Problems

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Total results29,109 problems

Gnalcats
Hard9
String, Stack+2
No attempts yet
Time limit
0.3s
Memory limit
512 MB
Judgeable
Pilgrim's Memories and the Impressed God
Hard9
Dynamic programming, String+1
No attempts yet
Time limit
8s
Memory limit
1024 MB
Judgeable
Sorcerers of the Round Table
Hard9
Dynamic programming, Bit manipulation+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Speed Reading Course
Hard9
Number theory, String matching+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Flavor of the Function
Hard9
Graph, Tree+1
No attempts yet
Time limit
1.5s
Memory limit
1024 MB
Judgeable
Good Word, Bad Word
Hard9
Shortest path, Graph+2
No attempts yet
Time limit
2.5s
Memory limit
1024 MB
Judgeable
Tree and the K-th Diameter
Hard9
Tree, BFS+1
No attempts yet
Time limit
3s
Memory limit
1024 MB
Judgeable
Patrol Route
Hard9
Graph, Dynamic programming+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Tenkey
Hard9
Graph, BFS+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Graph Counting
Hard9
Combinatorics, Graph+2
No attempts yet
Time limit
5s
Memory limit
512 MB
Judgeable
Interesting Graph
Hard9
Graph, Dynamic programming+1
No attempts yet
Time limit
5s
Memory limit
512 MB
Judgeable
Knowledge
Hard9
String, Combinatorics+2
No attempts yet
Time limit
1s
Memory limit
512 MB
Judgeable
Airplane Cliques
Hard9
Tree, Divide and conquer+1
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Giant Penguin
Hard9
Graph, Tree+2
No attempts yet
Time limit
3s
Memory limit
512 MB
Judgeable
One Goal
Hard9
Combinatorics, Tree+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Bitwise Xor
Hard9
Bit manipulation, Trie+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Determinant
Hard9
Graph, Dynamic programming+1
No attempts yet
Time limit
5s
Memory limit
512 MB
Judgeable
Easy Win
Hard9
Game theory, Union-find+2
No attempts yet
Time limit
1.5s
Memory limit
512 MB
Judgeable
Grammarly
Hard9
String, Dynamic programming+1
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Four Elements
Hard9
Math, Combinatorics+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Six Words
Hard9
Graph, Minimum spanning tree+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Seven Nevers
Hard9
Dynamic programming, Segment tree+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Um_nik's Algorithm
Hard9
Graph, Greedy+2
No attempts yet
Time limit
4s
Memory limit
512 MB
Judgeable
String Algorithm
Hard9
String, Hash map+2
No attempts yet
Time limit
20s
Memory limit
512 MB
Judgeable
FFT Algorithm
Hard9
Number theory, Math+2
No attempts yet
Time limit
1.5s
Memory limit
512 MB
Judgeable
Bracket Euler Tour
Hard9
Graph, DFS+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
One Root
Hard9
Math, Number theory+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Another Coin Weighing Puzzle
Hard9
Combinatorics, Math+2
No attempts yet
Time limit
1s
Memory limit
512 MB
Judgeable
Grid Guardian
Hard9
Dynamic programming, Bit manipulation
No attempts yet
Time limit
8s
Memory limit
512 MB
Judgeable
Counting Edit Distances
Hard9
Dynamic programming, String+2
No attempts yet
Time limit
10s
Memory limit
512 MB
Judgeable
Rooted Subtrees
Hard9
Tree, DFS+2
No attempts yet
Time limit
11s
Memory limit
512 MB
Judgeable
Tomb Raider
Hard9
Graph, BFS+1
No attempts yet
Time limit
3s
Memory limit
512 MB
Judgeable
Basis Change
Hard9
Math, Implementation+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Quoridor
Hard9
Graph, BFS+1
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Nightmare
Hard9
Geometry, Sorting+1
No attempts yet
Time limit
1s
Memory limit
512 MB
Judgeable
Employees
Hard9
Dynamic programming, Combinatorics+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Modulo-magic squares
Hard9
Math, Combinatorics+2
No attempts yet
Time limit
1s
Memory limit
512 MB
Judgeable
Call It What You Want
Hard9
Number theory, Math+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Kaleidoscope
Hard9
Combinatorics, Math+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Expected Cost
Hard9
Combinatorics, Tree+2
No attempts yet
Time limit
3s
Memory limit
512 MB
Judgeable
Humongous String
Hard9
String, Math+1
