Math and counting

Number theory, combinatorics, and geometry

Under construction

Still being built. Things may change

Total results13,164 problems

Horsemeet
Hard8
Probability, Graph+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Lighting
Hard8
Dynamic programming, Bit manipulation+1
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Numbers Generator
Hard8
String matching, Hash map+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Plate
Hard8
Math, Simulation+2
No attempts yet
Time limit
1s
Memory limit
512 MB
Judgeable
Secret Code
Hard8
Combinatorics, Geometry+2
No attempts yet
Time limit
1s
Memory limit
512 MB
Judgeable
TV Show Game
Hard8
Dynamic programming, Brute force+2
No attempts yet
Time limit
1s
Memory limit
512 MB
Judgeable
Chemical table
Hard8
Union-find, Graph+2
No attempts yet
Time limit
1s
Memory limit
512 MB
Judgeable
Prime Tree - 5
Hard8
Greedy, Number theory+2
No attempts yet
Time limit
10s
Memory limit
512 MB
Judgeable
Prime Tree - 8
Hard8
Tree, Greedy+2
No attempts yet
Time limit
10s
Memory limit
512 MB
Judgeable
Count the Bits
Hard8
Dynamic programming, Bit manipulation+1
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Knockout
Hard8
Dynamic programming, Bit manipulation+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Rectangles
Hard8
Segment tree, Prefix sum+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
A/B - 3
Hard8
Math, Implementation+2
No attempts yet
Time limit
0.5s
Memory limit
512 MB
Judgeable
Slackline Adventure
Hard8
Math, Number theory+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Joining Capitals
Hard8
Graph, Minimum spanning tree+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Kepler
Hard8
Geometry, Sorting+1
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Maple Leaf Story
Hard8
Brute force, Combinatorics+2
No attempts yet
Time limit
1s
Memory limit
256 MB
Judgeable
Decorating a Christmas Tree
Hard8
Dynamic programming, Tree+2
No attempts yet
Time limit
1s
Memory limit
512 MB
Judgeable
decrypt
Hard8
Bit manipulation, Math+2
No attempts yet
Time limit
1s
Memory limit
64 MB
Judgeable
cmp
Hard8
Bit manipulation, Binary search+2
No attempts yet
Time limit
10s
Memory limit
256 MB
Judgeable
Pikachu's Hard Problem
Hard8
Math, Implementation
No attempts yet
Time limit
1s
Memory limit
512 MB
Judgeable
Escape, Polygon!
Hard8
Geometry, Combinatorics+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Gathering Red-Black Fruits
Hard8
Geometry, Sorting+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Looking for the Risk Factor
Hard8
Math, Number theory+2
No attempts yet
Time limit
0.2s
Memory limit
512 MB
Judgeable
Pixel Triangles
Hard8
Prefix sum, Matrix+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Artilleries and Defensive Walls
Hard8
Geometry, Sorting+2
No attempts yet
Time limit
1s
Memory limit
512 MB
Judgeable
Discs
Hard8
Geometry, Dynamic programming+2
No attempts yet
Time limit
1s
Memory limit
512 MB
Judgeable
Fair Tournament
Hard8
Dynamic programming, Bit manipulation+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Access Points
Hard8
Dynamic programming, Divide and conquer+2
No attempts yet
Time limit
1s
Memory limit
512 MB
Judgeable
Jinxed Betting
Hard8
Game theory, Greedy+1
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Dropping Blocks
Hard8
Greedy, Math+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Far, Far Away
Hard8
Binary search, Graph+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Interesting World of Arrays
Hard8
Combinatorics, Math+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Knights and Dragons
Hard8
Geometry, Sorting+2
No attempts yet
Time limit
4s
Memory limit
512 MB
Judgeable
Adding Parentheses
Hard8
Dynamic programming, Recursion+2
No attempts yet
Time limit
0.5s
Memory limit
512 MB
Judgeable
Fraction Challenge
Hard8
String, Hash map+2
No attempts yet
Time limit
0.5s
Memory limit
512 MB
Judgeable
Counting Stairs
Hard8
Dynamic programming, Math+2
No attempts yet
Time limit
3s
Memory limit
512 MB
Judgeable
Distinct Substrings
Hard8
String matching, Math+1
No attempts yet
Time limit
3s
Memory limit
512 MB
Judgeable
Interactive Array Guessing
Hard8
Implementation, Divide and conquer+1
No attempts yet
Time limit
3s
Memory limit
512 MB
Judgeable
Fractions
Hard8
Math, Number theory+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Cutting Paper
Hard8
Geometry, Implementation+1
No attempts yet
Time limit
3s
Memory limit
128 MB
Judgeable
XOR Poker
Hard8
Bit manipulation, Greedy+1
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Trees Gump
Hard8
Divide and conquer, Geometry+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Incredible Hull
Hard8
Geometry, Graph+1
No attempts yet
Time limit
1s
Memory limit
512 MB
