Problems

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Total results29,065 problems

Very Simple Sum
Hard9
Math, Combinatorics+2
No attempts yet
Time limit
3s
Memory limit
256 MB
Judgeable
An Unsure Catch
Hard9
Graph, Tree+2
No attempts yet
Time limit
8s
Memory limit
256 MB
Judgeable
String Theory
Hard9
String, String matching+2
No attempts yet
Time limit
4s
Memory limit
512 MB
Judgeable
Data Structure
Hard9
Tree, DFS+1
No attempts yet
Time limit
20s
Memory limit
512 MB
Judgeable
Recursive String
Hard9
String, Recursion+2
No attempts yet
Time limit
1s
Memory limit
256 MB
Judgeable
Grid Triangle
Hard9
Math, Number theory+2
No attempts yet
Time limit
0.5s
Memory limit
1024 MB
Judgeable
Stock Price Prediction
Hard9
String matching, Sorting+2
No attempts yet
Time limit
1s
Memory limit
1024 MB
Judgeable
Clique Festival
Hard9
Graph, Shortest path+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Fibonaccis' vouchers
Hard9
Math, Combinatorics+2
No attempts yet
Time limit
1s
Memory limit
256 MB
Judgeable
Road
Hard9
Segment tree, Math+1
No attempts yet
Time limit
4s
Memory limit
512 MB
Judgeable
Subsequences
Hard9
Dynamic programming, Combinatorics+2
No attempts yet
Time limit
5s
Memory limit
512 MB
Judgeable
Road Inspection
Hard9
Graph, Tree+2
No attempts yet
Time limit
1.5s
Memory limit
512 MB
Judgeable
Modular Knapsack
Hard9
Dynamic programming, Number theory+1
No attempts yet
Time limit
1.5s
Memory limit
256 MB
Judgeable
Handsome multisets
Hard9
Number theory, Combinatorics+2
No attempts yet
Time limit
15s
Memory limit
256 MB
Judgeable
Polynomial
Hard9
Math, Combinatorics+2
No attempts yet
Time limit
3s
Memory limit
256 MB
Judgeable
Heretical Möbius
Hard9
Number theory, String matching+1
No attempts yet
Time limit
1s
Memory limit
256 MB
Judgeable
Immortal Universe
Hard9
Dynamic programming, Combinatorics
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Philosophical Balance
Hard9
String, Game theory+2
No attempts yet
Time limit
1s
Memory limit
256 MB
Judgeable
Desperate Fire Survive
Hard9
Segment tree, Greedy+1
No attempts yet
Time limit
3s
Memory limit
256 MB
Judgeable
Eventual Journey
Hard9
Graph, Shortest path+2
No attempts yet
Time limit
1s
Memory limit
256 MB
Judgeable
Hat With An Integer
Hard9
Array, Intervals+1
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Labeled Connected Graphs
Hard9
Combinatorics, Dynamic programming+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Number Of Vertices
Hard9
Graph, Implementation+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Inner Product
Hard9
Tree, Divide and conquer+1
No attempts yet
Time limit
3s
Memory limit
256 MB
Judgeable
Gleb Evstropov
Hard9
Segment tree, Array+2
No attempts yet
Time limit
20s
Memory limit
512 MB
Judgeable
Kunyavskiy Pavel
Hard9
Game theory, Dynamic programming+2
No attempts yet
Time limit
3s
Memory limit
512 MB
Judgeable
Dungeon Relay
Hard9
Segment tree, Sorting+2
No attempts yet
Time limit
2s
Memory limit
1024 MB
Judgeable
A Simple Tree Problem
Hard9
Tree, DFS+2
No attempts yet
Time limit
8s
Memory limit
1024 MB
Judgeable
Server Expansion
Hard9
Combinatorics, Dynamic programming+2
No attempts yet
Time limit
1s
Memory limit
512 MB
Judgeable
Kućice
Hard9
Geometry, Combinatorics+2
No attempts yet
Time limit
1s
Memory limit
512 MB
Judgeable
Yet Another Minimax Problem
Hard9
Geometry, Binary search+1
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Rooted MST
Hard9
Minimum spanning tree, Divide and conquer+1
No attempts yet
Time limit
3s
Memory limit
1024 MB
Judgeable
Bracelet Crossings
Hard9
Geometry, Implementation+2
No attempts yet
Time limit
2s
Memory limit
1024 MB
Judgeable
Tearing Barcodes
Hard9
String, Greedy+2
No attempts yet
Time limit
1s
Memory limit
1024 MB
Judgeable
Tree Reconstruction
Hard9
Tree, Graph+2
No attempts yet
Time limit
1s
Memory limit
512 MB
Judgeable
Regular Meeting 3
Hard9
Tree, Greedy+2
No attempts yet
Time limit
1s
Memory limit
1024 MB
Judgeable
Linear Algebra
Hard9
Geometry, Segment tree+1
No attempts yet
Time limit
2s
Memory limit
1024 MB
Judgeable
Sequence
Hard9
Bit manipulation, Math+2
No attempts yet
Time limit
1s
Memory limit
1024 MB
Judgeable
Abduction
Hard9
Dynamic programming, Combinatorics+1
No attempts yet
Time limit
1s
Memory limit
1024 MB
Judgeable
Rabbit
Hard9