No attempts yet
Time limit
1s
Memory limit
512 MB
Judgeable
Intellectual Prefix Maxima
Hard9
Tree, Divide and conquer+1
No attempts yet
Time limit
4s
Memory limit
512 MB
Judgeable
Long Game
Hard9
Game theory, Greedy+2
No attempts yet
Time limit
1s
Memory limit
512 MB
Judgeable
Milk Candy
Hard9
Matrix, Combinatorics+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Faraway
Hard9
Math, Number theory+2
No attempts yet
Time limit
1s
Memory limit
512 MB
Judgeable
TDL
Hard9
Number theory, Bit manipulation+2
No attempts yet
Time limit
1s
Memory limit
512 MB
Judgeable
Three Investigators
Hard9
Dynamic programming, Divide and conquer+1
No attempts yet
Time limit
5s
Memory limit
512 MB
Judgeable
Road Manager
Hard9
Minimum spanning tree, Graph+2
No attempts yet
Time limit
4s
Memory limit
512 MB
Judgeable
Monster Hunter
Hard9
Greedy, DFS+2
No attempts yet
Time limit
4s
Memory limit
512 MB
Judgeable
Line Graphs
Hard9
Graph, Combinatorics+1
No attempts yet
Time limit
5s
Memory limit
512 MB
Judgeable
Play Games with Rounddog
Hard9
String, String matching+2
No attempts yet
Time limit
5s
Memory limit
512 MB
Judgeable
Domino Covering
Hard9
Matrix, Dynamic programming+2
No attempts yet
Time limit
6s
Memory limit
512 MB
Judgeable
Make Rounddog Happy
Hard9
Divide and conquer, Two pointers+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Yet Another Convolution
Hard9
Number theory, Math+1
No attempts yet
Time limit
4s
Memory limit
512 MB
Judgeable
Magic Strings
Hard9
Dynamic programming, Matrix+2
No attempts yet
Time limit
4s
Memory limit
512 MB
Judgeable
Decimal Expansion
Hard9
Math, Number theory+2
No attempts yet
Time limit
1s
Memory limit
512 MB
Judgeable
Eevee
Hard9
Combinatorics, Probability+2
No attempts yet
Time limit
5s
Memory limit
512 MB
Judgeable
Hypno
Hard9
Graph, Shortest path+1
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Lati@s
Hard9
Game theory, Combinatorics+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Somewhere Over the Rainbow
Hard9
Dynamic programming, Math+1
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Goldberg Machine
Hard9
Tree, Segment tree+1
No attempts yet
Time limit
5s
Memory limit
512 MB
Judgeable
Linear Congruential Generator
Hard9
Math, Number theory+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
AtCoder Quality Problem
Hard9
Bit manipulation, Graph+1
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Count the Graphs
Hard9
Combinatorics, Dynamic programming+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Greatest Chicken Dish
Hard9
Dynamic programming, Number theory+2
No attempts yet
Time limit
15s
Memory limit
512 MB
Judgeable
The Halfwitters
Hard9
Dynamic programming, Graph+2
No attempts yet
Time limit
5s
Memory limit
512 MB
Judgeable
Lighthouses
Hard9
Dynamic programming, Geometry
No attempts yet
Time limit
15s
Memory limit
512 MB
Judgeable
Div
Hard9
Math, Number theory
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Ineq
Hard9
Geometry, Math+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Bitset Master
Hard9
Tree, Union-find+1
No attempts yet
Time limit
6s
Memory limit
512 MB
Judgeable
Cyclic Distance
Hard9
Tree, Dynamic programming+1
No attempts yet
Time limit
3s
Memory limit
512 MB
Judgeable
Data Structure Quiz
Hard9
Segment tree, Divide and conquer+1
No attempts yet
Time limit
8s
Memory limit
512 MB
Judgeable
Heavy Stones
Hard9
Greedy, Dynamic programming
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Knowledge-Oriented Problem
Hard9
Matrix, Math+1
No attempts yet
Time limit
5s
Memory limit
512 MB
Judgeable
LCM Sum
Hard9
Number theory, Math+1
No attempts yet
Time limit
7s
Memory limit
512 MB
Judgeable
Delightful (Hard)
Hard9
Number theory, Implementation+2
No attempts yet
Time limit
1s
Memory limit
512 MB
Judgeable
Xorshift32
Hard9
Math, Bit manipulation+2
No attempts yet
Time limit
1s
Memory limit
256 MB
Judgeable
Help Yourself (Platinum)
Hard9
Combinatorics, Dynamic programming+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
814 - 2
Hard9
Graph, DFS+2
No attempts yet
Time limit
0.814s
Memory limit
814 MB
Judgeable
Tree and Query 15
Hard9
Tree, Divide and conquer+1
No attempts yet
Time limit
5s
Memory limit
1024 MB
Judgeable
OR and Queries