Judgeable
Shooter Island
Hard8
Union-find, Intervals+2
No attempts yet
Time limit
3s
Memory limit
512 MB
Judgeable
Erasing Matrix
Hard8
Graph, Greedy+2
No attempts yet
Time limit
1s
Memory limit
256 MB
Judgeable
Metal Bar Cube
Hard8
Greedy, Implementation+2
No attempts yet
Time limit
1s
Memory limit
512 MB
Judgeable
Balance Beam
Hard8
Dynamic programming, Math+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Sort It Out
Hard8
Sorting, Combinatorics+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Bulldozer
Hard8
Geometry, Sorting+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Fox Observation
Hard8
Geometry, Divide and conquer+1
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Spotlight Movement
Hard8
Geometry, Simulation+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Gravity Point
Hard8
Geometry, Probability+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Identity Function
Hard8
Math, Number theory+1
No attempts yet
Time limit
5s
Memory limit
512 MB
Judgeable
Live Programming
Hard8
Dynamic programming, Sorting+2
No attempts yet
Time limit
5s
Memory limit
512 MB
Judgeable
Permutation Period
Hard8
Math, Number theory+2
No attempts yet
Time limit
5s
Memory limit
512 MB
Judgeable
Santa's Gift
Hard8
Dynamic programming, Greedy+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Nim without Zero
Hard8
Game theory, Bit manipulation+1
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Sum of QQ
Hard8
Math, Number theory+1
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Clique Coloring
Hard8
Combinatorics, Math+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Directions
Hard8
Geometry, Sorting+1
No attempts yet
Time limit
4s
Memory limit
512 MB
Judgeable
Difference
Hard8
Simulation, Math+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Pear-wise Voting
Hard8
Bit manipulation, Dynamic programming+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Sequential Yahtzee
Hard8
Dynamic programming, Prefix sum+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Funny Number Game
Hard8
Bit manipulation, Math+2
No attempts yet
Time limit
0.5s
Memory limit
512 MB
Judgeable
Fibonacci Nim
Hard8
Game theory, Math+2
No attempts yet
Time limit
0.5s
Memory limit
512 MB
Judgeable
Card Game
Hard8
Game theory, Dynamic programming+2
No attempts yet
Time limit
1s
Memory limit
512 MB
Judgeable
Knight Game
Hard8
Game theory, Math+2
No attempts yet
Time limit
1s
Memory limit
512 MB
Judgeable
Sum of Vectors
Hard8
Sorting, Geometry+2
No attempts yet
Time limit
0.5s
Memory limit
512 MB
Judgeable
Prime Power Game
Hard8
Math, Number theory+2
No attempts yet
Time limit
1s
Memory limit
512 MB
Judgeable
Ainta Game
Hard8
Game theory, Dynamic programming+1
No attempts yet
Time limit
1s
Memory limit
512 MB
Judgeable
Set and Queries
Hard8
Bit manipulation, Math+2
No attempts yet
Time limit
4s
Memory limit
512 MB
Judgeable
XOR Submatrix
Hard8
Bit manipulation, Trie+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Tail Star
Hard8
Number theory, Math
No attempts yet
Time limit
5s
Memory limit
256 MB
Judgeable
Number of Integer Lattice Points
Hard8
Math, Number theory+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Piece of Cake
Hard8
Combinatorics, Geometry+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
It's a Mod, Mod, Mod, Mod World
Hard8
Math, Number theory+2
No attempts yet
Time limit
5s
Memory limit
512 MB
Judgeable
Monotony
Hard8
Matrix, Dynamic programming+1
No attempts yet
Time limit
5s
Memory limit
512 MB
Judgeable
Heaps of Fun
Hard8
Probability, Dynamic programming+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Intersecting Rectangles
Hard8
Sorting, Segment tree+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Knight of the Tarot Cards
Hard8
Graph, Shortest path+2
No attempts yet
Time limit
10s
Memory limit
512 MB
Judgeable
3-SAT 2
Hard8
Graph, DFS+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Cow Dating
Hard8
Math, Two pointers+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Symphony
Hard8
Sorting, Binary search+2
No attempts yet
Time limit
1s
Memory limit
512 MB
Judgeable
Artifact Restoration
Hard8
Math, Number theory+2
No attempts yet
Time limit
1s
Memory limit
512 MB
Judgeable
Cat-First Search
Hard8
Tree, DFS+2
No attempts yet
Time limit
1s
Memory limit
512 MB
Judgeable
Ants on a Circle
Hard8
Math, Simulation+2
No attempts yet
Time limit
1s
Memory limit
512 MB
Judgeable
Raccoons Climb onto Jeongbo Island
Hard8
Number theory, Graph+1
No attempts yet
Time limit
3s
Memory limit
512 MB
Judgeable
SEGWAY
Hard8
Simulation, Implementation+2
No attempts yet
Time limit
1s
Memory limit
512 MB
Judgeable
Olympiads
Hard8
Binary search, Dynamic programming+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Outsider, You!