Game theory, Simulation
No attempts yet
Time limit
Not set
Memory limit
1024 MB
Judgeable
Pretty sequences
Hard9
Combinatorics, Math+2
No attempts yet
Time limit
0.4s
Memory limit
1024 MB
Judgeable
Sgame
Hard9
String, Sorting+2
No attempts yet
Time limit
4s
Memory limit
1024 MB
Judgeable
Game on two heaps
Hard9
Game theory, Math+2
No attempts yet
Time limit
2s
Memory limit
1024 MB
Judgeable
Uniform String
Hard9
String, Implementation+2
No attempts yet
Time limit
1s
Memory limit
1024 MB
Judgeable
Avoiding Asteroids
Hard9
Geometry, Math
No attempts yet
Time limit
1s
Memory limit
1024 MB
Judgeable
Integer Graph
Hard9
Number theory, Graph+2
No attempts yet
Time limit
1s
Memory limit
512 MB
Judgeable
King Shipri Station, Exit G
Hard9
Graph, Shortest path+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Autobus
Hard9
Graph, Shortest path+2
No attempts yet
Time limit
1s
Memory limit
512 MB
Judgeable
Izbori
Hard9
Divide and conquer, Hash map+2
No attempts yet
Time limit
3s
Memory limit
512 MB
Judgeable
Parks
Hard9
Binary search, Greedy+2
No attempts yet
Time limit
3s
Memory limit
512 MB
Judgeable
Railway Trip 2
Hard9
Graph, Greedy+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Sandcastle 2
Hard9
Sorting, Divide and conquer+1
No attempts yet
Time limit
4s
Memory limit
1024 MB
Judgeable
Land Purchase
Hard9
Graph, Minimum spanning tree+2
No attempts yet
Time limit
1s
Memory limit
1024 MB
Judgeable
Land Equality
Hard9
Dynamic programming, Bit manipulation+1
No attempts yet
Time limit
1s
Memory limit
1024 MB
Judgeable
Even Substrings
Hard9
Segment tree, Bit manipulation+2
No attempts yet
Time limit
7s
Memory limit
1024 MB
Judgeable
Problem Set Construction
Hard9
Probability, Combinatorics+2
No attempts yet
Time limit
1s
Memory limit
1024 MB
Judgeable
Super Nine
Hard9
Combinatorics, Backtracking+2
No attempts yet
Time limit
1s
Memory limit
512 MB
Judgeable
Notability Index
Hard9
Number theory, Prefix sum+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
First to Solve
Hard9
Probability, Combinatorics+2
No attempts yet
Time limit
5s
Memory limit
512 MB
Judgeable
High Powers
Hard9
Math, Combinatorics+2
No attempts yet
Time limit
2s
Memory limit
1024 MB
Judgeable
Tarzan Jumps
Hard9
Tree, Dynamic programming+1
No attempts yet
Time limit
2s
Memory limit
256 MB
Judgeable
Inversions
Hard9
Math, Combinatorics
No attempts yet
Time limit
3s
Memory limit
256 MB
Judgeable
Mountains
Hard9
Dynamic programming, Combinatorics+1
No attempts yet
Time limit
1s
Memory limit
256 MB
Judgeable
Casual Dancers
Hard9
Probability, Dynamic programming+1
No attempts yet
Time limit
4s
Memory limit
512 MB
Judgeable
First Occurrence
Hard9
String matching, Bit manipulation+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Mismatch
Hard9
Bit manipulation, Combinatorics+1
No attempts yet
Time limit
4s
Memory limit
512 MB
Judgeable
Spiral Matrix
Hard9
Matrix, Prefix sum+1
No attempts yet
Time limit
4s
Memory limit
512 MB
Judgeable
DCMSF
Hard9
Graph, Minimum spanning tree+1
No attempts yet
Time limit
2s
Memory limit
1024 MB
Judgeable
multiple edges
Hard9
Graph, Union-find+1
No attempts yet
Time limit
0.5s
Memory limit
1024 MB
Judgeable
Regional Tour
Hard9
Tree, Dynamic programming+1
No attempts yet
Time limit
4s
Memory limit
512 MB
Judgeable
Jail
Hard9
Tree, Graph+2
No attempts yet
Time limit
4s
Memory limit
1024 MB
Judgeable
Ants and Sugar
Hard9
Segment tree, Greedy+1
No attempts yet
Time limit
4s
Memory limit
1024 MB
Judgeable
Evolution
Hard9
Tree, Dynamic programming+1
No attempts yet
Time limit
2s
Memory limit
1024 MB
Judgeable
Find the Magic Bead
Hard9
Dynamic programming, Divide and conquer+1
No attempts yet
Time limit
2s
Memory limit
1024 MB
Judgeable
Security System
Hard9
Graph, Geometry
No attempts yet
Time limit
2.5s
Memory limit
1024 MB
Judgeable
Palindromi
Hard9
String, String matching+1
No attempts yet
Time limit
1s
Memory limit
512 MB
Judgeable
Farm
Hard9
Graph, Sorting+1
No attempts yet
Time limit
1s
Memory limit
1024 MB
Judgeable
Tree GCD
Hard9
Tree, Divide and conquer+1
No attempts yet
Time limit
2.5s
Memory limit
1024 MB
Judgeable
Cruel Borders
Hard9
Tree, Segment tree+2
No attempts yet
Time limit
1.5s
Memory limit
1024 MB
Judgeable
Uplifting Excursion
Hard9
Dynamic programming, Math
No attempts yet
Time limit