Hard9
Segment tree, Bit manipulation+2
No attempts yet
Time limit
1.5s
Memory limit
256 MB
Judgeable
Karaoke Meetup
Hard9
Tree, DFS+2
No attempts yet
Time limit
8s
Memory limit
512 MB
Judgeable
Nonogram QR
Hard9
Backtracking, Simulation+2
No attempts yet
Time limit
1s
Memory limit
512 MB
Judgeable
Chameleon's Love
Hard9
Graph, Combinatorics+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Constellation 3
Hard9
Divide and conquer, Dynamic programming+1
No attempts yet
Time limit
1s
Memory limit
512 MB
Judgeable
Something in the Chest
Hard9
Union-find, Divide and conquer+2
No attempts yet
Time limit
3s
Memory limit
1024 MB
Judgeable
Sprinklers 2: Return of the Alfalfa
Hard9
Dynamic programming, Prefix sum+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Exercise
Hard9
Combinatorics, Number theory+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Cow Exercise
Hard9
Math, Number theory+2
No attempts yet
Time limit
1s
Memory limit
512 MB
Judgeable
Cereal
Hard9
Greedy, Simulation+2
No attempts yet
Time limit
1s
Memory limit
512 MB
Judgeable
Seollal
Hard9
Graph, Matrix+1
No attempts yet
Time limit
3s
Memory limit
512 MB
Judgeable
Alternative Permutations
Hard9
Combinatorics, Tree+2
No attempts yet
Time limit
8s
Memory limit
256 MB
Judgeable
Laser Intensification
Hard9
Math, Combinatorics+2
No attempts yet
Time limit
2s
Memory limit
64 MB
Judgeable
Deja Vu
Hard9
Segment tree, Dynamic programming+2
No attempts yet
Time limit
5s
Memory limit
512 MB
Judgeable
Easiest Sum
Hard9
Prefix sum, Binary search+2
No attempts yet
Time limit
1s
Memory limit
512 MB
Judgeable
Histogram and Blue Rectangles
Hard9
Stack, Dynamic programming+1
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Integer Equation Checker
Hard9
Brute force, Implementation+2
No attempts yet
Time limit
1s
Memory limit
512 MB
Judgeable
Minimum spanning tree and queries
Hard9
Minimum spanning tree, Graph+2
No attempts yet
Time limit
5s
Memory limit
256 MB
Judgeable
Yet Another Problem on Empodia
Hard9
Combinatorics, Dynamic programming+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Curious Ball Game
Hard9
Number theory, Math+2
No attempts yet
Time limit
0.5s
Memory limit
256 MB
Judgeable

Title	Level	Topics	Solved	Time limit	Memory limit	Judge
GnalcatsDecide whether two genes, each a sequence of seven possible base transformations on proteins, produce identical results or both fail on every sufficiently long input protein.	Hard9	StringStack+2	No attempts yet	0.3s	512 MB	Judgeable
Pilgrim's Memories and the Impressed GodGiven an N by N grid of 0 and 1 trials, sum X^2+1 over every distinct color string formed by monotone chains of sites, where X counts how often that string occurs.	Hard9	Dynamic programmingString+1	No attempts yet	8s	1024 MB	Judgeable
Sorcerers of the Round TableCount the circular seatings of the other sorcerers, with the chairman fixed at height n, where neighbors' hat heights differ by at most p and no disliked pair sits adjacent.	Hard9	Dynamic programmingBit manipulation+2	No attempts yet	2s	512 MB	Judgeable
Speed Reading CourseCount how many positions i where c contains the given m-bit word w, with c defined by an arithmetic progression modulo n against threshold p.	Hard9	Number theoryString matching+2	No attempts yet	2s	512 MB	Judgeable
Flavor of the FunctionGiven a function f on 1 to N with node weights, process updates to f and weights, and answer the total weight of distinct nodes visited from a start node x.	Hard9	GraphTree+1	No attempts yet	1.5s	1024 MB	Judgeable
Good Word, Bad WordBacteria on an N by N grid can step to an orthogonal neighbor for cost a, or jump up to Chebyshev distance D from a good cell for cost b; for each meeting cell find the total minimum cost for all bacteria to reach it.	Hard9	Shortest pathGraph+2	No attempts yet	2.5s	1024 MB	Judgeable
Tree and the K-th DiameterGiven a tree, find the K-th smallest encoded diameter path, and answer queries that swap two vertex labels before asking for the L-th smallest.	Hard9	TreeBFS+1	No attempts yet	3s	1024 MB	Judgeable
Patrol RouteFind the minimum closed walk covering every edge of a connected weighted undirected multigraph at least once, with at most 15 vertices.	Hard9	GraphDynamic programming+2	No attempts yet	2s	512 MB	Judgeable
