Math and counting

Number theory, combinatorics, and geometry

Under construction

Still being built. Things may change

Total results13,153 problems

Hadron Colliders
Hard8
Geometry, Math+2
No attempts yet
Time limit
2s
Memory limit
1024 MB
Judgeable
Ring Line
Hard8
Math, Number theory+1
No attempts yet
Time limit
1s
Memory limit
1024 MB
Judgeable
Streetlights
Hard8
Segment tree, Intervals+2
No attempts yet
Time limit
2s
Memory limit
1024 MB
Judgeable
Mayor's House
Hard8
Geometry, Sorting+1
No attempts yet
Time limit
2s
Memory limit
1024 MB
Judgeable
Robot Assembler
Hard8
String, Prefix sum+2
No attempts yet
Time limit
1s
Memory limit
1024 MB
Judgeable
Preparing for War
Hard8
Math, Greedy+2
No attempts yet
Time limit
2s
Memory limit
256 MB
Judgeable
Space Bowling
Hard8
Geometry, Math+2
No attempts yet
Time limit
2s
Memory limit
1024 MB
Judgeable
Passing the Towel
Hard8
Math, Recursion+2
No attempts yet
Time limit
0.25s
Memory limit
256 MB
Judgeable
Find the Double Class
Hard8
Combinatorics, Math+2
No attempts yet
Time limit
1s
Memory limit
256 MB
Judgeable
Math Homework
Hard8
Number theory, Math+2
No attempts yet
Time limit
1s
Memory limit
1024 MB
Judgeable
Jumping Machine
Hard8
Combinatorics, Math+2
No attempts yet
Time limit
1s
Memory limit
512 MB
Judgeable
Multiple Subject Lessons
Hard8
Dynamic programming, Combinatorics+2
No attempts yet
Time limit
1s
Memory limit
512 MB
Judgeable
Cutting Logs
Hard8
Geometry, Binary search
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Permutations
Hard8
Backtracking, Dynamic programming+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Table
Hard8
Prefix sum, Dynamic programming+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Garden Informatization
Hard8
Geometry, Brute force+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Digits and Numbers
Hard8
Dynamic programming, Math+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Inversion Statistics
Hard8
Combinatorics, Number theory+1
No attempts yet
Time limit
1s
Memory limit
1536 MB
Judgeable
Bus Riding
Hard8
Simulation, Implementation+2
No attempts yet
Time limit
2s
Memory limit
1024 MB
Judgeable
Interesting Number
Hard8
Dynamic programming, BFS+2
No attempts yet
Time limit
2s
Memory limit
1024 MB
Judgeable
Colored zeros
Hard8
Math, Bit manipulation+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Histogram Connectivity Count
Hard8
Stack, Combinatorics+2
No attempts yet
Time limit
1s
Memory limit
1024 MB
Judgeable
Opinion Pool
Hard8
Binary search, Greedy+2
No attempts yet
Time limit
1s
Memory limit
1024 MB
Judgeable
Aerobatics 6
Hard8
Geometry, Greedy+1
No attempts yet
Time limit
1s
Memory limit
512 MB
Judgeable
Balanced Subsets
Hard8
Dynamic programming, Implementation+2
No attempts yet
Time limit
1s
Memory limit
512 MB
Judgeable
Swap Swap Sort
Hard8
Sorting, Hash map+2
No attempts yet
Time limit
3s
Memory limit
512 MB
Judgeable
Secret
Hard8
Divide and conquer, Implementation+2
No attempts yet
Time limit
1s
Memory limit
512 MB
Judgeable
Quarantine Math
Hard8
Number theory, Math+2
No attempts yet
Time limit
1.25s
Memory limit
256 MB
Judgeable
Hexagonal Region
Hard8
Geometry, Shortest path+1
No attempts yet
Time limit
2s
Memory limit
1024 MB
Judgeable
Walk
Hard8
Tree, DFS+2
No attempts yet
Time limit
1s
Memory limit
512 MB
Judgeable
GCDChel Loves GCD
Hard8
Dynamic programming, Greedy+2
No attempts yet
Time limit
1s
Memory limit
1024 MB
Judgeable
XOR Sum
Hard8
Bit manipulation, Math+1
No attempts yet
Time limit
1s
Memory limit
512 MB
Judgeable
Road Building
Hard8
Geometry, Sorting+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
High-Tech Detective
Hard8
Dynamic programming, Combinatorics+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Simple
Hard8
Segment tree, Linked list+2
No attempts yet
Time limit
1s
Memory limit
512 MB
Judgeable
Consul
Hard8
Divide and conquer, Brute force+2
No attempts yet
Time limit
1s
Memory limit
512 MB
Judgeable
Costinland
Hard8
Implementation, Bit manipulation+1
No attempts yet
Time limit
0.5s
Memory limit
512 MB
Judgeable
Monkey
Hard8
Dynamic programming, Sorting+2
No attempts yet
Time limit
2s
Memory limit
1024 MB
Judgeable
Need More T-shirts!