4s
Memory limit
512 MB
Judgeable
Game
Hard9
Graph, Divide and conquer+1
No attempts yet
Time limit
2s
Memory limit
256 MB
Judgeable
Race for the Galaxy
Hard9
Dynamic programming, Combinatorics+1
No attempts yet
Time limit
4s
Memory limit
1024 MB
Judgeable
Gravity Hackenbush
Hard9
Graph, Game theory+1
No attempts yet
Time limit
2s
Memory limit
1024 MB
Judgeable
Hide-and-Seek with a Spirit
Hard9
Implementation, Bit manipulation+1
No attempts yet
Time limit
1s
Memory limit
1024 MB
Judgeable
Nieun Forest Artist
Hard9
Combinatorics, Dynamic programming+1
No attempts yet
Time limit
2s
Memory limit
1024 MB
Judgeable
Trees, Sets, and Queries
Hard9
Tree, DFS+2
No attempts yet
Time limit
4s
Memory limit
512 MB
Judgeable
Thousand Islands
Hard9
Graph, DFS+1
No attempts yet
Time limit
1s
Memory limit
1024 MB
Judgeable
Simple Problem (Large)
Hard9
Number theory, Math+1
No attempts yet
Time limit
2.4s
Memory limit
1024 MB
Judgeable
Tokens
Hard9
Graph, DFS+1
No attempts yet
Time limit
2s
Memory limit
1024 MB
Judgeable
Lord of the Characteristic Polynomials (1)
Hard9
Matrix, Number theory+1
No attempts yet
Time limit
5s
Memory limit
1024 MB
Judgeable
MST
Hard9
Graph, Minimum spanning tree+1
No attempts yet
Time limit
3s
Memory limit
1024 MB
Judgeable
Younghee's Errand
Hard9
Combinatorics, Dynamic programming+1
No attempts yet
Time limit
2s
Memory limit
1024 MB
Judgeable
Make Numbers with Division
Hard9
Math, Combinatorics+1
No attempts yet
Time limit
1s
Memory limit
1024 MB
Judgeable
Floor Tiles in a Park
Hard9
Combinatorics, Math+1
No attempts yet
Time limit
1s
Memory limit
1024 MB
Judgeable
Rotate Sum 3
Hard9
Geometry, Math+1
No attempts yet
Time limit
1s
Memory limit
1024 MB
Judgeable
Great Party
Hard9
Game theory, Bit manipulation+1
No attempts yet
Time limit
1s
Memory limit
1024 MB
Judgeable
DS Team Selection
Hard9
Segment tree, Math+1
No attempts yet
Time limit
18s
Memory limit
1024 MB
Judgeable
Games
Hard9
Tree, Dynamic programming+1
No attempts yet
Time limit
4s
Memory limit
1024 MB
Judgeable
Half Plane
Hard9
Geometry, Segment tree+1
No attempts yet
Time limit
12s
Memory limit
1024 MB
Judgeable
WCWBTT
Hard9
Tree, Divide and conquer+1
No attempts yet
Time limit
20s
Memory limit
1024 MB
Judgeable

Title	Level	Topics	Solved	Time limit	Memory limit	Judge
Very Simple SumSum (a_x+a_y+a_z+a_w)^(b_x xor b_y xor b_z xor b_w) over all n^4 index quadruples, modulo 998244353, with a_i, b_i at most 500.	Hard9	MathCombinatorics+2	No attempts yet	3s	256 MB	Judgeable
An Unsure CatchGiven a functional graph of prisoner moves a_i, find the fewest a_i to change so every prisoner can be caught, and the most arrests possible for each change budget j.	Hard9	GraphTree+2	No attempts yet	8s	256 MB	Judgeable
String TheoryCount substrings of S that equal some nonempty string repeated exactly k times, counting each occurrence position separately.	Hard9	StringString matching+2	No attempts yet	4s	512 MB	Judgeable
Data StructureGiven a tree rooted at node 1, add z to the nodes at distance y mod x below node a, and answer queries for a node's current weight.	Hard9	TreeDFS+1	No attempts yet	20s	512 MB	Judgeable
Recursive StringGiven a string T built by recursively wrapping characters around previous blocks, recover the original string S and repetition counts A.	Hard9	StringRecursion+2	No attempts yet	1s	256 MB	Judgeable
Grid TriangleCount triangles with integer vertices, one at the origin, inside a box, where each pair is a diagonal of an X by Y by Z cuboid for three distinct positive integers X, Y, Z.	Hard9	MathNumber theory+2	No attempts yet	0.5s	1024 MB	Judgeable
Stock Price PredictionFind every start position in y where the length-m window has the same relative-rank pattern (order-isomorphic) as the pattern sequence x.	Hard9	String matchingSorting+2	No attempts yet	1s	1024 MB	Judgeable
Clique FestivalGiven up to 18 weighted cliques added to a graph on n vertices, compute the sum of shortest-path distances over all vertex pairs.	Hard9	GraphShortest path+2	No attempts yet	2s	512 MB	Judgeable
Fibonaccis' vouchersGiven k and n, find the n-th smallest number expressible as a sum of exactly k Fibonacci values, or report that it exceeds 10^18.	Hard9	MathCombinatorics+2	No attempts yet	1s	256 MB	Judgeable