Hard8
Simulation, Math+1
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Grid Query 2
Hard8
Segment tree, Math+1
No attempts yet
Time limit
15s
Memory limit
1024 MB
Judgeable
NC String
Hard8
Combinatorics, Dynamic programming+2
No attempts yet
Time limit
1s
Memory limit
512 MB
Judgeable
Making Everything White
Hard8
Greedy, Implementation+2
No attempts yet
Time limit
1s
Memory limit
512 MB
Judgeable
Superb Dart
Hard8
Geometry, Graph+2
No attempts yet
Time limit
1s
Memory limit
512 MB
Judgeable
Inner Product
Hard8
Matrix, Number theory+1
No attempts yet
Time limit
5s
Memory limit
512 MB
Judgeable
Highway Cycling
Hard8
Binary search, Math+2
No attempts yet
Time limit
1s
Memory limit
512 MB
Judgeable
Magic Chessboard
Hard8
Prefix sum, Number theory+2
No attempts yet
Time limit
5s
Memory limit
512 MB
Judgeable
Lost In The Park
Hard8
Tree, Dynamic programming+2
No attempts yet
Time limit
1s
Memory limit
512 MB
Judgeable
Rabbit Farming
Hard8
Matrix, Number theory+1
No attempts yet
Time limit
1s
Memory limit
512 MB
Judgeable

Title	Level	Topics	Solved	Time limit	Memory limit	Judge
HorsemeetTwo knights move randomly to legal knight-move squares on an 8x8 board; find which knight has the higher probability of being the first to land on the other's square.	Hard8	ProbabilityGraph+2	No attempts yet	2s	512 MB	Judgeable
LightingCount N-bit b such that standard addition a+b yields exactly K set bits, using digit DP over the carries of the binary addition.	Hard8	Dynamic programmingBit manipulation+1	No attempts yet	2s	512 MB	Judgeable
Numbers GeneratorGiven up to ten H/T patterns of the same length, compute the expected number of fair coin flips until one pattern first appears contiguous.	Hard8	String matchingHash map+2	No attempts yet	2s	512 MB	Judgeable
PlateAssign labels to odd lattice points on a quadrant-by-quadrant recursive spiral, then sum labels of points on x + y = k.	Hard8	MathSimulation+2	No attempts yet	1s	512 MB	Judgeable
Secret CodeFind the probability of three uniformly timed agents meeting pairwise through their fixed waiting windows, then print the scenario indices sorted by that probability.	Hard8	CombinatoricsGeometry+2	No attempts yet	1s	512 MB	Judgeable
TV Show GameAssign each of k lamps red or blue so that every one of n triples of color guesses has at least two matches, or report impossible.	Hard8	Dynamic programmingBrute force+2	No attempts yet	1s	512 MB	Judgeable
Chemical tableGiven some cells of an n by m grid, fill the rest by purchasing cells and closing 2x2 rectangles; find the minimum number of purchases.	Hard8	Union-findGraph+2	No attempts yet	1s	512 MB	Judgeable
Prime Tree - 5Assign labels 1 to n to a tree's vertices so that as few edges as possible join two labels sharing a common divisor.	Hard8	GreedyNumber theory+2	No attempts yet	10s	512 MB	Judgeable
Prime Tree - 8Relabel the vertices of a tree with 1..n to minimize edges whose endpoints share a common divisor greater than 1. Output only, no fixed answer.	Hard8	TreeGreedy+2	No attempts yet	10s	512 MB	Judgeable
Count the BitsGiven k and b, count the total number of 1-bits in all multiples of k from 0 to 2^b-1, and print the sum modulo 10^9+9.	Hard8	Dynamic programmingBit manipulation+1	No attempts yet	2s	512 MB	Judgeable
KnockoutGiven remaining digits 1-9 and a dice total, choose a subset summing to that total that minimizes or maximizes the expected final number read from the leftover digits under optimal play.	Hard8	Dynamic programmingBit manipulation+2	No attempts yet	2s	512 MB	Judgeable
RectanglesGiven up to 100,000 axis-aligned rectangles drawn by XOR-flipping pixels on a white field, find the total count of black pixels.	Hard8	Segment treePrefix sum+2	No attempts yet	2s	512 MB	Judgeable
A/B - 3Given A and B with up to 10000 digits (possibly negative), compute the quotient and nonnegative remainder of A divided by B.	Hard8	MathImplementation+2	No attempts yet	0.5s	512 MB	Judgeable
