Math and counting

Number theory, combinatorics, and geometry

Under construction

Still being built. Things may change

Total results13,153 problems

Shelter
Hard8
Geometry, Divide and conquer+2
No attempts yet
Time limit
8s
Memory limit
512 MB
Judgeable
Nezumi's Treasure
Hard8
Geometry, Simulation+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Shore Erosion
Hard8
Geometry, Implementation
No attempts yet
Time limit
8s
Memory limit
512 MB
Judgeable
Voronoi Island
Hard8
Geometry, Divide and conquer+2
No attempts yet
Time limit
8s
Memory limit
512 MB
Judgeable
Revenge of the Round Table
Hard8
Combinatorics, Math+2
No attempts yet
Time limit
8s
Memory limit
512 MB
Judgeable
Colored Octahedra
Hard8
Combinatorics, Math+2
No attempts yet
Time limit
8s
Memory limit
512 MB
Judgeable
Wind Passages
Hard8
Geometry, Graph+1
No attempts yet
Time limit
8s
Memory limit
512 MB
Judgeable
Cover Time
Hard8
Dynamic programming, Probability+2
No attempts yet
Time limit
8s
Memory limit
512 MB
Judgeable
Craftsman
Hard8
Dynamic programming, Bit manipulation+2
No attempts yet
Time limit
8s
Memory limit
512 MB
Judgeable
Divide the Water
Hard8
Tree, Greedy+2
No attempts yet
Time limit
8s
Memory limit
512 MB
Judgeable
Mickle's Beam
Hard8
Geometry, Greedy+2
No attempts yet
Time limit
8s
Memory limit
512 MB
Judgeable
Poor Computer
Hard8
Brute force, Dynamic programming+2
No attempts yet
Time limit
8s
Memory limit
512 MB
Judgeable
Tangram
Hard8
Backtracking, Geometry+1
No attempts yet
Time limit
8s
Memory limit
512 MB
Judgeable
Trading Ship
Hard8
Binary search, Graph+2
No attempts yet
Time limit
8s
Memory limit
512 MB
Judgeable
Princess' Marriage
Hard8
Greedy, Sorting+2
No attempts yet
Time limit
8s
Memory limit
512 MB
Judgeable
Princess, a Strategist
Hard8
Geometry, Simulation
No attempts yet
Time limit
8s
Memory limit
512 MB
Judgeable
Memory Match
Hard8
Probability, Dynamic programming+2
No attempts yet
Time limit
8s
Memory limit
512 MB
Judgeable
Girls' Party
Hard8
Simulation, Brute force+2
No attempts yet
Time limit
8s
Memory limit
512 MB
Judgeable
Do It
Hard8
Math, Divide and conquer+2
No attempts yet
Time limit
8s
Memory limit
512 MB
Judgeable
Robot Communication
Hard8
Minimum spanning tree, Geometry+2
No attempts yet
Time limit
8s
Memory limit
512 MB
Judgeable
Save the Energy
Hard8
Geometry, Graph+2
No attempts yet
Time limit
8s
Memory limit
512 MB
Judgeable
!
Hard8
Number theory, Math+2
No attempts yet
Time limit
8s
Memory limit
512 MB
Judgeable
Spirograph
Hard8
Math, Geometry+1
No attempts yet
Time limit
8s
Memory limit
512 MB
Judgeable
Nagashi Soumen
Hard8
Dynamic programming, Geometry+2
No attempts yet
Time limit
8s
Memory limit
512 MB
Judgeable
Walk under a Scorching Sun
Hard8
Geometry, Shortest path+1
No attempts yet
Time limit
8s
Memory limit
512 MB
Judgeable
Connect Line Segments
Hard8
Dynamic programming, Bit manipulation+2
No attempts yet
Time limit
8s
Memory limit
512 MB
Judgeable
Divisor Function
Hard8
Number theory, Math+2
No attempts yet
Time limit
8s
Memory limit
512 MB
Judgeable
Two Rings
Hard8
Geometry, Math+1
No attempts yet
Time limit
8s
Memory limit
512 MB
Judgeable
The Closest Circle
Hard8
Divide and conquer, Geometry+2
No attempts yet
Time limit
8s
Memory limit
512 MB
Judgeable
Ellipse Intersection
Hard8
Math, Geometry+2
No attempts yet
Time limit
8s
Memory limit
512 MB
Judgeable
A Treasure Or A Bomb
Hard8
Dynamic programming, Math+2
No attempts yet
Time limit
8s
Memory limit
512 MB
Judgeable
Up and Down
Hard8
Dynamic programming, Backtracking+2
No attempts yet
Time limit
8s
Memory limit
512 MB
Judgeable
Enclosing Circles
Hard8
Geometry, Graph+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Trapezoids
Hard8
Implementation, Simulation+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Guess the Formula Quiz Game
Hard8
Number theory, Math+1
No attempts yet
Time limit
3s
Memory limit
1024 MB
Judgeable
A Simple Problem
Hard8
Sorting, Divide and conquer+2
No attempts yet
Time limit
4s
Memory limit
1024 MB
Judgeable