RoadProcess plow, salt, and blizzard events on a road of n segments and report the maximum snow depth on a range at a given minute, modulo 1e9+7.	Hard9	Segment treeMath+1	No attempts yet	4s	512 MB	Judgeable
SubsequencesGiven up to 20 short strings, count the permutations whose concatenation has an even number of distinct subsequences.	Hard9	Dynamic programmingCombinatorics+2	No attempts yet	5s	512 MB	Judgeable
Road InspectionThe graph is a unicyclic connected graph (one cycle plus trees). A road can be inspected only if removing it keeps the graph connected, so only cycle edges qualify. For each cycle edge, removing it turns the graph into a tree; the inconvenience equals the tree's diameter. We must count cycle edges and find the maximum resulting diameter over all single cycle-edge removals, with N up to 200,000.	Hard9	GraphTree+2	No attempts yet	1.5s	512 MB	Judgeable
Modular KnapsackGiven n items with weights and costs and a prime p, find for each remainder mod p the maximum total cost of a subset whose weight sum has that remainder.	Hard9	Dynamic programmingNumber theory+1	No attempts yet	1.5s	256 MB	Judgeable
Handsome multisetsCount, over all multisets of positive integers summing to n that uniquely represent every value 1 to n as a subset sum, the total number of elements, modulo a prime near 1e9.	Hard9	Number theoryCombinatorics+2	No attempts yet	15s	256 MB	Judgeable
PolynomialGiven a 0/1 polynomial of degree at most 20 and a huge n up to 1e16, count the odd coefficients in P(x)^n.	Hard9	MathCombinatorics+2	No attempts yet	3s	256 MB	Judgeable
Heretical MöbiusGiven a 200-character binary string t, find the first position p where t appears in the sequence \|mu(1)\|, \|mu(2)\|, ... up to 10^9, or report -1.	Hard9	Number theoryString matching+1	No attempts yet	1s	256 MB	Judgeable
Immortal UniverseCount the ways to fill the '?' characters in two P/V strings so the boy never goes bankrupt, modulo 998244353.	Hard9	Dynamic programmingCombinatorics	No attempts yet	2s	512 MB	Judgeable
Philosophical BalanceGiven a string, choose a probability distribution over its suffixes to maximize the minimum expected LCP against any suffix the guard picks.	Hard9	StringGame theory+2	No attempts yet	1s	256 MB	Judgeable
Desperate Fire SurviveFor each query [l, r, k], count the sub-segments that can be merged and trimmed into one node of level exactly k.	Hard9	Segment treeGreedy+1	No attempts yet	3s	256 MB	Judgeable
Eventual JourneyIn a connected graph whose vertices are colored 0 or 1, moving inside one color costs nothing and each edge costs one ticket; for every vertex, sum the ticket distances to all other vertices.	Hard9	GraphShortest path+2	No attempts yet	1s	256 MB	Judgeable
Hat With An IntegerGiven an array a and bounds b and c on consecutive differences, find the day on which some wise one first deduces a value not on his hat, or report -1.	Hard9	ArrayIntervals+1	No attempts yet	2s	512 MB	Judgeable
Labeled Connected GraphsSum the distance between vertices 1 and 2 over every labeled connected graph on n vertices, modulo a prime m.	Hard9	CombinatoricsDynamic programming+2	No attempts yet	2s	512 MB	Judgeable
Number Of VerticesMaintain a graph under edge insertions and deletions, and after each query report whether its edges can be partitioned into zigzag cycles (locally alternating around each vertex).	Hard9	GraphImplementation+2	No attempts yet	2s	512 MB	Judgeable
Inner ProductGiven two trees on n labeled vertices, compute the sum over all ordered pairs (i, j) of the first-tree distance times the second-tree distance, modulo 10^9+7.	Hard9	TreeDivide and conquer+1	No attempts yet	3s	256 MB	Judgeable
Gleb EvstropovWith point updates on an array, for each query find the largest m such that k, k+1, ..., m is a subsequence of the half-open range a[l:r).	Hard9	Segment treeArray+2	No attempts yet	20s	512 MB	Judgeable
Kunyavskiy PavelCount, over all assignments of integer pairs to the leaves of a binary tree, the total number of pure-strategy Nash equilibria of a two-player game where Carol picks children at even depth and David at odd depth.	Hard9	Game theoryDynamic programming+2	No attempts yet	3s	512 MB	Judgeable