Slackline AdventureCount unordered pairs of grid trees at distance in [L, R] whose line segment passes through no other tree, using visible lattice points and inclusion-exclusion over strip indices.	Hard8	MathNumber theory+2	No attempts yet	2s	512 MB	Judgeable
Joining CapitalsConnect all capitals with degree exactly one through Steiner points (non-capitals) at minimum Euclidean total cost.	Hard8	GraphMinimum spanning tree+2	No attempts yet	2s	512 MB	Judgeable
KeplerGiven N circles that all enclose the origin, count their intersection points, or report greater if the count exceeds 2N.	Hard8	GeometrySorting+1	No attempts yet	2s	512 MB	Judgeable
Maple Leaf StoryBind n skills of 2n to n keys so maximum quests each needing k skills all bound can be cleared. n <= 10, m <= 100.	Hard8	Brute forceCombinatorics+2	No attempts yet	1s	256 MB	Judgeable
Decorating a Christmas TreeCount binary trees with exactly L levels and N distinct nodes, ordered by level and by a preorder placement rule, modulo 100030001.	Hard8	Dynamic programmingTree+2	No attempts yet	1s	512 MB	Judgeable
decryptQuery a black-box encoder up to 320 times to recover three secret seeds of a linear recurrence and a secret byte permutation.	Hard8	Bit manipulationMath+2	No attempts yet	1s	64 MB	Judgeable
cmpStore which of 12-bit buckets hold the remembered 12-bit value with 4095 bits, then read 12 prefix sums to binary search the bucket and compare it by a 12-bit count table to fit 20 memory accesses.	Hard8	Bit manipulationBinary search+2	No attempts yet	10s	256 MB	Judgeable
Pikachu's Hard ProblemUse Stewart's theorem on isosceles ABC with equal legs N to prove F(i) = N^2, so the answer for any K points is floor(K*N^2).	Hard8	MathImplementation	No attempts yet	1s	512 MB	Judgeable
Escape, Polygon!Given an integer convex polygon of up to 100000 vertices, count the triples of its sides whose supporting lines form a triangle containing the polygon. Output that count.	Hard8	GeometryCombinatorics+2	No attempts yet	2s	512 MB	Judgeable
Gathering Red-Black FruitsCount how many distinct rankings of N children can arise from scoring each red fruit r and black fruit b for some positive integers r, b.	Hard8	GeometrySorting+2	No attempts yet	2s	512 MB	Judgeable
Looking for the Risk FactorCount integers in [2, N] whose prime factors are all at most K, for up to 50000 queries on N and K up to 100000.	Hard8	MathNumber theory+2	No attempts yet	0.2s	512 MB	Judgeable
Pixel TrianglesGiven up to four million right isosceles triangles on a 2000x2000 grid, count the total number of grid cells covered by at least one triangle.	Hard8	Prefix sumMatrix+2	No attempts yet	2s	512 MB	Judgeable
Artilleries and Defensive WallsFor each of up to 40000 tower positions below the border, count the artilleries whose line of sight avoids up to 5 horizontal walls.	Hard8	GeometrySorting+2	No attempts yet	1s	512 MB	Judgeable
DiscsAssign nested discs to N given lattice centers and choose radii so every pair of discs is nested, minimizing the total radius sum.	Hard8	GeometryDynamic programming+2	No attempts yet	1s	512 MB	Judgeable
Fair TournamentArrange 2^N players in a knockout bracket so player 1 wins every match, minimizing the sum of the efforts paid along the way; print -1 if impossible.	Hard8	Dynamic programmingBit manipulation+2	No attempts yet	2s	512 MB	Judgeable
Access PointsPlace n teams so both coordinates are nondecreasing along IDs, minimizing the sum of squared distances to fixed access points.	Hard8	Dynamic programmingDivide and conquer+2	No attempts yet	1s	512 MB	Judgeable
Jinxed BettingGiven everyone's scores with Julia listed first, find how many more matches she is guaranteed to stay in the lead against worst-case bets and outcomes.	Hard8	Game theoryGreedy+1	No attempts yet	2s	512 MB	Judgeable
Dropping BlocksGiven pile heights, decide whether prefix-wise operations (add 1 to a prefix or a suffix starting at k) can produce exactly that array, and say valid or invalid.	Hard8	GreedyMath+2	No attempts yet	2s	512 MB	Judgeable