Beacon Fire Towers
Hard8
Dynamic programming, Divide and conquer+2
No attempts yet
Time limit
1s
Memory limit
1024 MB
Judgeable
Prime Time
Hard8
Dynamic programming, Math+2
No attempts yet
Time limit
45s
Memory limit
1024 MB
Judgeable
Orange Number
Hard8
Math, Number theory+2
No attempts yet
Time limit
1s
Memory limit
1024 MB
Judgeable
Cutting Cake
Hard8
Geometry, Math+1
No attempts yet
Time limit
45s
Memory limit
1024 MB
Judgeable
Contest Construction
Hard8
Sorting, Dynamic programming+2
No attempts yet
Time limit
1s
Memory limit
2048 MB
Judgeable
k Subarrays
Hard8
Array, Sorting+2
No attempts yet
Time limit
1s
Memory limit
1024 MB
Judgeable
The Snail Wants to Rest in the Shade
Hard8
Geometry, Sorting+1
No attempts yet
Time limit
1s
Memory limit
512 MB
Judgeable
Number of Increasing Subsequences K
Hard8
Combinatorics, Dynamic programming+2
No attempts yet
Time limit
2s
Memory limit
1024 MB
Judgeable
Truck Delivery
Hard8
Tree, DFS+2
No attempts yet
Time limit
Not set
Memory limit
1024 MB
Judgeable
Primes and Queries
Hard8
Number theory, Segment tree+2
No attempts yet
Time limit
90s
Memory limit
1024 MB
Judgeable
Hiking Trails
Hard8
Dynamic programming, Bit manipulation+2
No attempts yet
Time limit
1s
Memory limit
512 MB
Judgeable
Leaping Pieces
Hard8
Math, Number theory+2
No attempts yet
Time limit
0.5s
Memory limit
1024 MB
Judgeable
Kyojun Stargazing
Hard8
Geometry, Combinatorics+2
No attempts yet
Time limit
1.5s
Memory limit
1024 MB
Judgeable
Stones
Hard8
Game theory, Greedy+2
No attempts yet
Time limit
3s
Memory limit
512 MB
Judgeable
Graph Travel
Hard8
Graph, Dynamic programming+2
No attempts yet
Time limit
Not set
Memory limit
1024 MB
Judgeable
Generate the Sequences
Hard8
Combinatorics, Dynamic programming+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Multiple Parentheses
Hard8
Combinatorics, Dynamic programming+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Fancy Formulas
Hard8
Math, Number theory+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Glory Graph
Hard8
Combinatorics, Graph+1
No attempts yet
Time limit
3s
Memory limit
512 MB
Judgeable
Little LCS
Hard8
Combinatorics, String+1
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Nimber Sequence
Hard8
Matrix, Math+1
No attempts yet
Time limit
1s
Memory limit
256 MB
Judgeable
PlayerUnknown's Battlegrounds
Hard8
Divide and conquer, Implementation+2
No attempts yet
Time limit
1.5s
Memory limit
256 MB
Judgeable
Sum
Hard8
Matrix, Math+1
No attempts yet
Time limit
3s
Memory limit
512 MB
Judgeable
Historic Breakthrough
Hard8
Number theory, Math+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Yes, Prime Minister
Hard8
Math, Number theory+2
No attempts yet
Time limit
10s
Memory limit
512 MB
Judgeable
Nikanor Loves Games
Hard8
Math, Geometry+2
No attempts yet
Time limit
1s
Memory limit
512 MB
Judgeable
Roads of the Empire
Hard8
Graph, Number theory+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Automatic Sprayer 2
Hard8
Math, Implementation+2
No attempts yet
Time limit
2s
Memory limit
1024 MB
Judgeable
Organizing Beads
Hard8
Prefix sum, Sorting+2
No attempts yet
Time limit
2s
Memory limit
1024 MB
Judgeable
Periodic Ruler
Hard8
Math, Number theory+2
No attempts yet
Time limit
2s
Memory limit
1024 MB
Judgeable
The Islands
Hard8
Dynamic programming, Geometry+2
No attempts yet
Time limit
2s
Memory limit
1024 MB
Judgeable
Cardiology
Hard8
Math, Number theory+1
No attempts yet
Time limit
2s
Memory limit
2048 MB
Judgeable
Domes
Hard8
Geometry, Combinatorics+2
No attempts yet
Time limit
2s
Memory limit
2048 MB
Judgeable
Ley Lines
Hard8
Geometry, Sorting+2
No attempts yet
Time limit
15s
Memory limit
2048 MB
Judgeable
Opportunity Cost
Hard8
Geometry, Binary search+2
No attempts yet
Time limit
5s
Memory limit
2048 MB
Judgeable
Quests
Hard8
Dynamic programming, Greedy+2
No attempts yet
Time limit
10s
Memory limit
2048 MB
Judgeable
Trailing Digits
Hard8
Number theory, Math+2
No attempts yet
Time limit
1s
Memory limit
2048 MB
Judgeable
What's Our Vector, Victor?