Hard8
Number theory, Math+2
No attempts yet
Time limit
1s
Memory limit
512 MB
Judgeable
Cartesian Trees
Hard8
Tree, Dynamic programming+2
No attempts yet
Time limit
3s
Memory limit
256 MB
Judgeable
Internet Cable
Hard8
Geometry, Math+2
No attempts yet
Time limit
4s
Memory limit
256 MB
Judgeable
Homework
Hard8
Math, Number theory+2
No attempts yet
Time limit
2s
Memory limit
256 MB
Judgeable
Lottery
Hard8
Combinatorics, Sorting+2
No attempts yet
Time limit
2s
Memory limit
256 MB
Judgeable
Game
Hard8
Graph, Greedy+2
No attempts yet
Time limit
2s
Memory limit
256 MB
Judgeable
Physics Lab
Hard8
Math, Number theory+2
No attempts yet
Time limit
2s
Memory limit
256 MB
Judgeable
Cryptographically Strong Keys
Hard8
Number theory, Math+2
No attempts yet
Time limit
2s
Memory limit
256 MB
Judgeable
Travel Tax
Hard8
Tree, Combinatorics+2
No attempts yet
Time limit
2s
Memory limit
256 MB
Judgeable
Deposit
Hard8
Dynamic programming, Greedy+2
No attempts yet
Time limit
2s
Memory limit
256 MB
Judgeable
Lasers
Hard8
Geometry, Binary search+2
No attempts yet
Time limit
2s
Memory limit
256 MB
Judgeable
Wheel
Hard8
Dynamic programming, Probability+2
No attempts yet
Time limit
2s
Memory limit
256 MB
Judgeable
Match of the Century
Hard8
Combinatorics, Math+2
No attempts yet
Time limit
2s
Memory limit
256 MB
Judgeable
Forest Phenomenon
Hard8
Probability, Math+2
No attempts yet
Time limit
2s
Memory limit
256 MB
Judgeable
Olympiad
Hard8
Geometry, Brute force+2
No attempts yet
Time limit
1s
Memory limit
256 MB
Judgeable
Mluran Storage
Hard8
Graph, Math+2
No attempts yet
Time limit
2s
Memory limit
256 MB
Judgeable
Planet Defense
Hard8
Math, Sorting+2
No attempts yet
Time limit
2s
Memory limit
256 MB
Judgeable
Interference
Hard8
Math, Dynamic programming+2
No attempts yet
Time limit
2s
Memory limit
256 MB
Judgeable
Road Reform
Hard8
Graph, Union-find+2
No attempts yet
Time limit
2s
Memory limit
256 MB
Judgeable
Time Shift
Hard8
Sorting, Prefix sum+2
No attempts yet
Time limit
3s
Memory limit
256 MB
Judgeable
Rails
Hard8
Geometry, Hash map+2
No attempts yet
Time limit
2s
Memory limit
256 MB
Judgeable
Plus Minus
Hard8
Combinatorics, Union-find+2
No attempts yet
Time limit
1s
Memory limit
512 MB
Judgeable
Table 10
Hard8
Backtracking, Brute force+2
No attempts yet
Time limit
1s
Memory limit
512 MB
Judgeable
Gahui and the Airplane
Hard8
Combinatorics, Number theory+2
No attempts yet
Time limit
1s
Memory limit
512 MB
Judgeable
Game of Slots
Hard8
Combinatorics, Greedy+2
No attempts yet
Time limit
1s
Memory limit
1024 MB
Judgeable
Impenetrable Wall
Hard8
Geometry, Dynamic programming+2
No attempts yet
Time limit
1s
Memory limit
1024 MB
Judgeable
Driving Lanes
Hard8
Dynamic programming, Implementation+1
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
twOBoOgEr
Hard8
Math, Simulation+2
No attempts yet
Time limit
1s
Memory limit
512 MB
Judgeable
XOR 5
Hard8
Greedy, Implementation+2
No attempts yet
Time limit
1s
Memory limit
512 MB
Judgeable
Making UCPC
Hard8
Tree, DFS+2
No attempts yet
Time limit
3s
Memory limit
1024 MB
Judgeable
Must Stay Hidden
Hard8
Graph, Shortest path+2
No attempts yet
Time limit
8s
Memory limit
512 MB
Judgeable
Edamame Energy Engineering
Hard8
Two pointers, Implementation+2
No attempts yet
Time limit
8s
Memory limit
512 MB
Judgeable
Rebound Sequences
Hard8
Dynamic programming, Combinatorics
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Yet Another Expression Mining
Hard8
Dynamic programming, Combinatorics+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Irreversible Reactions
Hard8
Graph, Probability+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Casino
Hard8
Dynamic programming, Probability+2
No attempts yet
Time limit
8s
Memory limit
512 MB
Judgeable
Prison
Hard8
Math, Combinatorics+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Bit Operation Game
Hard8
Game theory, Tree+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Alternate Escape
Hard8
Graph, Game theory+2
No attempts yet
Time limit
8s
Memory limit
512 MB
Judgeable
Wish upon a shooting star
Hard8
Simulation, Geometry+2
No attempts yet
Time limit
8s
Memory limit
512 MB
Judgeable
Koto Distance
Hard8
Geometry, Sorting+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Apples
Hard8
Geometry, Math+2
No attempts yet