TenkeyFind the minimum number of keypad operations (cursor moves plus key presses) to type a positive integer congruent to R modulo M, starting from the 0 key.	Hard9	GraphBFS+2	No attempts yet	2s	512 MB	Judgeable
Graph CountingCount, modulo 998244353, the non-isomorphic undirected graphs on 2n vertices that have no perfect matching but lose that property when any missing edge is added.	Hard9	CombinatoricsGraph+2	No attempts yet	5s	512 MB	Judgeable
Interesting GraphGiven a graph where every 7-vertex subset has a pair separated by a outside vertex, output the chromatic polynomial values for 1 to n colors modulo 998244353.	Hard9	GraphDynamic programming+1	No attempts yet	5s	512 MB	Judgeable
KnowledgeCount strings of length x reachable from s by inserting or deleting the blocks aa, bbb, and ababab, modulo 998244353.	Hard9	StringCombinatorics+2	No attempts yet	1s	512 MB	Judgeable
Airplane CliquesGiven a tree of n cities and a distance limit x, count the sets of k cities whose pairwise distances are all at most x, for every k from 1 to n.	Hard9	TreeDivide and conquer+1	No attempts yet	2s	512 MB	Judgeable
Giant PenguinGiven a connected graph where each vertex lies on at most k simple cycles, support marking vertices and querying the distance from a vertex to the nearest marked vertex.	Hard9	GraphTree+2	No attempts yet	3s	512 MB	Judgeable
One GoalGiven a tree of n cities and k friends, sum the smallest optimal meeting city over all n^k placements of the friends, modulo 998244353.	Hard9	CombinatoricsTree+2	No attempts yet	2s	512 MB	Judgeable
Bitwise XorCount non-empty subsequences in which the pairwise xor of every two chosen elements is at least x, modulo 998244353.	Hard9	Bit manipulationTrie+2	No attempts yet	2s	512 MB	Judgeable
DeterminantFind the determinant mod 998244353 of the adjacency matrix of a connected graph where every (k+1)-vertex set has a pair separated by one edge.	Hard9	GraphDynamic programming+1	No attempts yet	5s	512 MB	Judgeable
Easy WinAfter each edge insertion, find the maximum total weight of a subset of edges such that no non-empty edge-disjoint union of cycles in it has Nim value (xor of stone counts) equal to zero.	Hard9	Game theoryUnion-find+2	No attempts yet	1.5s	512 MB	Judgeable
GrammarlyGiven a string up to 300,000 characters, count simple paths from the whole string through distinct substrings where each step deletes one character, modulo 998244353.	Hard9	StringDynamic programming+1	No attempts yet	2s	512 MB	Judgeable
Four ElementsCount the 4-element subsets of a union of n disjoint integer ranges whose sum equals s, modulo 998244353.	Hard9	MathCombinatorics+2	No attempts yet	2s	512 MB	Judgeable
Six WordsGiven a connected graph whose vertex i has potential i and edge i has weight i, find the total weight of a minimum spanning tree of the line graph of the line graph.	Hard9	GraphMinimum spanning tree+2	No attempts yet	2s	512 MB	Judgeable
Seven NeversFor every window of k consecutive elements in a permutation, compute the LIS length after deleting that window.	Hard9	Dynamic programmingSegment tree+2	No attempts yet	2s	512 MB	Judgeable
Um_nik's AlgorithmGiven an undirected bipartite graph with up to 2e6 vertices and edges per side, output a matching whose size is at least 0.95 times the maximum matching size, with heavy constant-factor optimization required.	Hard9	GraphGreedy+2	No attempts yet	4s	512 MB	Judgeable
String AlgorithmFor every k, cut s into blocks of length k, discard the tail, and count block pairs whose Hamming distance is at most one.	Hard9	StringHash map+2	No attempts yet	20s	512 MB	Judgeable
FFT AlgorithmGiven m and k, find a primitive 2^k-th root of unity modulo m, or report that none exists.	Hard9	Number theoryMath+2	No attempts yet	1.5s	512 MB	Judgeable
Bracket Euler TourFind an Euler tour of an undirected graph whose vertex bracket labels, read in traversal order, form a correct bracket sequence, or report that none exists.	Hard9	GraphDFS+2	No attempts yet	2s	512 MB	Judgeable
One RootCount pairs (p, q) with \|p\|, \|q\| <= m for which x^n + px + q has exactly one real root.	Hard9	MathNumber theory+2	No attempts yet	2s	512 MB	Judgeable