Hard8
Math, Geometry+2
No attempts yet
Time limit
6s
Memory limit
2048 MB
Judgeable
The Return of Carl
Hard8
Geometry, Shortest path+2
No attempts yet
Time limit
2s
Memory limit
1024 MB
Judgeable
Conduit Packing
Hard8
Geometry, Math+2
No attempts yet
Time limit
2s
Memory limit
1024 MB
Judgeable
Colorful Tower of Hanoi
Hard8
Dynamic programming, Recursion+1
No attempts yet
Time limit
1s
Memory limit
1024 MB
Judgeable
Histogram
Hard8
Dynamic programming, Prefix sum+2
No attempts yet
Time limit
3s
Memory limit
1024 MB
Judgeable
Similarity
Hard8
Divide and conquer, Sorting+2
No attempts yet
Time limit
1s
Memory limit
1024 MB
Judgeable
Twenty-Three
Hard8
Math, Dynamic programming+2
No attempts yet
Time limit
2.3s
Memory limit
1023 MB
Judgeable
Hiring Help
Hard8
Geometry, Divide and conquer
No attempts yet
Time limit
4s
Memory limit
1024 MB
Judgeable
Intact Intervals
Hard8
Array, Hash map+2
No attempts yet
Time limit
6s
Memory limit
1024 MB
Judgeable
Line Fighter 2
Hard8
Geometry, Divide and conquer+2
No attempts yet
Time limit
1s
Memory limit
1024 MB
Judgeable
Squares
Hard8
Number theory, Math+2
No attempts yet
Time limit
2s
Memory limit
1024 MB
Judgeable
K-Calculator
Hard8
Linked list, Math+2
No attempts yet
Time limit
1.5s
Memory limit
512 MB
Judgeable
Matrix Partition
Hard8
Binary search, Brute force+2
No attempts yet
Time limit
1s
Memory limit
1024 MB
Judgeable
Hard All-Pairs Shortest Path
Hard8
Graph, Union-find+2
No attempts yet
Time limit
1s
Memory limit
1024 MB
Judgeable
Digion
Hard8
Recursion, Combinatorics+2
No attempts yet
Time limit
2s
Memory limit
1024 MB
Judgeable
Flip
Hard8
Segment tree, Prefix sum+2
No attempts yet
Time limit
3s
Memory limit
1024 MB
Judgeable
Inverting Everything
Hard8
Math, Tree+1
No attempts yet
Time limit
1s
Memory limit
1024 MB
Judgeable
Just Bootfall
Hard8
Dynamic programming, Graph+2
No attempts yet
Time limit
1s
Memory limit
1024 MB
Judgeable
Listing Passwords
Hard8
Union-find, String+1
No attempts yet
Time limit
3s
Memory limit
1024 MB
Judgeable
Tote
Hard8
Dynamic programming, Probability+2
No attempts yet
Time limit
2s
Memory limit
256 MB
Judgeable
Pulse Nova
Hard8
Geometry, Brute force
No attempts yet
Time limit
20s
Memory limit
256 MB
Judgeable
Flow
Hard8
Graph, Greedy+2
No attempts yet
Time limit
1s
Memory limit
256 MB
Judgeable
Value
Hard8
Number theory, Dynamic programming+2
No attempts yet
Time limit
1s
Memory limit
256 MB
Judgeable
All in good fun!