Far, Far AwayGiven an n by n cost matrix and budget m, find the maximum number of edges on a walk from vertex 1 with total cost at most m; vertices and edges may repeat.	Hard8	Binary searchGraph+2	No attempts yet	2s	512 MB	Judgeable
Interesting World of ArraysCount arrays of length n whose values each satisfy a[i] = count(i) mod m, for n up to 12 and m up to 1e9.	Hard8	CombinatoricsMath+2	No attempts yet	2s	512 MB	Judgeable
Knights and DragonsGiven n distinct points (strength, magic), decide for each whether it lies in the convex hull of the others, since a point is reachable by repeated weighted averaging of the other points exactly when it is not a vertex of the hull.	Hard8	GeometrySorting+2	No attempts yet	4s	512 MB	Judgeable
Adding ParenthesesParenthesize a single-digit expression with non-nested single-operator parentheses to maximize its left-to-right value.	Hard8	Dynamic programmingRecursion+2	No attempts yet	0.5s	512 MB	Judgeable
Fraction ChallengeMultiply many huge fractions given as digit strings and output the reduced product as a/b.	Hard8	StringHash map+2	No attempts yet	0.5s	512 MB	Judgeable
Counting StairsCount symmetric stairs (partitions of n into distinct parts) with n cubes, modulo 998244353, for up to 1e4 queries with n up to 2e5.	Hard8	Dynamic programmingMath+2	No attempts yet	3s	512 MB	Judgeable
Distinct SubstringsGiven a period string p and length n, count distinct substrings of the string formed by repeating p and cutting to n. n may be 1e9.	Hard8	String matchingMath+1	No attempts yet	3s	512 MB	Judgeable
Interactive Array GuessingGiven n hidden arrays of up to 10 distinct values each, find all arrays using queries that return concatenated contents of chosen arrays, without delimiters.	Hard8	ImplementationDivide and conquer+1	No attempts yet	3s	512 MB	Judgeable
FractionsGiven n, represent 1 - 1/n as a sum of fractions with denominators dividing n and strictly between 1 and n, or report that no such sum exists.	Hard8	MathNumber theory+2	No attempts yet	2s	512 MB	Judgeable
Cutting PaperGiven a simple polygon, count how many pieces of paper lie inside and outside it after cutting along the full extended lines of every edge.	Hard8	GeometryImplementation+1	No attempts yet	3s	128 MB	Judgeable
XOR PokerGiven N integers, choose a nonempty subset of even size whose XOR is maximum and print that value.	Hard8	Bit manipulationGreedy+1	No attempts yet	2s	512 MB	Judgeable
Trees GumpPlace the N units of a given tree onto the N points so that the tree's edges, drawn as straight segments, never cross.	Hard8	Divide and conquerGeometry+2	No attempts yet	2s	512 MB	Judgeable
Incredible HullGiven N points sorted by profit, with the outer points forming a convex perimeter, the task is to find the size of a largest clique, how many largest cliques exist, and how many points belong to one.	Hard8	GeometryGraph+1	No attempts yet	1s	512 MB	Judgeable
Shooter IslandOn a 50 by 100000 grid, rectangles flood when hit, and after each query decide whether a radius-0.31416 boat can sail between two given squares on the remaining water.	Hard8	Union-findIntervals+2	No attempts yet	3s	512 MB	Judgeable
Erasing MatrixDecide whether all cells of a grid can be driven to zero by repeatedly adding the same integer k to two adjacent cells while keeping every value non-negative, and print a valid sequence of at most 10^6 operations.	Hard8	GraphGreedy+2	No attempts yet	1s	256 MB	Judgeable
Metal Bar CubeGiven the four viewing counts from left, right, top and bottom of an N by N grid, decide whether any placement of blocked cells can produce exactly those counts.	Hard8	GreedyImplementation+2	No attempts yet	1s	512 MB	Judgeable
Balance BeamChoose at each beam position a cash value or a fair coin random walk stopped at the ends, maximizing expected payment for every starting position.	Hard8	Dynamic programmingMath+2	No attempts yet	2s	512 MB	Judgeable