Time limit
5s
Memory limit
512 MB
Judgeable
Perm Query
Hard8
Math, Prefix sum+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Unordered Operators
Hard8
Dynamic programming, Brute force+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Sister Ports
Hard8
Dynamic programming, Geometry+2
No attempts yet
Time limit
8s
Memory limit
512 MB
Judgeable
DNA
Hard8
Dynamic programming, Math+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Enumeration
Hard8
Probability, Combinatorics+2
No attempts yet
Time limit
5s
Memory limit
512 MB
Judgeable
Sun and Moon
Hard8
Math, Number theory
No attempts yet
Time limit
5s
Memory limit
512 MB
Judgeable
Marathon Match
Hard8
Probability, Dynamic programming+2
No attempts yet
Time limit
5s
Memory limit
512 MB
Judgeable
Beautiful Currency
Hard8
Binary search, Greedy+2
No attempts yet
Time limit
5s
Memory limit
512 MB
Judgeable
Vector Compression
Hard8
Greedy, Geometry+2
No attempts yet
Time limit
5s
Memory limit
512 MB
Judgeable
6÷2(1+2)
Hard8
Dynamic programming, Brute force+2
No attempts yet
Time limit
8s
Memory limit
512 MB
Judgeable
Divide the Cake
Hard8
Geometry, Probability+2
No attempts yet
Time limit
8s
Memory limit
512 MB
Judgeable
Network Reliability
Hard8
Dynamic programming, Bit manipulation+2
No attempts yet
Time limit
3s
Memory limit
512 MB
Judgeable
Immortal Jewels
Hard8
Geometry, Brute force+2
No attempts yet
Time limit
8s
Memory limit
512 MB
Judgeable
My Friends Are Small
Hard8
Dynamic programming, Sorting+2
No attempts yet
Time limit
8s
Memory limit
512 MB
Judgeable
Ten-Year-Old Dynamic Programming
Hard8
Combinatorics, Dynamic programming+2
No attempts yet
Time limit
8s
Memory limit
512 MB
Judgeable
Carrot Tour
Hard8
Dynamic programming, Graph+2
No attempts yet
Time limit
1s
Memory limit
512 MB
Judgeable
Usagitobi
Hard8
Graph, DFS+2
No attempts yet
Time limit
1s
Memory limit
512 MB
Judgeable
Cruel Bingo
Hard8
Combinatorics, Dynamic programming+2
No attempts yet
Time limit
8s
Memory limit
512 MB
Judgeable
Ika Number
Hard8
Combinatorics, Dynamic programming+2
No attempts yet
Time limit
8s
Memory limit
512 MB
Judgeable
Carrot breeding
Hard8
Geometry, Combinatorics
No attempts yet
Time limit
8s
Memory limit
512 MB
Judgeable

Title	Level	Topics	Solved	Time limit	Memory limit	Judge
Hadron CollidersFind a circle that intersects each of up to three given disjoint circles at two diametrically opposite points, i.e. cuts every circle in half.	Hard8	GeometryMath+2	No attempts yet	2s	1024 MB	Judgeable
Ring LineCount ordered pairs of distinct stations A and B on a ring of n equally spaced stations such that the distance pair (dist from A, dist from B) is unique for every station.	Hard8	MathNumber theory+1	No attempts yet	1s	1024 MB	Judgeable
StreetlightsMaintain a binary string under range set-to-0 and set-to-1 operations, and after each report how many substrings have ever been all ones at some point in time.	Hard8	Segment treeIntervals+2	No attempts yet	2s	1024 MB	Judgeable
Mayor's HouseFor each home location, find a route from city hall with at most two turns that never enters the interior of a closed rectangular block, or report NO.	Hard8	GeometrySorting+1	No attempts yet	2s	1024 MB	Judgeable
Robot AssemblerGiven a string of N operation types and a memory size K, count the ways to pick a K-character cyclic memory pattern and a starting position so that the robot runs at least K+1 operations before repeating the intended sequence.	Hard8	StringPrefix sum+2	No attempts yet	1s	1024 MB	Judgeable
Preparing for WarGiven group sizes in strict order, place all soldiers in a rectangle X by Y so that adjacent different-group pairs are at most k, and find the maximum Y for each k from 0 to N-1.	Hard8	MathGreedy+2	No attempts yet	2s	256 MB	Judgeable
Space BowlingGiven a triangular array of n rows of circular pins and a ball moving in a straight line, count how many pins the ball touches.	Hard8	GeometryMath+2	No attempts yet	2s	1024 MB	Judgeable
Passing the TowelIn a Josephus-style circle game where the towel skips one person each pass, find the number of the person who receives the towel on the K-th pass.	Hard8	MathRecursion+2	No attempts yet	0.25s	256 MB	Judgeable