Another Coin Weighing PuzzleGiven m weighings and k coins per bag, find the maximum number of bags whose unique heavy bag can be identified, modulo 998244353.	Hard9	CombinatoricsMath+2	No attempts yet	1s	512 MB	Judgeable
Grid GuardianCount the ways to place the minimum number of obstacles in an n by m grid so that every 2x2 subgrid contains at least one, modulo a prime p.	Hard9	Dynamic programmingBit manipulation	No attempts yet	8s	512 MB	Judgeable
Counting Edit DistancesCount the number of distinct strings over 'A' to 'Z' whose Levenshtein distance from a given string s is exactly d, modulo 998244353.	Hard9	Dynamic programmingString+2	No attempts yet	10s	512 MB	Judgeable
Rooted SubtreesFor each query with two roots r and p, count the distinct non-empty sets that are the intersection of a subtree of the tree rooted at r and a subtree of the tree rooted at p.	Hard9	TreeDFS+2	No attempts yet	11s	512 MB	Judgeable
Tomb RaiderFind the fewest gargoyles to rotate so every gargoyle face can see some gargoyle face by light beams in a mirror grid.	Hard9	GraphBFS+1	No attempts yet	3s	512 MB	Judgeable
Basis ChangeGiven one linear recurrence with coefficients a_i, find the unique recurrence with prescribed lags b_i that every sequence satisfying the first also satisfies.	Hard9	MathImplementation+2	No attempts yet	2s	512 MB	Judgeable
QuoridorGiven a hexagonal three-player Quoridor position as ASCII art, count the legal wall placements for player A that leave every player a path to their goal.	Hard9	GraphBFS+1	No attempts yet	2s	512 MB	Judgeable
NightmareFind how far a rectangular car can drive along its normal before it hits one more pothole than it can withstand, among n pothole polyhedra.	Hard9	GeometrySorting+1	No attempts yet	1s	512 MB	Judgeable
EmployeesGiven n employees with distinct workloads and hall size k, output for each employee the product of two permutation-based scores, modulo 1e9+7.	Hard9	Dynamic programmingCombinatorics+2	No attempts yet	2s	512 MB	Judgeable
Modulo-magic squaresCount n x n matrices over Z_m whose row, column, and two diagonal sums are all congruent to one constant, for n and m up to 1e9.	Hard9	MathCombinatorics+2	No attempts yet	1s	512 MB	Judgeable
Call It What You WantFor each n, factor x^n - 1 over the integers into cyclotomic polynomials, print the factors in a specified coefficient order and a specific sign and exponent format.	Hard9	Number theoryMath+2	No attempts yet	2s	512 MB	Judgeable
KaleidoscopeCount colorings of the 60 faces of a rhombic hexecontahedron with n colors, each color i used at least c_i times, where colorings are identified under the rotational symmetry group, modulo p.	Hard9	CombinatoricsMath+2	No attempts yet	2s	512 MB	Judgeable
Expected CostPick a labeled tree on n vertices uniformly at random and find the expected value of the minimum sum of distances from any vertex to all others, modulo a prime.	Hard9	CombinatoricsTree+2	No attempts yet	3s	512 MB	Judgeable
Humongous StringGiven n and k, count the distinct non-empty substrings of the length-n prefix of the infinite string S built by concatenating the growing blocks T_i.	Hard9	StringMath+1	No attempts yet	1s	512 MB	Judgeable
Intellectual Prefix MaximaFor each query on a weighted tree, compute the sum of prefix maxima of the edge weights along the path from u to v.	Hard9	TreeDivide and conquer+1	No attempts yet	4s	512 MB	Judgeable
Long GamePlayers alternately cut a strip of a permutation while every cut must leave at least one strip containing an inversion; decide the winner with optimal play.	Hard9	Game theoryGreedy+2	No attempts yet	1s	512 MB	Judgeable
Milk CandyGiven hints that reveal range sums with costs, and NPCs that force exactly k_i purchases each, find the minimum total cost to determine all n values, or report -1.	Hard9	MatrixCombinatorics+2	No attempts yet	2s	512 MB	Judgeable
FarawayCount lattice points (xe, ye) in [0, m]^2 such that for each of up to 10 constraints, (\|xi - xe\| + \|yi - ye\|) mod ki equals ti, with ki at most 5 and m up to 1e9.	Hard9	MathNumber theory+2	No attempts yet	1s	512 MB	Judgeable