Hard8
Geometry, Binary search+2
No attempts yet
Time limit
1s
Memory limit
512 MB
Judgeable
Sum Modulo
Hard8
Math, Probability+1
No attempts yet
Time limit
4s
Memory limit
1024 MB
Judgeable
Xor Sum
Hard8
Bit manipulation, Binary search+1
No attempts yet
Time limit
2s
Memory limit
1024 MB
Judgeable
Matrix Inversion
Hard8
Matrix, Math+1
No attempts yet
Time limit
1s
Memory limit
1024 MB
Judgeable

Title	Level	Topics	Solved	Time limit	Memory limit	Judge
ShelterGiven a convex polygon town and N interior shelters, compute the expected squared distance from a uniformly random point in the town to its nearest shelter.	Hard8	GeometryDivide and conquer+2	No attempts yet	8s	512 MB	Judgeable
Nezumi's TreasureCount the points where a mouse that turns left at each rectangle obstacle could hide his fish at the first turn after entering an infinite loop.	Hard8	GeometrySimulation+2	No attempts yet	2s	512 MB	Judgeable
Shore ErosionGiven a counterclockwise polygon and erosion distance R, find the total boundary length left after removing points within Manhattan distance R of the coast.	Hard8	GeometryImplementation	No attempts yet	8s	512 MB	Judgeable
Voronoi IslandFor each dataset, divide a convex island polygon among M castles by nearest-castle rule and print each lord's resulting area within 1e-4.	Hard8	GeometryDivide and conquer+2	No attempts yet	8s	512 MB	Judgeable
Revenge of the Round TableCount circular binary sequences of length n with no run of more than k equal symbols, modulo 1000003, up to rotation.	Hard8	CombinatoricsMath+2	No attempts yet	8s	512 MB	Judgeable
Colored OctahedraCount how many distinct octahedra can be formed from eight colored triangular panels, treating two octahedra as identical when a rotation maps one to the other.	Hard8	CombinatoricsMath+2	No attempts yet	8s	512 MB	Judgeable
Wind PassagesGiven a corridor of width W with non-overlapping polygonal pillars, find the maximum flow from south to north where each path's capacity is its narrowest gap.	Hard8	GeometryGraph+1	No attempts yet	8s	512 MB	Judgeable
Cover TimeCompute the expected number of steps for a random walk starting at vertex 1 to visit every vertex of a connected undirected graph with N at most 10.	Hard8	Dynamic programmingProbability+2	No attempts yet	8s	512 MB	Judgeable
CraftsmanChoose which orders to accept and which tools to buy, where discounted tool pairs bought together change the cost, to maximize income minus tool cost.	Hard8	Dynamic programmingBit manipulation+2	No attempts yet	8s	512 MB	Judgeable
Divide the WaterGiven the target integer proportions of N ordered columns, find the minimum number of faucets (each splitting into halves via binary tubes) whose flow, laid out without crossing, realizes those proportions.	Hard8	TreeGreedy+2	No attempts yet	8s	512 MB	Judgeable
Mickle's BeamGiven up to 2000 disjoint axis-aligned rectangles that avoid the origin, find the minimum number of rays from the origin needed to hit every rectangle.	Hard8	GeometryGreedy+2	No attempts yet	8s	512 MB	Judgeable
Poor ComputerGiven distinct multipliers between 2 and 42, find the shortest sequence of additions, subtractions, and left shifts that builds all values a_i*x from x without exceeding 42x.	Hard8	Brute forceDynamic programming+2	No attempts yet	8s	512 MB	Judgeable
TangramGiven a simple polygon whose edges run horizontally, vertically, or diagonally, decide whether all seven tangram pieces can tile it without overlap.	Hard8	BacktrackingGeometry+1	No attempts yet	8s	512 MB	Judgeable
Trading ShipFind a path from the bottom edge y=0 to the top edge y=H inside a rectangle that maximizes the minimum distance to any of N given points.	Hard8	Binary searchGraph+2	No attempts yet	8s	512 MB	Judgeable
Princess' MarriageWith budget M, choose how much of each road segment to guard (cost 1 per unit, reducing attacks proportionally) to minimize the total expected number of attacks along the route.	Hard8	GreedySorting+2	No attempts yet	8s	512 MB	Judgeable
Princess, a StrategistGiven a moving polygon and bullet segments that travel with their own velocities, report every time a bullet first touches the polygon.	Hard8	GeometrySimulation	No attempts yet	8s	512 MB	Judgeable
Memory MatchWith perfect memory of every card seen, compute the expected number of mismatches when playing memory match optimally on 2M cards.	Hard8	ProbabilityDynamic programming+2	No attempts yet	8s	512 MB	Judgeable
Girls' PartyIn a Josephus-style elimination game on a circular string of B and G girls, Bella may switch the count start from 1 to 0 at most once; find the maximum number of B girls that can survive at the end.	Hard8	SimulationBrute force+2	No attempts yet	8s	512 MB	Judgeable
