length 2^k, answer q queries for suf[p], the suffix array entries, with k up to 60.	Hard9	ArrayString+2	No attempts yet	2s	512 MB	Judgeable
Process with Constant SumGiven an array with point updates, find for each range query the maximum number of zeroes left after a maximal sequence of the two operations.	Hard9	Segment treePrefix sum+2	No attempts yet	2s	512 MB	Judgeable
GeneratorFind the expected number of random draws until all n given length-L sequences have each appeared as a contiguous block of the stream.	Hard9	ProbabilityString matching+2	No attempts yet	3s	256 MB	Judgeable
Honey TourFor each top entrance and bottom exit of K stacked copies of an N by M grid, find the maximum honey pots on a simple path and how many paths reach it.	Hard9	Dynamic programmingBit manipulation+2	No attempts yet	1s	256 MB	Judgeable
Jong Hyok and StringGiven n pattern strings, for each query string Q count the substrings T of the patterns with the same set of (pattern, end position) occurrence pairs as Q.	Hard9	StringTrie+2	No attempts yet	1s	1024 MB	Judgeable
Less Time, More ProfitChoose a subset of plants to build; a shop pays off only when every plant it needs is built. Minimize the maximum build time, then maximize profit within that time.	Hard9	Dynamic programmingGraph+2	No attempts yet	1s	256 MB	Judgeable
Pet TreeCount assignments of edge lengths (each within its own interval) to a tree's edges so the resulting tree diameter falls between S and E, modulo 1e9+7.	Hard9	Dynamic programmingTree+2	No attempts yet	8s	1024 MB	Judgeable
Matrix and QueriesGiven an N x N integer matrix and Q values x, output det(A - xI) mod 998244353 for each query.	Hard9	MathMatrix+2	No attempts yet	5s	512 MB	Judgeable
RectangleConstruct a 30 by 30 table of integers from 0 to 10^6 so that among all axis-aligned sub-rectangles, every integer from 1 to 50000 appears as some rectangle's sum.	Hard9	MathCombinatorics+2	No attempts yet	1s	256 MB	Judgeable
Navigation GameConstruct a 100x100 arrangement of the numbers 1 to 10000 that maximizes a navigation score, where jumps off the current row or column cost points.	Hard9	GreedyImplementation+2	No attempts yet	1s	256 MB	Judgeable
FenceGiven up to 50,000 points, find the minimum perimeter of a rectangle with arbitrary orientation that contains all of them.	Hard9	GeometryBinary search+2	No attempts yet	1s	1024 MB	Judgeable
Shopping PlansGiven items with types and costs and a count range per type, find the K cheapest subsets whose per-type counts fall within their ranges.	Hard9	Divide and conquerHeap+2	No attempts yet	2s	512 MB	Judgeable
Human ErrorGiven a grid of Justin and Donald pieces where each turn a player must capture an adjacent piece, and each player may restrict their candidate moves to a set of fixed size, compute Justin's win probability under optimal play with random move choice.	Hard9	Game theoryBit manipulation+2	No attempts yet	1s	512 MB	Judgeable
Wrong AnswerConstruct a cost matrix that makes a greedy two-character solution as far from optimal as possible, maximizing the ratio of its output to the true minimum.	Hard9	GreedyDynamic programming+2	No attempts yet	1s	512 MB	Judgeable
Sequence and Queries 39Maintain an array under range updates that add an arithmetic progression, and answer queries for the longest arithmetic-progression subarray inside a range.	Hard9	Segment treeMath+2	No attempts yet	2s	512 MB	Judgeable
JumpGiven cities at integer grid points and portals that jump from one city to any city inside an axis-aligned rectangle at a given cost, find the shortest time from city 1 to every city.	Hard9	Shortest pathGraph+2	No attempts yet	1s	512 MB	Judgeable
LandlordsGiven m riffle shuffles with split sizes A_i, find the expected value of f(i) for the card at each queried position c after all shuffles, modulo 998244353.	Hard9	ProbabilityMath+1	No attempts yet	1s	512 MB	Judgeable
ExploreAn interactive graph-reconstruction task: with limited modify, query, report, and check calls, determine every edge of an unknown undirected graph.	Hard9	GraphDivide and conquer+2	No attempts yet	1s	512 MB	Judgeable
Holy cow, Vim! (Easy)Construct a stack-language program that outputs x, but outputs 2x when its lines are reversed and -x when its lines are sorted lexicographically.	Hard9	ImplementationSimulation+2	No attempts yet	1s	512 MB	Judgeable
Holy cow, Vim! (Hard)Construct a stack-program whose lines, read normally, reversed, and lexicographically sorted, compute x, x squared, and negative x respectively.	Hard9	ImplementationStack+2	No attempts yet	1s	512 MB	Judgeable
Star TrekPlayers alternately claim unvisited planets in a tree copied into D universes and linked by D portals; count the portal placements where the first player wins.	Hard9	Game theoryTree+2	No attempts yet	1s	32 MB	Judgeable