Dungeon RelayGiven dungeons with difficulty, fee, and reward, and point updates to fee or reward, answer range queries asking whether a relay over a difficulty interval can be completed with starting cash c, and the final cash if so.	Hard9	Segment treeSorting+2	No attempts yet	2s	1024 MB	Judgeable
A Simple Tree ProblemMaintain a weighted tree under point updates to vertex and edge weights, and after each update report the sum over all paths of (vertex-weight sum) times (edge-weight sum).	Hard9	TreeDFS+2	No attempts yet	8s	1024 MB	Judgeable
Server ExpansionCount the ways to choose some of a distinguishable disks of each size 2^0..2^(k-1) so the chosen capacities sum to exactly n, modulo 1048573.	Hard9	CombinatoricsDynamic programming+2	No attempts yet	1s	512 MB	Judgeable
KućiceGiven n points in general position, each chosen independently with probability 1/2, find the expected number of points inside the convex hull of the chosen subset, output as the numerator over 2^n modulo 1e9+7.	Hard9	GeometryCombinatorics+2	No attempts yet	1s	512 MB	Judgeable
Yet Another Minimax ProblemGiven n integer points, pick a line with points on both sides so that the smallest distance from any point to the line is as large as possible, and print that distance.	Hard9	GeometryBinary search+1	No attempts yet	2s	512 MB	Judgeable
Rooted MSTEach query changes the weight of edge 0-i to w, and the task is to print the minimum spanning tree weight after every change.	Hard9	Minimum spanning treeDivide and conquer+1	No attempts yet	3s	1024 MB	Judgeable
Bracelet CrossingsGiven vertical sweep readings of colors along M lines, decide whether the closed non-crossing polygonal chains could still exist.	Hard9	GeometryImplementation+2	No attempts yet	2s	1024 MB	Judgeable
Tearing BarcodesGiven a long bracket string (a pattern repeated many times) and a second string attached to each purchased drink, find the maximum number of drinks you can buy, where each drink costs K valid-barcode fragments and each purchase yields a new string to tear.	Hard9	StringGreedy+2	No attempts yet	1s	1024 MB	Judgeable
Tree ReconstructionGiven a weighted tree, each query adds an edge and removes the heaviest edge on the resulting cycle except the new one, then reports the distance between two vertices in the new tree.	Hard9	TreeGraph+2	No attempts yet	1s	512 MB	Judgeable
Regular Meeting 3For each distance X from 1 to N, find the maximum number of vertices in a tree such that every pair is at distance exactly X.	Hard9	TreeGreedy+2	No attempts yet	1s	1024 MB	Judgeable
Linear AlgebraToggle 2D vectors in and out of a set, and report whether (a, b) is a sum of chosen vectors scaled by coefficients between 0 and 1.	Hard9	GeometrySegment tree+1	No attempts yet	2s	1024 MB	Judgeable
SequenceGiven the first m terms of a linear recurrence A_i = A_{i-1} + A_{i-m}, count how many of A_p through A_q are odd, with q up to 2^60.	Hard9	Bit manipulationMath+2	No attempts yet	1s	1024 MB	Judgeable
AbductionCount grid paths from the southwest corner to the northeast corner of a W by H street grid whose sequence of left and right turns matches a given string, with no U-turns and possible revisits, modulo 10^7.	Hard9	Dynamic programmingCombinatorics+1	No attempts yet	1s	1024 MB	Judgeable
RabbitGiven N cells and a rabbit that alternates S scared seconds and C curious seconds, output a fixed check sequence that finds the rabbit from any start.	Hard9	Game theorySimulation	No attempts yet	Not set	1024 MB	Judgeable
Pretty sequencesCount permutations of 1..N that contain at least one adjacent pair (x, x+1), modulo M, where N can reach 10^18 and M is up to 10^7 (not necessarily prime).	Hard9	CombinatoricsMath+2	No attempts yet	0.4s	1024 MB	Judgeable
SgameGiven a string and many queries (m, k), find the maximum occurrence count of a substring with length between m and k that cannot be extended to a longer string with the same count.	Hard9	StringSorting+2	No attempts yet	4s	1024 MB	Judgeable
Game on two heapsCount the first-player moves that win a subtraction game on two heaps, where a move taking x and y balls is illegal exactly when the ratio x:y equals the fixed starting ratio A:B.	Hard9	Game theoryMath+2	No attempts yet	2s	1024 MB	Judgeable
Uniform StringRepeatedly apply a reduction that maps zero-runs to 1 or 0 based on their lengths and count, and report when the string stops being uniform.	Hard9	StringImplementation+2	No attempts yet	1s	1024 MB	Judgeable