Sort It OutFind the smallest subset of cow IDs S such that repeatedly yelling at each ID in S in increasing order eventually sorts the permutation, then output the K-th lexicographically smallest such subset.	Hard8	SortingCombinatorics+2	No attempts yet	2s	512 MB	Judgeable
BulldozerChoose two parallel lines and take every weighted point between them, maximizing the sum of gold values minus rock costs.	Hard8	GeometrySorting+2	No attempts yet	2s	512 MB	Judgeable
Fox ObservationGiven weighted lattice points, find the two-corner rectangle that maximizes total enclosed weight divided by its area, printed as a reduced fraction.	Hard8	GeometryDivide and conquer+1	No attempts yet	2s	512 MB	Judgeable
Spotlight MovementGiven N spotlights whose centers move around polygonal orbits, decide whether Ciel can walk from a start point to an end point while staying inside at least one illuminated circle at all times.	Hard8	GeometrySimulation+2	No attempts yet	2s	512 MB	Judgeable
Gravity PointA random mass for tiles A and B is drawn from given ranges; find the chance the grid's center of gravity falls in a filled cell.	Hard8	GeometryProbability+2	No attempts yet	2s	512 MB	Judgeable
Identity FunctionGiven N, find the smallest positive k with every iterate F_k(a)=a for 1<=a<N under f(a)=a^N mod N, or output -1.	Hard8	MathNumber theory+1	No attempts yet	5s	512 MB	Judgeable
Live ProgrammingChoose a subset of songs within total length T and order them to maximize the sum of basic points minus squared feature differences between consecutive songs.	Hard8	Dynamic programmingSorting+2	No attempts yet	5s	512 MB	Judgeable
Permutation PeriodStarting from the identity permutation, apply swaps one at a time and after each swap report the permutation's period modulo 1e9+7, where the period is the LCM of its cycle lengths.	Hard8	MathNumber theory+2	No attempts yet	5s	512 MB	Judgeable
Santa's GiftFor each family size k from 1 to M, choose a subset of gift kinds so k copies of each fit in capacity C, maximizing total price.	Hard8	Dynamic programmingGreedy+2	No attempts yet	2s	512 MB	Judgeable
Nim without ZeroAn impartial game where a move loses if it makes the XOR of all heap sizes equal zero. Decide the winner with optimal play.	Hard8	Game theoryBit manipulation+1	No attempts yet	2s	512 MB	Judgeable
Sum of QQCount axis-parallel rectangles in the multiplication table whose entries sum to exactly S, with S up to 100000.	Hard8	MathNumber theory+1	No attempts yet	2s	512 MB	Judgeable
Clique ColoringGiven up to five clique sizes, find the smallest number of vertices in a complete graph whose edges can be covered by cliques of those sizes with no repeated edge.	Hard8	CombinatoricsMath+2	No attempts yet	2s	512 MB	Judgeable
DirectionsPick the cheapest set of direction vectors whose nonnegative multiples let Snuke reach any point from any other, or print -1 if no set works.	Hard8	GeometrySorting+1	No attempts yet	4s	512 MB	Judgeable
DifferenceBuild the sequence from A1 incrementally, adding each next gap so that m hits as a value or an existing difference; report the first step that covers it.	Hard8	SimulationMath+2	No attempts yet	2s	512 MB	Judgeable
Pear-wise VotingGiven ranked ballots and a selectable candidate order, decide for each candidate whether some agenda makes that candidate win sequential pairwise contests.	Hard8	Bit manipulationDynamic programming+2	No attempts yet	2s	512 MB	Judgeable
Sequential YahtzeeGiven up to 195 sequential dice rolls, assign consecutive segments to the 13 Yahtzee categories in order to maximize the total score.	Hard8	Dynamic programmingPrefix sum+2	No attempts yet	2s	512 MB	Judgeable
Funny Number GameGiven a 4-digit N and M turns of incrementing one digit with 9 wrapping to 0, decide which player forces the final value above N.	Hard8	Bit manipulationMath+2	No attempts yet	0.5s	512 MB	Judgeable