Find the Double ClassGiven M distinct rows of N section numbers, output at most M new rows so that each input row agrees with some new row in every column, yet no new row equals an input row.	Hard8	CombinatoricsMath+2	No attempts yet	1s	256 MB	Judgeable
Math HomeworkConstruct a sequence of N integers in [1, 10^9] so that the GCD of each given subarray equals a given value at most 16, or report impossibility.	Hard8	Number theoryMath+2	No attempts yet	1s	1024 MB	Judgeable
Jumping MachineGiven n springs with jump lengths, the machine at (0,0) uses each spring once in any order, moving l up or l right; count the grid cells it can ever land on or pass over.	Hard8	CombinatoricsMath+2	No attempts yet	1s	512 MB	Judgeable
Multiple Subject LessonsCount the multisets of colored positive integers that sum to n, where two solutions match when every value has the same count in every color.	Hard8	Dynamic programmingCombinatorics+2	No attempts yet	1s	512 MB	Judgeable
Cutting LogsFind the largest-area isosceles triangle with its base on the x-axis, centered at the origin, that fits inside every polyline section.	Hard8	GeometryBinary search	No attempts yet	2s	512 MB	Judgeable
PermutationsGiven n distinct integers, list all permutations where adjacent elements share gcd at least k, and output the m-th one in lexicographic order or -1.	Hard8	BacktrackingDynamic programming+2	No attempts yet	2s	512 MB	Judgeable
TableGiven the first row of an n by m table, each lower cell is the sum of the triangular region above it mod r; output the last row.	Hard8	Prefix sumDynamic programming+2	No attempts yet	2s	512 MB	Judgeable
Garden InformatizationGiven a rectangle with up to 10 axis-aligned obstacle rectangles, place one or two non-overlapping axis-aligned beds to maximize total area.	Hard8	GeometryBrute force+2	No attempts yet	2s	512 MB	Judgeable
Digits and NumbersA binary number is ugly if no smaller number reaches it by adding its own digit sum; count the ugly numbers up to n (n up to 10^18).	Hard8	Dynamic programmingMath+2	No attempts yet	2s	512 MB	Judgeable
Inversion StatisticsCount permutations of 1 to n with exactly k inversions, modulo the prime 10^6+3, for n up to 2*10^10 over up to 10 test cases.	Hard8	CombinatoricsNumber theory+1	No attempts yet	1s	1536 MB	Judgeable
Bus RidingSimulate people riding circular bus routes, tracking boarding order by smallest route number and each transfer's one-minute wait, to report the finish time and stop or 0 0.	Hard8	SimulationImplementation+2	No attempts yet	2s	1024 MB	Judgeable
Interesting NumberGiven n up to 1000, find the smallest positive integer with digit sum n that is also divisible by n.	Hard8	Dynamic programmingBFS+2	No attempts yet	2s	1024 MB	Judgeable
Colored zerosCount how many zero bits get marked when writing 1 to n in binary and flagging every k-th zero in each row.	Hard8	MathBit manipulation+2	No attempts yet	2s	512 MB	Judgeable
Histogram Connectivity CountCount choices of x_i with 0 <= x_i < h_i so that the remaining part of the histogram stays connected, modulo 1e9+7.	Hard8	StackCombinatorics+2	No attempts yet	1s	1024 MB	Judgeable
Opinion PoolGiven sets of voters and a fraction p, find the largest p for which some assignment with at least one opponent still satisfies every set's support quota.	Hard8	Binary searchGreedy+2	No attempts yet	1s	1024 MB	Judgeable
Aerobatics 6Given N checkpoints in the plane, find a visiting order whose polyline has the largest possible minimum turning angle at its inner checkpoints.	Hard8	GeometryGreedy+1	No attempts yet	1s	512 MB	Judgeable
Balanced SubsetsCount connected subsets of grass cells in an N by N grid where every row and column intersects the subset in a single contiguous run, modulo 1e9+7.	Hard8	Dynamic programmingImplementation+2	No attempts yet	1s	512 MB	Judgeable
Swap Swap SortMaintain a target permutation of 1..K under adjacent swaps, and after each swap report the minimum adjacent-swap count to sort the fixed array by that ordering.	Hard8	SortingHash map+2	No attempts yet	3s	512 MB	Judgeable
SecretGiven a hidden associative operation on 0..1e9 and an array, answer range-fold queries while minimizing calls to an oracle that returns x star y, especially after each query.	Hard8	Divide and conquerImplementation+2	No attempts yet	1s	512 MB	Judgeable