TDLGiven m and k, find the smallest n such that the m-th integer above n coprime to n differs from n by a value whose XOR with n equals k.	Hard9	Number theoryBit manipulation+2	No attempts yet	1s	512 MB	Judgeable
Three InvestigatorsFor each prefix length k, find the maximum total sum of at most 5 disjoint non-decreasing subsequences taken from that prefix.	Hard9	Dynamic programmingDivide and conquer+1	No attempts yet	5s	512 MB	Judgeable
Road ManagerGiven a weighted n by m grid that wraps around horizontally, each query removes columns l to r and asks for the MST weight of the remaining graph.	Hard9	Minimum spanning treeGraph+2	No attempts yet	4s	512 MB	Judgeable
Monster HunterGiven a tree rooted at node 1, each node has a cost and a reward; find the minimum starting HP so some walk clearing every monster never drops below zero.	Hard9	GreedyDFS+2	No attempts yet	4s	512 MB	Judgeable
Line GraphsGiven a simple graph G and k, find the size of a maximum clique in the k-th iterated line graph L_k(G) and count such cliques modulo 1000000007.	Hard9	GraphCombinatorics+1	No attempts yet	5s	512 MB	Judgeable
Play Games with RounddogFor each query substring T, find the largest total stone count of Calabash's piles such that he wins Nim no matter which piles Rounddog removes, or -1.	Hard9	StringString matching+2	No attempts yet	5s	512 MB	Judgeable
Domino CoveringCount the domino tilings of an n by m grid for up to 20000 queries, with n at most 35, m up to 10^18, and a prime modulus p given per query.	Hard9	MatrixDynamic programming+2	No attempts yet	6s	512 MB	Judgeable
Make Rounddog HappyCount subarrays whose elements are all distinct and whose maximum minus length is at most k, for arrays up to 300,000 with values bounded by n.	Hard9	Divide and conquerTwo pointers+2	No attempts yet	2s	512 MB	Judgeable
Yet Another ConvolutionGiven arrays a and b of length n, compute for each k the maximum of \|a_i - b_j\| over all pairs (i, j) with gcd(i, j) equal to k.	Hard9	Number theoryMath+1	No attempts yet	4s	512 MB	Judgeable
Magic StringsGiven n up to 10^18, count the distinct subsequences of the recursively doubled string F_n modulo 10^9+7 for up to 10 test cases.	Hard9	Dynamic programmingMatrix+2	No attempts yet	4s	512 MB	Judgeable
Decimal ExpansionFor each query n up to 10^18, find the n-th digit after the decimal point of the infinite product (9/10)(99/100)(999/1000)...	Hard9	MathNumber theory+2	No attempts yet	1s	512 MB	Judgeable
EeveeGiven k random stacks of n fragments, find the expected sum over all ranges of 2 or more stacks of interleavings with no k equal-stone fragments in a row.	Hard9	CombinatoricsProbability+2	No attempts yet	5s	512 MB	Judgeable
HypnoFind the minimum expected time to walk from intersection 1 to intersection n when each road may put you to sleep with a Hypno you are susceptible to, and you learn each road's result after trying it.	Hard9	GraphShortest path+1	No attempts yet	2s	512 MB	Judgeable
Lati@sDetermine the winner of a finite impartial game whose starting multiset is built from all permutation diagonals of an n by n matrix.	Hard9	Game theoryCombinatorics+2	No attempts yet	2s	512 MB	Judgeable
Somewhere Over the RainbowGiven lower bounds a_x at n points, find the minimum sum of a strictly convex integer sequence with a_0 = a_m = 0, modulo 998244353.	Hard9	Dynamic programmingMath+1	No attempts yet	2s	512 MB	Judgeable
Goldberg MachineA marble starts at node 1 and moves along rotating tree tracks; answer its position after x steps, with point updates to the active tracks.	Hard9	TreeSegment tree+1	No attempts yet	5s	512 MB	Judgeable
Linear Congruential GeneratorGiven a linear congruential generator and two index ranges, sum X_i mod (X_j+1) over all pairs i in the first range and j in the second.	Hard9	MathNumber theory+2	No attempts yet	2s	512 MB	Judgeable
AtCoder Quality ProblemGiven costs to paint each of the 2^n subsets red or blue, find the minimum total cost so that the union of any two same-colored subsets has that same color.	Hard9	Bit manipulationGraph+1	No attempts yet	2s	512 MB	Judgeable
Count the GraphsCount labeled connected undirected graphs on N nodes with exactly K bridges, modulo a possibly composite M, for up to 100 test cases.	Hard9	CombinatoricsDynamic programming+2	No attempts yet	2s	512 MB	Judgeable