Fibonacci NimFind which piles lose the Fibonacci-Nim take-away game and decide the winner of the multi-pile sum game with optimal play.	Hard8	Game theoryMath+2	No attempts yet	0.5s	512 MB	Judgeable
Card GameTwo players alternately remove a chosen card and every card with a smaller number; decide the winner under optimal play.	Hard8	Game theoryDynamic programming+2	No attempts yet	1s	512 MB	Judgeable
Knight GameTwo players alternately place non-attacking knights on an N x N board; decide who wins under optimal play, with N up to 10,000.	Hard8	Game theoryMath+2	No attempts yet	1s	512 MB	Judgeable
Sum of VectorsChoose two of N vectors, each optionally sign-flipped per coordinate, to minimize the norm of their sum and output the pair with the chosen flips.	Hard8	SortingGeometry+2	No attempts yet	0.5s	512 MB	Judgeable
Prime Power GameTwo players alternately choose a prime power p^k that divides some element and divide every element it divides by p^k; the player who cannot move loses, so print the winner.	Hard8	MathNumber theory+2	No attempts yet	1s	512 MB	Judgeable
Ainta GameGiven K, N, and M, decide who wins a game where a piece moves down, right, or diagonally by K on an N by M board, starting from the top-left corner.	Hard8	Game theoryDynamic programming+1	No attempts yet	1s	512 MB	Judgeable
Set and QueriesAfter each insertion or deletion in a set of up to 500,000 integers, report the maximum XOR achievable by any subset of the current set.	Hard8	Bit manipulationMath+2	No attempts yet	4s	512 MB	Judgeable
XOR SubmatrixBuild the N by M matrix with A[i][j] = V[i] xor U[j] and find the submatrix whose elementwise xor is maximal.	Hard8	Bit manipulationTrie+2	No attempts yet	2s	512 MB	Judgeable
Tail StarGiven prime P and year Q, find the sum of p^Q over all primes p up to P, taken modulo P, since only prime-numbered days have no overtime.	Hard8	Number theoryMath	No attempts yet	5s	256 MB	Judgeable
Number of Integer Lattice PointsCount pairs of lattice points in a grid whose connecting segment contains exactly K lattice points.	Hard8	MathNumber theory+2	No attempts yet	2s	512 MB	Judgeable
Piece of CakeGiven a convex polygon with n vertices in clockwise order, compute the expected area of the convex polygon formed by picking k of the vertices uniformly at random.	Hard8	CombinatoricsGeometry+2	No attempts yet	2s	512 MB	Judgeable
It's a Mod, Mod, Mod, Mod WorldGiven p, q, n, compute the sum of (p*i mod q) for i from 1 to n, for up to 100000 queries with values up to 10^6.	Hard8	MathNumber theory+2	No attempts yet	5s	512 MB	Judgeable
MonotonyCount the subgrids where every row and every column is strictly increasing or strictly decreasing, in a grid of distinct values up to 20 by 20.	Hard8	MatrixDynamic programming+1	No attempts yet	5s	512 MB	Judgeable
Heaps of FunGiven a rooted tree where each node i draws a uniform random real in [0, b_i], compute the probability that every parent's value is less than both its children's values, modulo 1e9+7.	Hard8	ProbabilityDynamic programming+2	No attempts yet	2s	512 MB	Judgeable
Intersecting RectanglesGiven n axis-aligned rectangles with all x and y coordinates distinct, decide whether any two boundaries cross or touch. One rectangle fully containing another does not count.	Hard8	SortingSegment tree+2	No attempts yet	2s	512 MB	Judgeable
Knight of the Tarot CardsFind the minimum total price of tarot cards the knight must buy to reach (0, 0), where each card's values unlock new knight jumps.	Hard8	GraphShortest path+2	No attempts yet	10s	512 MB	Judgeable
3-SAT 2Given a 3-CNF formula with N variables and M clauses, decide whether it is satisfiable and, if so, output a satisfying assignment.	Hard8	GraphDFS+2	No attempts yet	2s	512 MB	Judgeable
Cow DatingGiven probabilities p_i, choose a contiguous interval maximizing the chance that exactly one bull accepts, and print 10^6 times that probability rounded down.	Hard8	MathTwo pointers+2	No attempts yet	2s	512 MB	Judgeable