Avoiding AsteroidsDecide whether a ship with unknown speed can reach the base without hitting asteroids that move and tumble at unknown rates, printing Go or Surrender.	Hard9	GeometryMath	No attempts yet	1s	1024 MB	Judgeable
Integer GraphGiven n integers, find the minimum over removals of one value of the sum of pairwise shortest-path distances in a graph where each number connects to its smallest-prime-factor quotient.	Hard9	Number theoryGraph+2	No attempts yet	1s	512 MB	Judgeable
King Shipri Station, Exit GA graph with fixed edge lengths and a global offset added to edges outside a chosen path; queries walk from a node to G picking a lexicographically minimized path under a four-level rule, and updates add v to all edges off that path.	Hard9	GraphShortest path+2	No attempts yet	2s	512 MB	Judgeable
AutobusGiven a weighted directed graph with n up to 70 and m up to 10^6 edges, answer queries for the minimum travel time using at most k routes, where k can be as large as 10^9.	Hard9	GraphShortest path+2	No attempts yet	1s	512 MB	Judgeable
IzboriGiven a sequence of n dish values, count the subarrays whose most frequent value occurs strictly more times than every other value combined in that subarray.	Hard9	Divide and conquerHash map+2	No attempts yet	3s	512 MB	Judgeable
ParksOn a weighted tree, choose exactly k vertices as parks so the largest distance from any vertex to its nearest park is minimized, and output that distance plus one optimal choice.	Hard9	Binary searchGreedy+2	No attempts yet	3s	512 MB	Judgeable
Railway Trip 2Given lines as station intervals and a boarding rule that only allows the first K stops, find the minimum number of trains needed for each of Q trips, or -1 if impossible.	Hard9	GraphGreedy+2	No attempts yet	2s	512 MB	Judgeable
Sandcastle 2Count the rectangles whose cells can be visited by a path that steps only to adjacent cells with strictly lower heights.	Hard9	SortingDivide and conquer+1	No attempts yet	4s	1024 MB	Judgeable
Land PurchaseAssign every cell of an N by M grid to one of two owners to maximize per-cell profits plus bonuses for same-owner adjacent pairs, and output the assignment.	Hard9	GraphMinimum spanning tree+2	No attempts yet	1s	1024 MB	Judgeable
Land EqualitySplit an r by c grid of 0, 1, and 2 values into two connected pieces and find the smallest possible difference between the products of their cells.	Hard9	Dynamic programmingBit manipulation+1	No attempts yet	1s	1024 MB	Judgeable
Even SubstringsGiven a string over six letters and point updates, count for each range query the substrings in which every distinct letter occurs an even number of times.	Hard9	Segment treeBit manipulation+2	No attempts yet	7s	1024 MB	Judgeable
Problem Set ConstructionFor each problem, compute the probability that a randomly chosen k-problem set contains it and the team solves it, given teams maximize count then minimize total time under limit t.	Hard9	ProbabilityCombinatorics+2	No attempts yet	1s	1024 MB	Judgeable
Super NineGiven some triples of players from 1 to 9, extend them to a Steiner triple system on 9 points, or report that none exists.	Hard9	CombinatoricsBacktracking+2	No attempts yet	1s	512 MB	Judgeable
Notability IndexGiven a prime P and a digit string T, answer queries that ask how many substrings of T[l..r] form numbers divisible by P.	Hard9	Number theoryPrefix sum+2	No attempts yet	2s	512 MB	Judgeable
First to SolveFor each contestant in a contest with random problem orderings, compute the expected number of problems where they are among the earliest solvers, modulo 998244353.	Hard9	ProbabilityCombinatorics+2	No attempts yet	5s	512 MB	Judgeable
High PowersGiven symmetric sums s, t, u of three distinct complex numbers, compute a symmetric alternating expression in a, b, c raised to huge powers n and m, modulo 998244353.	Hard9	MathCombinatorics+2	No attempts yet	2s	1024 MB	Judgeable
Tarzan JumpsGiven tree heights, find for each k the fewest height changes needed so Tarzan can reach the last tree in at most k jumps.	Hard9	TreeDynamic programming+1	No attempts yet	2s	256 MB	Judgeable
InversionsFor length-n permutations, the task is to sum inv(p)^k over all permutations modulo 998244353, with n up to 10^18 and k up to 1000.	Hard9	MathCombinatorics	No attempts yet	3s	256 MB	Judgeable