Quarantine MathGiven n and m up to 1e9, sum the divisor counts of all positive k with (n mod k) + (m mod k) >= k, using number theory.	Hard8	Number theoryMath+2	No attempts yet	1.25s	256 MB	Judgeable
Hexagonal RegionGiven a closed, simple hex-grid path of N moves, sum A + d*B over every cell in the enclosed region, where d is the distance from the start.	Hard8	GeometryShortest path+1	No attempts yet	2s	1024 MB	Judgeable
WalkGiven a rooted tree and an ordered list of m distinct nodes, count the shortest closed walks from the root that visit all nodes and hit the listed nodes in the given order, modulo 1e9+7.	Hard8	TreeDFS+2	No attempts yet	1s	512 MB	Judgeable
GCDChel Loves GCDGiven an array, repeatedly split off either the left floor(n/2) elements or the right ceil(n/2) elements, sum the GCDs of the removed blocks, and maximize that sum.	Hard8	Dynamic programmingGreedy+2	No attempts yet	1s	1024 MB	Judgeable
XOR SumGiven n k-bit numbers, compute the sum over all pairs of (a_i XOR a_j) raised to the power x, modulo 998244353.	Hard8	Bit manipulationMath+1	No attempts yet	1s	512 MB	Judgeable
Road BuildingGiven n non-overlapping circles and a direction line, find the widest infinite strip parallel to that line that touches no circle and has at least one circle on each side.	Hard8	GeometrySorting+2	No attempts yet	2s	512 MB	Judgeable
High-Tech DetectiveGiven a sequence of 2n entry and exit events where some visitor IDs are lost, count the ways to fill the zeros so each visitor enters once and exits once with proper nesting.	Hard8	Dynamic programmingCombinatorics+2	No attempts yet	2s	512 MB	Judgeable
SimpleSupport range add updates and range queries for the minimum even and maximum odd value, printing -1 for a missing parity.	Hard8	Segment treeLinked list+2	No attempts yet	1s	512 MB	Judgeable
ConsulGiven N hidden votes, use point queries and value-count queries to find a candidate with strictly more than N/3 votes, or report that none exists.	Hard8	Divide and conquerBrute force+2	No attempts yet	1s	512 MB	Judgeable
CostinlandGiven K, build an N x M grid of X, r, d, and . cells so that exactly K Costins (clones) reach the bottom-right corner (N,M).	Hard8	ImplementationBit manipulation+1	No attempts yet	0.5s	512 MB	Judgeable
MonkeyGiven M allowed (x, y) handle pairs with banana counts on each handle, find the maximum total bananas collectable along a monotone path that only increases x or y.	Hard8	Dynamic programmingSorting+2	No attempts yet	2s	1024 MB	Judgeable
Need More T-shirts!Given a list where each entry is either a T-shirt count or a percentage, find every possible total number of T-shirts consistent with the list.	Hard8	Number theoryMath+2	No attempts yet	1s	512 MB	Judgeable
Cartesian TreesCount the number of distinct Cartesian trees (BST over keys 1..n, max-heap over given priorities) modulo 1e9+7, summed over test cases with total n up to 2e5.	Hard8	TreeDynamic programming+2	No attempts yet	3s	256 MB	Judgeable
Internet CableChoose a line and a distance d so that as many given points as possible lie exactly at distance d from the line; output that maximum count.	Hard8	GeometryMath+2	No attempts yet	4s	256 MB	Judgeable
HomeworkFor each triple of decimal strings x, y, z, decide whether infinitely many bases k make x times y equal z when read in base k.	Hard8	MathNumber theory+2	No attempts yet	2s	256 MB	Judgeable
LotteryCount arrays of length n with entries in 1..k such that the maximum on each of m given segments [l,r] equals a specified x.	Hard8	CombinatoricsSorting+2	No attempts yet	2s	256 MB	Judgeable
GameGiven the hint sets of n first-team and m second-team players, decide whether the first team can guarantee collecting all k hints when each first-team player may ask at most one second-team player for one hint he lacks, and if so, output the assignment.	Hard8	GraphGreedy+2	No attempts yet	2s	256 MB	Judgeable
Physics LabGiven cold and hot vessel volumes and temperatures C and H, decide for each reported fraction p/q whether some cold and hot vessel pair can produce that mixture temperature.	Hard8	MathNumber theory+2	No attempts yet	2s	256 MB	Judgeable
Cryptographically Strong KeysGiven numbers a_i, the closure under gcd and lcm defines a set S; decide whether a query value v lies in S.	Hard8	Number theoryMath+2	No attempts yet	2s	256 MB	Judgeable