Greatest Chicken DishCount, for each query range [L, R] and value D, the number of contiguous subarrays inside [L, R] whose GCD equals D.	Hard9	Dynamic programmingNumber theory+2	No attempts yet	15s	512 MB	Judgeable
The HalfwittersFor each start permutation, compute the minimum expected time to reach the identity order using adjacent swaps (cost a), a full reversal (cost b), or a random reshuffle (cost c).	Hard9	Dynamic programmingGraph+2	No attempts yet	5s	512 MB	Judgeable
LighthousesFind the longest simple path along given tram segments between vertices of a convex polygon, where the path must never cross itself.	Hard9	Dynamic programmingGeometry	No attempts yet	15s	512 MB	Judgeable
DivCount positive integers x for which a signed sum of powers of x is divisible by 1 + x + ... + x^(m-1), or report -1 if there are infinitely many.	Hard9	MathNumber theory	No attempts yet	2s	512 MB	Judgeable
IneqGiven a finite set S of integer lattice points, decide whether S can be cut out as exactly the integer points lying strictly below every line of some finite family of half-planes.	Hard9	GeometryMath+2	No attempts yet	2s	512 MB	Judgeable
Bitset MasterEach vertex starts with its own set, edge operations merge the sets at both endpoints, and queries count how many sets contain a given vertex.	Hard9	TreeUnion-find+1	No attempts yet	6s	512 MB	Judgeable
Cyclic DistanceChoose k distinct vertices of a weighted tree to maximize the total tree distance along the cycle p1 to pk and back to p1, and output that maximum.	Hard9	TreeDynamic programming+1	No attempts yet	3s	512 MB	Judgeable
Data Structure QuizApply m1 weighted rectangle additions to an n by n grid, then answer m2 queries for the maximum cell value inside each query rectangle.	Hard9	Segment treeDivide and conquer+1	No attempts yet	8s	512 MB	Judgeable
Heavy StonesFor each starting pile k, find the minimum total cost of merging all piles into one when every merge must extend the currently selected pile to a neighbor.	Hard9	GreedyDynamic programming	No attempts yet	2s	512 MB	Judgeable
Knowledge-Oriented ProblemGiven a graph G with n vertices and k copies stacked in a chain with matching vertex edges, count the spanning trees of the result modulo 10^9+7.	Hard9	MatrixMath+1	No attempts yet	5s	512 MB	Judgeable
LCM SumGiven n up to 10^18 and k up to 30, compute the sum of lcm(x, x+1, ..., x+k) for x from 1 to n, modulo 10^9+7.	Hard9	Number theoryMath+1	No attempts yet	7s	512 MB	Judgeable
Delightful (Hard)Write a program of at most 5000 commands for a ternary computer with 26 forty-trit registers that sets Y to 1 if the input X (0 to 109) is prime and 0 otherwise.	Hard9	Number theoryImplementation+2	No attempts yet	1s	512 MB	Judgeable
Xorshift32Given a starting value x and a target t, find the index at which t first appears in the Xorshift32 pseudorandom sequence.	Hard9	MathBit manipulation+2	No attempts yet	1s	256 MB	Judgeable
Help Yourself (Platinum)Sum the K-th power of the number of connected components of the union over all 2^N subsets of N intervals, modulo 1e9+7.	Hard9	CombinatoricsDynamic programming+2	No attempts yet	2s	512 MB	Judgeable
814 - 2Print an 8 by 14 grid of digits so that every number from 1 up to some X can be traced as an adjacent-cell path, maximizing X.	Hard9	GraphDFS+2	No attempts yet	0.814s	814 MB	Judgeable
Tree and Query 15For each query, count the tree vertices within distance r_i of at least one of the k given vertices v_i.	Hard9	TreeDivide and conquer+1	No attempts yet	5s	1024 MB	Judgeable
OR and QueriesProcess range bitwise-OR updates on an array and count how many positions in a range currently equal a fixed K.	Hard9	Segment treeBit manipulation+2	No attempts yet	1.5s	256 MB	Judgeable
Karaoke MeetupIn a weighted tree, some vertices are marked as houses. For each vertex compute the ratio of the nearest marked vertex distance to the farthest, and output the maximum ratio as a reduced fraction.	Hard9	TreeDFS+2	No attempts yet	8s	512 MB	Judgeable
Nonogram QRSolve a chain of 2000 nonograms to reconstruct QR codes, decode them, follow indicator links, and recover a flag.	Hard9	BacktrackingSimulation+2	No attempts yet	1s	512 MB	Judgeable