MountainsCount n by m grids of non-negative heights, each at most k, whose maximum-weight monotone path from (1,1) to (n,m) has total sum at most k.	Hard9	Dynamic programmingCombinatorics+1	No attempts yet	1s	256 MB	Judgeable
Casual DancersThree friends random-walk on a number line, one random friend moves each second (+1 with p percent); output the expected final span modulo 998244353.	Hard9	ProbabilityDynamic programming+1	No attempts yet	4s	512 MB	Judgeable
First OccurrenceGiven l and r up to 10^18, find the smallest index where the Thue-Morse substring t[l..r] first appears in the sequence.	Hard9	String matchingBit manipulation+2	No attempts yet	2s	512 MB	Judgeable
MismatchFor each k from 1 to n, count the size-k subsequences whose bitwise AND is zero, modulo 998244353.	Hard9	Bit manipulationCombinatorics+1	No attempts yet	4s	512 MB	Judgeable
Spiral MatrixFor each query submatrix, decide whether some neighbour-connected path through all its cells visits a contiguous range of values.	Hard9	MatrixPrefix sum+1	No attempts yet	4s	512 MB	Judgeable
DCMSFFor each edge count from 1 to N-1, find the minimum weight spanning forest where special vertices meet degree caps and nice vertices have degree at most 1.	Hard9	GraphMinimum spanning tree+1	No attempts yet	2s	1024 MB	Judgeable
multiple edgesEdges are added and removed one query at a time in an online interactive stream, and after each query the program prints the number of connected components.	Hard9	GraphUnion-find+1	No attempts yet	0.5s	1024 MB	Judgeable
Regional TourFind a tree path with promotions in at least one of every M consecutive regions, maximizing total support and the ratio of support to time.	Hard9	TreeDynamic programming+1	No attempts yet	4s	512 MB	Judgeable
JailGiven a tree and M prisoner routes from bedroom to workroom, decide whether every prisoner can walk a shortest path without entering a room that is occupied.	Hard9	TreeGraph+2	No attempts yet	4s	1024 MB	Judgeable
Ants and SugarGiven Q online insertions of ants and sugar cubes on a line, after each operation report the maximum number of sugar cubes one ant can eat within distance L.	Hard9	Segment treeGreedy+1	No attempts yet	4s	1024 MB	Judgeable
EvolutionGiven a rooted tree that grows one leaf at a time, each query picks a subtree and finds the smallest possible maximum count of additional edges on any path after choosing main children.	Hard9	TreeDynamic programming+1	No attempts yet	2s	1024 MB	Judgeable
Find the Magic BeadSplit k+1 beads into M pouches to minimize the worst-case cleanup cost of finding the magic bead, for every k from 0 to N-1.	Hard9	Dynamic programmingDivide and conquer+1	No attempts yet	2s	1024 MB	Judgeable
Security SystemChoose which laser sensors to activate so that their beams to the walls never meet, maximizing the total importance of the chosen sensors.	Hard9	GraphGeometry	No attempts yet	2.5s	1024 MB	Judgeable
PalindromiEach concatenation joins two binary strings in a given order, and the task asks for the number of distinct palindromic substrings after each join.	Hard9	StringString matching+1	No attempts yet	1s	512 MB	Judgeable
FarmFind a longest route of trees Mr. P can visit by driving straight left, right, up, or diagonally up, and the fewest road rollers that cover the non-horizontal ruts.	Hard9	GraphSorting+1	No attempts yet	1s	1024 MB	Judgeable
Tree GCDGiven a tree with N vertices labeled 1 to N, compute the sum of gcd(i, j, dist(i, j)) over all pairs i less than j.	Hard9	TreeDivide and conquer+1	No attempts yet	2.5s	1024 MB	Judgeable
Cruel BordersGiven a tree rooted at state 1 with duties, handle online duty changes and new leaf states, and report what each representative pays while traveling to state 1.	Hard9	TreeSegment tree+2	No attempts yet	1.5s	1024 MB	Judgeable
Uplifting ExcursionGiven how many art pieces have each uplift from -M to M, find the maximum number you can pick so their uplifts sum to exactly L, or report impossible.	Hard9	Dynamic programmingMath	No attempts yet	4s	512 MB	Judgeable
GameAfter each added teleporter, report whether a cycle passes through a special planet 0 to k-1, which lets a tourist collect infinitely many stamps.	Hard9	GraphDivide and conquer+1	No attempts yet	2s	256 MB	Judgeable