Travel TaxIn a tree of n cities, each road has a toll range [l, r]; count assignments of tolls whose total weighted income (each road weighted by how many shortest paths cross it) equals m, modulo 1e9+7.	Hard8	TreeCombinatorics+2	No attempts yet	2s	256 MB	Judgeable
DepositEach year Vasily can move money between banks after paying fixed withdrawal fees, and the task is to maximize the final total after m years.	Hard8	Dynamic programmingGreedy+2	No attempts yet	2s	256 MB	Judgeable
LasersGiven n points where a laser sits at the first and refractors at the rest, find the minimum voltage a so a beam can be bent back to its start, where each turn angle is bounded by a.	Hard8	GeometryBinary search+2	No attempts yet	2s	256 MB	Judgeable
WheelEach city on a wheel graph is captured by one of two parties at random; find the expected size of the largest connected group of cities held by a single party.	Hard8	Dynamic programmingProbability+2	No attempts yet	2s	256 MB	Judgeable
Match of the CenturyGiven 2n distinct heights, randomly split into two teams of n, then order one team by decreasing height and the other by increasing height; find the expected sum of same-position height differences.	Hard8	CombinatoricsMath+2	No attempts yet	2s	256 MB	Judgeable
Forest PhenomenonFor each n by m grid, every cell ships its firewood to a uniformly random orthogonal neighbor; find the expected number of cells that end up with at least one shipment.	Hard8	ProbabilityMath+2	No attempts yet	2s	256 MB	Judgeable
OlympiadGiven three rectangles with fixed side lengths, arrange them axis-parallel so the union covers the least area, allowing overlaps.	Hard8	GeometryBrute force+2	No attempts yet	1s	256 MB	Judgeable
Mluran StorageCount the ways to 2-color isotopes 1..n so that no two masses summing to a given power-of-two critical number share a color, mod 1e9+7.	Hard8	GraphMath+2	No attempts yet	2s	256 MB	Judgeable
Planet DefenseGiven each asteroid's initial position and constant velocity, count for each queried integer time how many asteroids lie strictly within distance R of the origin.	Hard8	MathSorting+2	No attempts yet	2s	256 MB	Judgeable
InterferenceFor each received n-bit string (n up to 34) and target polynomial hash, find a string within minimum Hamming distance whose hash matches, and report the flipped bit indices.	Hard8	MathDynamic programming+2	No attempts yet	2s	256 MB	Judgeable
Road ReformCount ordered pairs (removed edge, added edge) that make the graph connected after the swap, where the added edge is not already present.	Hard8	GraphUnion-find+2	No attempts yet	2s	256 MB	Judgeable
Time ShiftGiven daily clock shifts in n cities over a year, compute the sum over all hours of the pairwise absolute differences of each city's elapsed time from the capital.	Hard8	SortingPrefix sum+2	No attempts yet	3s	256 MB	Judgeable
RailsGiven 2n distinct lines, pair them so each pair has two parallel lines at the same distance d, and find the smallest such d.	Hard8	GeometryHash map+2	No attempts yet	2s	256 MB	Judgeable
Plus MinusCount the spin grids on an N by M board, consistent with K fixed cells, where every 2 by 2 block has two pluses and two minuses, modulo 1e9+7.	Hard8	CombinatoricsUnion-find+2	No attempts yet	1s	512 MB	Judgeable
Table 10Build an N by N digit table (2 <= N <= 10) where every row, column, and main diagonal reads as a distinct multiple of M with no leading zero.	Hard8	BacktrackingBrute force+2	No attempts yet	1s	512 MB	Judgeable
Gahui and the AirplaneCount the flight paths of horizontal length d that start and end at altitude 0, stay positive in between, and consist of straight constant-slope segments, modulo a prime m.	Hard8	CombinatoricsNumber theory+2	No attempts yet	1s	512 MB	Judgeable
Game of SlotsAlice arranges her cards into slots first, then Bob responds; compute Alice's optimal expected score when all card values are drawn uniformly from [1, 10^18].	Hard8	CombinatoricsGreedy+2	No attempts yet	1s	1024 MB	Judgeable
Impenetrable WallCount simple polygons through a fixed gate vertex, using tower vertices only, that strictly contain the house, are star-shaped from it, and have all tower angles convex, modulo 1e9+7.	Hard8	GeometryDynamic programming+2	No attempts yet	1s	1024 MB	Judgeable