Chameleon's LoveUsing at most 20000 queries that return the number of distinct skin colors in a chosen subset, recover every pair of chameleons sharing an original color.	Hard9	GraphCombinatorics+2	No attempts yet	2s	512 MB	Judgeable
Constellation 3Given a histogram of white building columns and weighted yellow star pixels, find the minimum total cost of removing stars so no rectangle free of buildings contains two or more stars.	Hard9	Divide and conquerDynamic programming+1	No attempts yet	1s	512 MB	Judgeable
Something in the ChestMaintain a dynamic graph under edge insertions and global threshold changes, and answer the largest threshold at which two cells stay connected.	Hard9	Union-findDivide and conquer+2	No attempts yet	3s	1024 MB	Judgeable
Sprinklers 2: Return of the AlfalfaCount the ways to place sweet corn and alfalfa sprinklers on an N by N grid, with some blocked squares, so that every square is covered by exactly one sprinkler type.	Hard9	Dynamic programmingPrefix sum+2	No attempts yet	2s	512 MB	Judgeable
ExerciseGiven N and prime M, compute modulo M the product over all N! permutations of the order (number of iterations until identity) of each permutation.	Hard9	CombinatoricsNumber theory+2	No attempts yet	2s	512 MB	Judgeable
Cow ExerciseGiven N and prime M, sum every positive integer K for which some permutation of length N has order K, then output the sum modulo M.	Hard9	MathNumber theory+2	No attempts yet	1s	512 MB	Judgeable
CerealGiven a queue of cows each with a favorite and second-favorite cereal, report for every prefix removal how many cows still get a box.	Hard9	GreedySimulation+2	No attempts yet	1s	512 MB	Judgeable
SeollalGiven a grid with rocks, build a spanning tree of the free cells where every black cell except (1,1) has degree at least 2, or report NO.	Hard9	GraphMatrix+1	No attempts yet	3s	512 MB	Judgeable
Alternative PermutationsGiven k, find the smallest n for which some BST on 1 to n is produced by exactly k permutations, and print the lexicographically smallest one.	Hard9	CombinatoricsTree+2	No attempts yet	8s	256 MB	Judgeable
Laser IntensificationFind probability p so that one photon entering the lower-left of a w by h grid, with nodes independently faulty with probability 1-p except n known faulty cells, yields k photons in expectation at the upper-right; print -1 if impossible.	Hard9	MathCombinatorics+2	No attempts yet	2s	64 MB	Judgeable
Deja VuMaintain an array under point updates and answer queries asking for the earliest position d that ends an increasing subsequence of length 4 starting at or after l.	Hard9	Segment treeDynamic programming+2	No attempts yet	5s	512 MB	Judgeable
Easiest SumGiven an array, each coin decreases one element by 1, so find the minimum possible maximum subarray sum for each budget from 1 to k and sum them modulo 998244353.	Hard9	Prefix sumBinary search+2	No attempts yet	1s	512 MB	Judgeable
Histogram and Blue RectanglesFor each prefix of j columns of a histogram with heights a_i, find the largest axis-aligned rectangle whose interior lies entirely within those columns.	Hard9	StackDynamic programming+1	No attempts yet	2s	512 MB	Judgeable
Integer Equation CheckerClassify an equation string as correct, format error, math error, or a typo fixable by replacing at most two characters with a valid correct equation.	Hard9	Brute forceImplementation+2	No attempts yet	1s	512 MB	Judgeable
Minimum spanning tree and queriesGiven a weighted directed graph G, find the MST weight of G tensor Path_i for each i from 2 to Q+1, where Path_i is a chain of i vertices.	Hard9	Minimum spanning treeGraph+2	No attempts yet	5s	256 MB	Judgeable
Yet Another Problem on EmpodiaCount, for each length i up to N, the number of equivalence classes of permutations of length i under the relation that agrees on which intervals are framed (max minus min equals length minus one), modulo a prime.	Hard9	CombinatoricsDynamic programming+2	No attempts yet	2s	512 MB	Judgeable
Curious Ball GameFor each query (N, M), find the M-th smallest bag size A such that drawing two balls gives probability exactly 1/N^2 that at least one is not red, outputting A and B mod 1e9+7.	Hard9	Number theoryMath+2	No attempts yet	0.5s	256 MB	Judgeable