Race for the GalaxyCount non-intersecting monotone grid paths for N runners with puddles and mud rows, grouped by how many runners cross the mud row S to S+1.	Hard9	Dynamic programmingCombinatorics+1	No attempts yet	4s	1024 MB	Judgeable
Gravity HackenbushGiven a graph of points grounded at y=0 with red, blue, and green segments, determine the winner when both players cut optimally.	Hard9	GraphGame theory+1	No attempts yet	2s	1024 MB	Judgeable
Hide-and-Seek with a SpiritThe spirit fills a 200x200 grid with values 1 to 24 so the seeker can find each of nine hiders' quadrants using one Find call and four Get calls.	Hard9	ImplementationBit manipulation+1	No attempts yet	1s	1024 MB	Judgeable
Nieun Forest ArtistCount the ways to tile an N by N square with L-shaped pieces of sizes 1 to N, where equal-town pieces never share an edge, up to rotation, modulo 998244353.	Hard9	CombinatoricsDynamic programming+1	No attempts yet	2s	1024 MB	Judgeable
Trees, Sets, and QueriesFor a tree, after each query adds u to U and v to V, decide whether the stones on U can slide one move at a time into V while staying independent, and sum the answers.	Hard9	TreeDFS+2	No attempts yet	4s	512 MB	Judgeable
Thousand IslandsFind a closed trip from island 0 that visits another island and leaves every canoe at its starting island U[i], using at most 2,000,000 sailings, or report that none exists.	Hard9	GraphDFS+1	No attempts yet	1s	1024 MB	Judgeable
Simple Problem (Large)Count triples (x, y, z) with x up to a, y up to b, z up to c where x mod y, y mod z, and z mod x are all equal, for up to 600,000 queries.	Hard9	Number theoryMath+1	No attempts yet	2.4s	1024 MB	Judgeable
TokensGiven a directed graph and two token placements of equal size, decide whether tokens can move from the red set to the blue set and back to the red set.	Hard9	GraphDFS+1	No attempts yet	2s	1024 MB	Judgeable
Lord of the Characteristic Polynomials (1)Given an n by n integer matrix and a modulus M, output the coefficients of its characteristic polynomial modulo M.	Hard9	MatrixNumber theory+1	No attempts yet	5s	1024 MB	Judgeable
MSTGiven M queries that each add k cyclically shifted edges to a graph on N vertices, find the MST weight or print -1 if none exists.	Hard9	GraphMinimum spanning tree+1	No attempts yet	3s	1024 MB	Judgeable
Younghee's ErrandGiven an N by N grid of candies (o) and chocolates (x), find the average expected candy and chocolate counts over all target cells after each label flip.	Hard9	CombinatoricsDynamic programming+1	No attempts yet	2s	1024 MB	Judgeable
Make Numbers with DivisionGiven how many copies of each number 1 to 9 are available, count the distinct values reachable with division and parentheses, modulo 998244353.	Hard9	MathCombinatorics+1	No attempts yet	1s	1024 MB	Judgeable
Floor Tiles in a ParkCount the ways to draw grid-line segments on a W by H grid so that it splits into exactly k subrectangles, modulo 998244353.	Hard9	CombinatoricsMath+1	No attempts yet	1s	1024 MB	Judgeable
Rotate Sum 3Given a convex polygon, find the volume swept when it is repeatedly rotated in 3D about its symmetry axes, which move with it.	Hard9	GeometryMath+1	No attempts yet	1s	1024 MB	Judgeable
Great PartyFor each query range [l, r], count the sub-segments whose stone piles give the first player a win in the merge-and-remove game.	Hard9	Game theoryBit manipulation+1	No attempts yet	1s	1024 MB	Judgeable
DS Team SelectionEach update adds a square pyramid of weights centered at (x, y), and each query asks for the weight sum over a rectangle modulo 2^30.	Hard9	Segment treeMath+1	No attempts yet	18s	1024 MB	Judgeable
GamesCount the labelings of a tree's vertices with values 0 to m that keep the uncolored vertices connected at every stage, after each single-label update.	Hard9	TreeDynamic programming+1	No attempts yet	4s	1024 MB	Judgeable
Half PlaneEach query sums the vectors of points strictly below the line ax+by=c, then multiplies those vectors by a 3x3 matrix in place.	Hard9	GeometrySegment tree+1	No attempts yet	12s	1024 MB	Judgeable
WCWBTTMaintain a rooted tree under parent changes and output the vertex set on each path query using set-union operations under strict cost limits.	Hard9	TreeDivide and conquer+1	No attempts yet	20s	1024 MB	Judgeable