Driving LanesGiven n straightaways separated by n-1 curves whose cost grows by c per lane, find the minimum total distance from lane 1 back to lane 1, where lane changes cost k+r and must fit within a straightaway.	Hard8	Dynamic programmingImplementation+1	No attempts yet	2s	512 MB	Judgeable
twOBoOgErCount every collision (A-B or A-wall) when B of mass n kg hits resting A of mass 1 kg elastically between a wall and B, for n up to 10^6.	Hard8	MathSimulation+2	No attempts yet	1s	512 MB	Judgeable
XOR 5Given an N by N black-and-white image, write a file of rectangle XOR operations that turns an all-white screen into the image using as few operations as possible.	Hard8	GreedyImplementation+2	No attempts yet	1s	512 MB	Judgeable
Making UCPCGiven a tree whose vertices are labeled U, C, or P, count pairs (a, b) whose path letters can be rearranged into (UCPC)^k for some k >= 1.	Hard8	TreeDFS+2	No attempts yet	3s	1024 MB	Judgeable
Must Stay HiddenGiven N axis-aligned square sensors on a grid, find the minimum number to destroy so a monotone shortest path from (sx,sy) to (gx,gy) avoids all remaining sensors.	Hard8	GraphShortest path+2	No attempts yet	8s	512 MB	Judgeable
Edamame Energy EngineeringChoose a subset of N chemicals and a contiguous block of beans so that every bean in the block is satisfied by one of its two literal properties, maximizing the block length.	Hard8	Two pointersImplementation+2	No attempts yet	8s	512 MB	Judgeable
Rebound SequencesCount distinct rearrangements of the given multiset that contain indices i<j<k with a_i > a_k > a_j, modulo 1000000007.	Hard8	Dynamic programmingCombinatorics	No attempts yet	2s	512 MB	Judgeable
Yet Another Expression MiningCount subsequences of a string of digits and plus signs, with no leading, trailing, or doubled plus, whose arithmetic evaluation equals A.	Hard8	Dynamic programmingCombinatorics+2	No attempts yet	2s	512 MB	Judgeable
Irreversible ReactionsGiven a directed graph with random transitions, find the expected time to leave the set of states that can still return to the start, or report infinity.	Hard8	GraphProbability+2	No attempts yet	2s	512 MB	Judgeable
CasinoRoll N dice up to M times, stopping whenever you like, and find the expected score under the optimal stopping strategy.	Hard8	Dynamic programmingProbability+2	No attempts yet	8s	512 MB	Judgeable
PrisonSimulate a process that repeatedly removes multiples of k from an infinite list of prisoners and renumbers, then report the original label released on step N.	Hard8	MathCombinatorics+2	No attempts yet	2s	512 MB	Judgeable
Bit Operation GameFind the final value of T for each query (X, Y) when Alice and Bob alternately walk down a rooted tree and apply bitwise operations with X or Y.	Hard8	Game theoryTree+2	No attempts yet	2s	512 MB	Judgeable
Alternate EscapeOn a grid where walls can all be inverted by Bob on his turn, decide whether Alice can walk the token off the board against optimal play.	Hard8	GraphGame theory+2	No attempts yet	8s	512 MB	Judgeable
Wish upon a shooting starGiven moving spheres whose radii shrink linearly, find the vanish time of each, where touching pairs annihilate each other, in order.	Hard8	SimulationGeometry+2	No attempts yet	8s	512 MB	Judgeable
Koto DistanceGiven N access points, each covering points whose Koto distance (the minimum of the x-gap and y-gap) is at most w_i, decide whether their union covers the whole W by H rectangle.	Hard8	GeometrySorting+2	No attempts yet	2s	512 MB	Judgeable
ApplesEach of N people carries an apple and moves at constant velocity; find the maximum number of apples a single infinite-speed straight-line shot fired at some time t >= 0 can pass through.	Hard8	GeometryMath+2	No attempts yet	5s	512 MB	Judgeable
Perm QueryGiven a permutation whose cycles all have length at most 40, answer queries summing iterates of the permutation on an interval until the interval returns to the identity.	Hard8	MathPrefix sum+2	No attempts yet	2s	512 MB	Judgeable
Unordered OperatorsGiven an expression with +, -, * and parentheses, choose one precedence order for the three operators so the left-associative evaluation is maximized.	Hard8	Dynamic programmingBrute force+2	No attempts yet	2s	512 MB	Judgeable