Do ItIntegrate a product of N sine functions over [0, R], with N up to 16, to absolute or relative error 1e-8.	Hard8	MathDivide and conquer+2	No attempts yet	8s	512 MB	Judgeable
Robot CommunicationRobots move linearly on a plane over time; choose a single moment and a connected communication graph to minimize the total distance of its edges.	Hard8	Minimum spanning treeGeometry+2	No attempts yet	8s	512 MB	Judgeable
Save the EnergyGiven N infinite straight lines in 3D, find the minimum off-line distance needed to travel from a source point on some line to a destination point on some line, where travel along lines is free.	Hard8	GeometryGraph+2	No attempts yet	8s	512 MB	Judgeable
!For each pair of a base N (8 to 36) and a number M written in base N, output how many trailing zeros M! has when written in base N.	Hard8	Number theoryMath+2	No attempts yet	8s	512 MB	Judgeable
SpirographFor each test case, compute the total arc length of a hypotrochoid traced by a pinhole in a circle of radius Q rolling inside a fixed circle of radius P, with pinhole offset R.	Hard8	MathGeometry+1	No attempts yet	8s	512 MB	Judgeable
Nagashi SoumenGiven N points in space and at most K strictly descending flumes (paths whose z-coordinate decreases), find the minimum total length of flumes that cover every point.	Hard8	Dynamic programmingGeometry+2	No attempts yet	8s	512 MB	Judgeable
Walk under a Scorching SunGiven convex building footprints, sun angles, and road segments, find a route from S to T whose portion outside building shadows is as short as possible.	Hard8	GeometryShortest path+1	No attempts yet	8s	512 MB	Judgeable
Connect Line SegmentsGiven up to 14 line segments, add connecting segments between endpoints to join all of them into one polyline of minimum total length.	Hard8	Dynamic programmingBit manipulation+2	No attempts yet	8s	512 MB	Judgeable
Divisor FunctionFor each k up to 10^15, find the maximum value of sigma(n)/n over all n from 1 to k, printed to six decimals.	Hard8	Number theoryMath+2	No attempts yet	8s	512 MB	Judgeable
Two RingsGiven two circles on the unit sphere, each defined by two latitude/longitude endpoints, find and print their intersection points or report that none exist.	Hard8	GeometryMath+1	No attempts yet	8s	512 MB	Judgeable
The Closest CircleGiven up to 100000 non-overlapping circles whose radii differ by at most a factor of two, find the pair of circles with the smallest gap between them and print that distance.	Hard8	Divide and conquerGeometry+2	No attempts yet	8s	512 MB	Judgeable
Ellipse IntersectionGiven two concentric axis-aligned ellipses with perpendicular major axes, compute the area of their intersection to within 0.001.	Hard8	MathGeometry+2	No attempts yet	8s	512 MB	Judgeable
A Treasure Or A BombAssign each key to a distinct keyhole to maximize the product of (1 - p_ij), printing the chosen key per keyhole; N up to 100, multiple test cases.	Hard8	Dynamic programmingMath+2	No attempts yet	8s	512 MB	Judgeable
Up and DownCount permutations of 1..N whose up-sequence and down-sequence (nearest larger/smaller distance to the right) match the given arrays; N is at most 17.	Hard8	Dynamic programmingBacktracking+2	No attempts yet	8s	512 MB	Judgeable
Enclosing CirclesGiven up to 100 circles that may overlap or nest, find the shortest rope that encloses them all, allowing straight segments and arcs along circle boundaries.	Hard8	GeometryGraph+2	No attempts yet	2s	512 MB	Judgeable
TrapezoidsGiven an ASCII picture made of asterisks, find all trapezoids whose sides are horizontal and vertical or 45-degree lines, and report counts of trapezoids grouped by area.	Hard8	ImplementationSimulation+2	No attempts yet	2s	512 MB	Judgeable
Guess the Formula Quiz GameGiven f(x) mod p for x = 1 to p-1, recover the coefficients a_1 to a_(p-1) in the range 0 to p-1 of f(x) = sum of a_i * i^x mod p.	Hard8	Number theoryMath+1	No attempts yet	3s	1024 MB	Judgeable
A Simple ProblemGiven two length-N sequences p and q, compute the sum over all ordered pairs of the smaller of the p-distance and the q-distance. N can reach one million.	Hard8	SortingDivide and conquer+2	No attempts yet	4s	1024 MB	Judgeable
Beacon Fire TowersGiven a permutation of heights 1..N, count the ways to cut the line into consecutive segments so that the segment maxima strictly increase left to right, modulo 1e9+7.	Hard8	Dynamic programmingDivide and conquer+2	No attempts yet	1s	1024 MB	Judgeable
Prime TimeSplit a multiset of prime cards into two nonempty groups so the first group's sum equals the second group's product, maximizing that common value.	Hard8	Dynamic programmingMath+2	No attempts yet	45s	1024 MB	Judgeable