SymphonyAdd one integer X to every element of A, then change at most K elements to any values, minimizing the sum of absolute differences against B.	Hard8	SortingBinary search+2	No attempts yet	1s	512 MB	Judgeable
Artifact RestorationGiven a grid with some unknown cells, fill unknowns with 0 or 1 so that the total number of people summed over all subrectangles is divisible by K.	Hard8	MathNumber theory+2	No attempts yet	1s	512 MB	Judgeable
Cat-First SearchGiven a tree and the order Taehee wrote down in a cat-guided DFS, find the minimum number of cats and count their possible starting placements.	Hard8	TreeDFS+2	No attempts yet	1s	512 MB	Judgeable
Ants on a CircleAnts move on a circle of N points, reversing on collision; for each query (P, X) find the earliest time point P has been visited at least X times.	Hard8	MathSimulation+2	No attempts yet	1s	512 MB	Judgeable
Raccoons Climb onto Jeongbo IslandFind the maximum number of raccoons that can eat cotton candy, tracking candy weights modulo K under form uniqueness and sticker costs.	Hard8	Number theoryGraph+1	No attempts yet	3s	512 MB	Judgeable
SEGWAYSimulate N riders over a 300 m track with three speed sections and accelerators granting 1 s/m boost for X mod 20 meters, where X counts riders strictly ahead, and print each finish time.	Hard8	SimulationImplementation+2	No attempts yet	1s	512 MB	Judgeable
OlympiadsGiven N contestants with scores in K events, find the total score of the C-th best K-member team, where a team scores the per-event maximum over its members.	Hard8	Binary searchDynamic programming+2	No attempts yet	2s	512 MB	Judgeable
Outsider, You!Given N and M, decide whether Junseo's motion can end up at seat M after a sequence of pointings, and if so, print one such pointing sequence.	Hard8	SimulationMath+1	No attempts yet	2s	512 MB	Judgeable
Grid Query 2Process up to 250,000 online queries on a 10^5 by 10^5 grid: add V to a rectangle, or return the rectangle's sum modulo 10^9+7, with each query decoded using the last printed answer.	Hard8	Segment treeMath+1	No attempts yet	15s	1024 MB	Judgeable
NC StringCount the permutations of chosen words (spaced apart) that contain an N before a later C, modulo 1e9+7.	Hard8	CombinatoricsDynamic programming+2	No attempts yet	1s	512 MB	Judgeable
Making Everything WhiteGiven an N by M black/white grid, choose for each cell one of three local color-inversion actions so that every cell ends up white, or report impossibility.	Hard8	GreedyImplementation+2	No attempts yet	1s	512 MB	Judgeable
Superb DartGiven a planar straight-line graph, list the areas of its bounded faces in increasing order, rounded to two decimals.	Hard8	GeometryGraph+2	No attempts yet	1s	512 MB	Judgeable
Inner ProductGiven n vectors of d nonnegative integers and a number k, find two vectors whose inner product is a multiple of k, or report that no such pair exists.	Hard8	MatrixNumber theory+1	No attempts yet	5s	512 MB	Judgeable
Highway CyclingChoose a constant speed for each of N road segments so the total energy spent stays within EU and the total travel time is minimized.	Hard8	Binary searchMath+2	No attempts yet	1s	512 MB	Judgeable
Magic ChessboardGiven an N by M grid and a guardian cell, answer GCD queries over rectangles anchored at that cell while supporting rectangle range additions.	Hard8	Prefix sumNumber theory+2	No attempts yet	5s	512 MB	Judgeable
Lost In The ParkGiven a connected weighted graph with at most one cycle, find the expected total length of a random walk that never revisits a vertex, when the start vertex is chosen uniformly at random.	Hard8	TreeDynamic programming+2	No attempts yet	1s	512 MB	Judgeable
Rabbit FarmingCount rabbit pairs in month n modulo p, where Fibonacci-style growth loses one pair whenever the total leaves remainder 1 when divided by k.	Hard8	MatrixNumber theory+1	No attempts yet	1s	512 MB	Judgeable