Sister PortsCount the perfect matchings of a planar graph formed by a convex polygon's boundary plus non-crossing chords, modulo 1000003.	Hard8	Dynamic programmingGeometry+2	No attempts yet	8s	512 MB	Judgeable
DNAGiven a context-free grammar over DNA letters and target counts of A, T, G, C, count the strings the grammar generates with exactly those letter counts, modulo 1e9+7.	Hard8	Dynamic programmingMath+2	No attempts yet	2s	512 MB	Judgeable
EnumerationEach integer a_k is chosen independently with probability p_k%, and we need the expected count of numbers in [1,m] divisible by at least one chosen integer.	Hard8	ProbabilityCombinatorics+2	No attempts yet	5s	512 MB	Judgeable
Sun and MoonFind the smallest positive day x at which the Sun and Moon power totals can match, with the option of skipping the Sun ritual.	Hard8	MathNumber theory	No attempts yet	5s	512 MB	Judgeable
Marathon MatchFor each of N runners who may rest at each of M stops with given probabilities, compute the probability that the runner finishes in strictly least time.	Hard8	ProbabilityDynamic programming+2	No attempts yet	5s	512 MB	Judgeable
Beautiful CurrencyGiven N increasing coin values, assign new positive integers so each value divides the next, minimizing the maximum relative change \|a_i - b_i\| / a_i.	Hard8	Binary searchGreedy+2	No attempts yet	5s	512 MB	Judgeable
Vector CompressionGiven M vectors in N dimensions and a free ordering, minimize the total squared length when each vector is stored either as is or as the residual after subtracting a real multiple of an earlier vector.	Hard8	GreedyGeometry+2	No attempts yet	5s	512 MB	Judgeable
6÷2(1+2)Count the distinct integer results obtainable by parenthesizing an expression in any order, with integer division truncated toward zero and division by zero treated as invalid.	Hard8	Dynamic programmingBrute force+2	No attempts yet	8s	512 MB	Judgeable
Divide the CakeGiven 2N strawberry points on a W by H cake, find the probability that two uniformly random points, one on each vertical side, define a line splitting the strawberries into N and N.	Hard8	GeometryProbability+2	No attempts yet	8s	512 MB	Judgeable
Network ReliabilityEach edge of an undirected graph vanishes independently with the same probability; find the probability that what remains is connected.	Hard8	Dynamic programmingBit manipulation+2	No attempts yet	3s	512 MB	Judgeable
Immortal JewelsPlace an infinite line so it touches as many disjoint circles as possible without crossing any, where circle i is usable only if the line's distance to its surface is at most m_i.	Hard8	GeometryBrute force+2	No attempts yet	8s	512 MB	Judgeable
My Friends Are SmallCount subsets of friend weights that can be the final backpack load when items are added one by one in any order until no further friend fits under weight limit W.	Hard8	Dynamic programmingSorting+2	No attempts yet	8s	512 MB	Judgeable
Ten-Year-Old Dynamic ProgrammingCount monotone grid paths from (0,0) to (N,M) that contain exactly K backward steps (left or down), allowing the walk to overshoot the target and never step to a negative coordinate, modulo 1e9+7.	Hard8	CombinatoricsDynamic programming+2	No attempts yet	8s	512 MB	Judgeable
Carrot TourA rabbit walks a polyline of total length at most r, turning at most theta at each corner, earning one carrot per visited city; maximize carrots.	Hard8	Dynamic programmingGraph+2	No attempts yet	1s	512 MB	Judgeable
UsagitobiA rabbit on an m by n torus jumps by two fixed offset vectors; find the maximum number of jumps without revisiting a cell.	Hard8	GraphDFS+2	No attempts yet	1s	512 MB	Judgeable
Cruel BingoGiven up to 8 pre-marked cells on an N by N bingo card, count the ways to reach exactly N unmarked cells while avoiding any full row, column, or diagonal, modulo 10007.	Hard8	CombinatoricsDynamic programming+2	No attempts yet	8s	512 MB	Judgeable
Ika NumberFind the K-th smallest positive integer that counts squid paths from one point to another (jumps of 1 or 2) while avoiding a forbidden integer coordinate.	Hard8	CombinatoricsDynamic programming+2	No attempts yet	8s	512 MB	Judgeable
Carrot breedingPlace the fewest lattice points in the square so that each point lies on exactly N lines through at least two points, or report -1 if impossible.	Hard8	GeometryCombinatorics	No attempts yet	8s	512 MB	Judgeable