Orange NumberGiven K between 1000 and 10000, output three distinct natural numbers N under 100000 digits, not divisible by 10, such that the digit sum of N and of N squared both equal K, or -1 if impossible.	Hard8	MathNumber theory+2	No attempts yet	1s	1024 MB	Judgeable
Cutting CakeGiven triangular icing patches on a cake, find the vertical cut that minimizes the absolute gap between the two pieces' enjoyment, reported as an exact fraction.	Hard8	GeometryMath+1	No attempts yet	45s	1024 MB	Judgeable
Contest ConstructionCount k-element subsets of n given difficulties such that, sorted ascending, each element from the third onward is at most the sum of the two before it.	Hard8	SortingDynamic programming+2	No attempts yet	1s	2048 MB	Judgeable
k SubarraysGiven a permutation of distinct integers, find the smallest k such that repeatedly cutting the array into k contiguous pieces and reordering them can sort it.	Hard8	ArraySorting+2	No attempts yet	1s	1024 MB	Judgeable
The Snail Wants to Rest in the ShadeGiven a rectilinear polygon lit by 45-degree sunlight from the upper right, find the total length of shaded surface where a snail can avoid the sun.	Hard8	GeometrySorting+1	No attempts yet	1s	512 MB	Judgeable
Number of Increasing Subsequences KGiven K, construct a sequence of at most 34 positive integers that has exactly K increasing subsequences.	Hard8	CombinatoricsDynamic programming+2	No attempts yet	2s	1024 MB	Judgeable
Truck DeliveryFor each query (city C, weight W) on a tree, find the gcd of toll charges on edges from C to the root whose load-limit is at most W, or 0 if none apply.	Hard8	TreeDFS+2	No attempts yet	Not set	1024 MB	Judgeable
Primes and QueriesGiven a prime P, an array A, and point updates, answer range queries summing V(A_i^S - (A_i mod P)^S), where V counts the exponent of P.	Hard8	Number theorySegment tree+2	No attempts yet	90s	1024 MB	Judgeable
Hiking TrailsCount ordered alternating sequences of distinct east and west trails, bridged by x, whose total length falls in [C, D].	Hard8	Dynamic programmingBit manipulation+2	No attempts yet	1s	512 MB	Judgeable
Leaping PiecesGiven N and M, find the minimum number of lattice points that must hold presents so that a leaping (N,M)-piece starting anywhere can always reach one of them.	Hard8	MathNumber theory+2	No attempts yet	0.5s	1024 MB	Judgeable
Kyojun StargazingCount the ordered splits of N points into two nonempty labeled groups that a single line, avoiding all points, can separate, modulo 1e9+7.	Hard8	GeometryCombinatorics+2	No attempts yet	1.5s	1024 MB	Judgeable
StonesIn this take-away game, each player points to a non-empty pile on their turn and the opponent chooses how many stones to remove; decide whether the first pointer (Ankica) wins.	Hard8	Game theoryGreedy+2	No attempts yet	3s	512 MB	Judgeable
Graph TravelGiven rooms with point rewards and shields that open only while the running total lies in [L, R], count the distinct orders of first-time room entries that end with exactly K points.	Hard8	GraphDynamic programming+2	No attempts yet	Not set	1024 MB	Judgeable
Generate the SequencesCount the ordered tuples of sequences built from (1) by repeatedly appending 1 or m, or inserting any integer strictly between two adjacent elements, modulo 998244353.	Hard8	CombinatoricsDynamic programming+2	No attempts yet	2s	512 MB	Judgeable
Multiple ParenthesesCount ways to place a regular bracket sequence in each of N boxes so the total number of opening brackets is M and no box holds a sequence of length 2K, modulo 998244353.	Hard8	CombinatoricsDynamic programming+2	No attempts yet	2s	512 MB	Judgeable
Fancy FormulasGiven a prime p and pairs (a,b) with a+b not divisible by p, find the minimum number of operations to transform one pair into another, or report impossibility.	Hard8	MathNumber theory+2	No attempts yet	2s	512 MB	Judgeable
Glory GraphGiven a complete graph on n vertices with yellow and blue edges, compute Y minus A, the difference between two counts of 4-vertex subgraphs.	Hard8	CombinatoricsGraph+1	No attempts yet	3s	512 MB	Judgeable
Little LCSCount the ways to fill the question marks in two good ternary strings of length 2n+1 so that their LCS is exactly n.	Hard8	CombinatoricsString+1	No attempts yet	2s	512 MB	Judgeable
Nimber SequenceGiven a recurrence over nimbers using nim sum and nim product, find the m-th term a_m for m up to 10^18.	Hard8	MatrixMath+1	No attempts yet	1s	256 MB	Judgeable
PlayerUnknown's BattlegroundsFor each value x, count the subgrids whose minimum equals x, given an n by m grid holding a permutation of 1 to n*m.	Hard8	Divide and conquerImplementation+2	No attempts yet	1.5s	256 MB	Judgeable
SumGiven an n by m matrix modulo a prime p, find K rank-one style pairs of vectors b and c whose sum of outer products equals the matrix, with nonzero row and column sums.	Hard8	MatrixMath+1	No attempts yet	3s	512 MB	Judgeable
Historic BreakthroughGiven m, find n such that m equals the sum of integers in 1..n coprime to n, which also equals n*phi(n)/2.	Hard8	Number theoryMath+2	No attempts yet	2s	512 MB	Judgeable
Yes, Prime MinisterFor each x, find the shortest interval [l, r] containing x whose sum of consecutive integers is prime, or report -1.	Hard8	MathNumber theory+2	No attempts yet	10s	512 MB	Judgeable
Nikanor Loves GamesChoose positive integers a and b for one coin, paying a*b, to maximize expected winnings across n friends whose two-sided coins are known, where ties go to Nikanor.	Hard8	MathGeometry+2	No attempts yet	1s	512 MB	Judgeable
Roads of the EmpireFor each query (n, u, v), build the graph on 1..n with an edge x-y when y divides x+n (x<y), then output the shortest path length between u and v, or -1 if unreachable.	Hard8	GraphNumber theory+2	No attempts yet	2s	512 MB	Judgeable
Automatic Sprayer 2Given the matrix E where E[i][j] is the total Manhattan-distance-weighted spray from all cells, reconstruct any nonnegative integer matrix A that produces it.	Hard8	MathImplementation+2	No attempts yet	2s	1024 MB	Judgeable
Organizing BeadsAfter each toggle of a cell, report the minimum pushes to gather all beads into a contiguous block at the left or right end of the barrel.	Hard8	Prefix sumSorting+2	No attempts yet	2s	1024 MB	Judgeable
Periodic RulerGiven colors at up to 50 integer positions, find every positive integer that cannot be the minimal period of the full coloring, and report how many such numbers exist and their sum.	Hard8	MathNumber theory+2	No attempts yet	2s	1024 MB	Judgeable
The IslandsTwo monotone passes across islands in increasing x order visit every island, with the two special islands split between the passes; find the shortest total tour and print the visiting order.	Hard8	Dynamic programmingGeometry+2	No attempts yet	2s	1024 MB	Judgeable
CardiologyGiven r rows and c columns, choose the column to collect second so the stable position is nearest the center, and report that position and the iteration count.	Hard8	MathNumber theory+1	No attempts yet	2s	2048 MB	Judgeable
DomesGiven n domes inside a rectangle and a target left-to-right order, find the area of points in the rectangle from which the domes appear in that order in a 180-degree photo.	Hard8	GeometryCombinatorics+2	No attempts yet	2s	2048 MB	Judgeable
Ley LinesGiven n points with no three collinear and a pencil thickness t, find the largest number of points that can be covered by a single strip of width t.	Hard8	GeometrySorting+2	No attempts yet	15s	2048 MB	Judgeable
Opportunity CostGiven n triples, find the point minimizing the maximum over all points of the sum of positive coordinate gaps, and report its index.	Hard8	GeometryBinary search+2	No attempts yet	5s	2048 MB	Judgeable
QuestsOrder all n quests to maximize total XP, where a quest finished below its target level d pays c times its XP instead of x.	Hard8	Dynamic programmingGreedy+2	No attempts yet	10s	2048 MB	Judgeable
Trailing DigitsGiven a per-item price b, a digit d, and a huge maximum price a, find the largest count of trailing d's achievable by a multiple of b not exceeding a.	Hard8	Number theoryMath+2	No attempts yet	1s	2048 MB	Judgeable
What's Our Vector, Victor?Given the distances from an unknown point to n known points in d-dimensional space, reconstruct any point that matches all the distances.	Hard8	MathGeometry+2	No attempts yet	6s	2048 MB	Judgeable
The Return of CarlCompute the shortest path along the surface of a regular octahedron between two points given in spherical coordinates, for multiple test cases.	Hard8	GeometryShortest path+2	No attempts yet	2s	1024 MB	Judgeable
Conduit PackingGiven four wire diameters, find the smallest enclosing circle diameter that holds all four circular cross sections without overlap, and round it to the nearest micrometer.	Hard8	GeometryMath+2	No attempts yet	2s	1024 MB	Judgeable
Colorful Tower of HanoiFind the fewest moves to shift a Hanoi tower with repeated disk sizes, where each color sets whether that size's order must reverse, stay, or not matter.	Hard8	Dynamic programmingRecursion+1	No attempts yet	1s	1024 MB	Judgeable
HistogramGiven a frequency array over values 1..n, split it into at most B contiguous buckets minimizing the total sum of squared deviations from each bucket's mean.	Hard8	Dynamic programmingPrefix sum+2	No attempts yet	3s	1024 MB	Judgeable
SimilarityGiven two length-n sequences p and q, count triples i<j<k with p_i<p_j<p_k and q_i<q_j<q_k.	Hard8	Divide and conquerSorting+2	No attempts yet	1s	1024 MB	Judgeable
Twenty-ThreeFind the k-th smallest number that can be written as a sum of repunit-like numbers made only of the digits 2 and 3 (23, 2323, ...).	Hard8	MathDynamic programming+2	No attempts yet	2.3s	1023 MB	Judgeable
Hiring HelpFor each consultant request, decide whether the current coders can match its lines and bugs per hour, with coders removed over time.	Hard8	GeometryDivide and conquer	No attempts yet	4s	1024 MB	Judgeable
Intact IntervalsCount the ways to cut a circular array into at least two contiguous arcs so that each arc's multiset equals the corresponding multiset of the target array b.	Hard8	ArrayHash map+2	No attempts yet	6s	1024 MB	Judgeable
Line Fighter 2Given N lines and Q queries (x, a), output the maximum (a=1) or minimum (a=2) value among all lines at x, within 1e-4 error.	Hard8	GeometryDivide and conquer+2	No attempts yet	1s	1024 MB	Judgeable
SquaresGiven N up to 10^18 whose prime factors are all at most 100000, output four non-negative integers whose squares sum to N.	Hard8	Number theoryMath+2	No attempts yet	2s	1024 MB	Judgeable
K-CalculatorEvaluate an expression of rational operands by repeatedly applying the operator selected by u_i XOR the modular value of the previous result, removing it and merging its operands.	Hard8	Linked listMath+2	No attempts yet	1.5s	512 MB	Judgeable
Matrix PartitionCut an n by m grid with exactly a horizontal and b vertical cuts, maximizing no piece, and report the smallest possible largest piece sum.	Hard8	Binary searchBrute force+2	No attempts yet	1s	1024 MB	Judgeable
Hard All-Pairs Shortest PathIn a connected graph where exactly one edge has weight 1 and all others weight 0, compute the sum of shortest-path distances over all vertex pairs.	Hard8	GraphUnion-find+2	No attempts yet	1s	1024 MB	Judgeable
DigionGiven a Digion string built from nesting rule (A)B, output the next Digion in the weight-then-inner-then-outer ordering.	Hard8	RecursionCombinatorics+2	No attempts yet	2s	1024 MB	Judgeable
FlipMaintain a binary array under range bit flips and report how many subarrays inside a query range are alternating.	Hard8	Segment treePrefix sum+2	No attempts yet	3s	1024 MB	Judgeable
Inverting EverythingCount the city subsets whose flipping turns the active railroads of a complete graph into a spanning tree, modulo 1e9+7.	Hard8	MathTree+1	No attempts yet	1s	1024 MB	Judgeable
Just BootfallAssign N players to M ordered positions, scoring each player's position value minus C times the distance for every best-friend pair, and maximize total team performance.	Hard8	Dynamic programmingGraph+2	No attempts yet	1s	1024 MB	Judgeable
Listing PasswordsCount the 0/1 strings of length N that fit the fixed digits and M required palindrome intervals, modulo 1e9+7, or 0 on conflict.	Hard8	Union-findString+1	No attempts yet	3s	1024 MB	Judgeable
ToteGiven match outcome probabilities and ticket types with fixed counts of single, double and triple bets, choose how many tickets of each type to buy within budget S to maximize expected prize money.	Hard8	Dynamic programmingProbability+2	No attempts yet	2s	256 MB	Judgeable
Pulse NovaPlace a circle of radius R so that the total length of the given lines' segments inside the circle is maximized.	Hard8	GeometryBrute force	No attempts yet	20s	256 MB	Judgeable
FlowGiven a graph that is k vertex-independent paths from 1 to n, move capacity between edges at unit cost to maximize the max flow, and output the minimum number of moves.	Hard8	GraphGreedy+2	No attempts yet	1s	256 MB	Judgeable
ValueChoose a subset of 1..n maximizing the sum of a_i minus b_j for every selected pair where j is a higher power of i.	Hard8	Number theoryDynamic programming+2	No attempts yet	1s	256 MB	Judgeable
All in good fun!Given three non-parallel lines, find the minimum possible value of the largest distance from a point to any of the three lines.	Hard8	GeometryBinary search+2	No attempts yet	1s	512 MB	Judgeable
Sum ModuloGiven a generator that outputs 1 to N with weights A_i, find the expected number of draws until the running sum modulo M first equals K, printed modulo 998244353.	Hard8	MathProbability+1	No attempts yet	4s	1024 MB	Judgeable
Xor SumFind the minimum possible maximum of N nonnegative integers whose sum is S and whose XOR is X, or report -1 if no such sequence exists.	Hard8	Bit manipulationBinary search+1	No attempts yet	2s	1024 MB	Judgeable
Matrix InversionFill an N by N grid with the integers 1 to N^2 so that the inversion number of the row-major reading is X and the column-major reading is Y, or report that it is impossible.	Hard8	MatrixMath+1	No attempts yet	1s	1024 MB	Judgeable