Math and counting

Number theory, combinatorics, and geometry

Under construction

Still being built. Things may change

Total results13,153 problems

Circle Bounce
Hard8
Math, Geometry+2
No attempts yet
Time limit
1s
Memory limit
1024 MB
Judgeable
Rise and Fall
Hard8
Greedy, String+2
No attempts yet
Time limit
1s
Memory limit
1024 MB
Judgeable
Redistributing Gifts
Hard8
Dynamic programming, Bit manipulation+1
No attempts yet
Time limit
2s
Memory limit
1024 MB
Judgeable
Cow Camp
Hard8
Probability, Dynamic programming+1
No attempts yet
Time limit
2s
Memory limit
1024 MB
Judgeable
Robot Instructions
Hard8
Divide and conquer, Hash map+2
No attempts yet
Time limit
4s
Memory limit
1024 MB
Judgeable
Substrings and Subsequences
Hard8
String, Combinatorics+2
No attempts yet
Time limit
1s
Memory limit
512 MB
Judgeable
If We Add Them Up...
Hard8
Math, Number theory+1
No attempts yet
Time limit
1s
Memory limit
512 MB
Judgeable
Cactus Eater
Hard8
Graph, DFS+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Extreme Problem
Hard8
Math, Implementation+1
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Journey in Fog
Hard8
Probability, Greedy+1
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Destructive Game
Hard8
Game theory, Math+2
No attempts yet
Time limit
2s
Memory limit
1024 MB
Judgeable
Math String
Hard8
Dynamic programming, Math+2
No attempts yet
Time limit
2s
Memory limit
1024 MB
Judgeable
Two Trees
Hard8
Tree, Divide and conquer+1
No attempts yet
Time limit
8s
Memory limit
256 MB
Judgeable
Fancy Arrays
Hard8
Dynamic programming, Number theory+2
No attempts yet
Time limit
2.5s
Memory limit
256 MB
Judgeable
Restricted Arrays
Hard8
Graph, Union-find+2
No attempts yet
Time limit
4s
Memory limit
256 MB
Judgeable
Stone Pile Game 1
Hard8
Game theory, Math+2
No attempts yet
Time limit
1s
Memory limit
1024 MB
Judgeable
Pentagons Filling the Plane
Hard8
Math, Number theory+1
No attempts yet
Time limit
2s
Memory limit
1024 MB
Judgeable
Interesting Subsegments
Hard8
Prefix sum, Math+2
No attempts yet
Time limit
1s
Memory limit
512 MB
Judgeable
Lucky Tickets
Hard8
Dynamic programming, Number theory+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Disbalance
Hard8
Probability, Dynamic programming+1
No attempts yet
Time limit
1s
Memory limit
512 MB
Judgeable
Gachapon
Hard8
Dynamic programming, Probability+1
No attempts yet
Time limit
5s
Memory limit
512 MB
Judgeable
Build a City
Hard8
Geometry, Greedy+1
No attempts yet
Time limit
3s
Memory limit
1024 MB
Judgeable
Three Countries
Hard8
Geometry, Math+1
No attempts yet
Time limit
1s
Memory limit
512 MB
Judgeable
Radio
Hard8
Segment tree, Number theory+1
No attempts yet
Time limit
1.5s
Memory limit
512 MB
Judgeable
XOR-ABC
Hard8
Bit manipulation, Combinatorics+1
No attempts yet
Time limit
1s
Memory limit
1024 MB
Judgeable
Three Spheres and a Tetrahedron
Hard8
Geometry, Math+1
No attempts yet
Time limit
1s
Memory limit
1024 MB
Judgeable
Yurik and Woodwork Lesson
Hard8
Math, Combinatorics
No attempts yet
Time limit
1s
Memory limit
512 MB
Judgeable
Birthday
Hard8
Prefix sum, Stack+2
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
A+B
Hard8
Dynamic programming, Combinatorics+1
No attempts yet
Time limit
1s
Memory limit
512 MB
Judgeable
Sorting Fractions
Hard8
Binary search, Sorting+2
No attempts yet
Time limit
1s
Memory limit
512 MB
Judgeable
Dart
Hard8
Geometry, Binary search+1
No attempts yet
Time limit
2s
Memory limit
1024 MB
Judgeable
Forest Game
Hard8
Tree, Game theory+2
No attempts yet
Time limit
2s
Memory limit
1024 MB
Judgeable
Inventor Outlasting
Hard8
Game theory, Simulation+1
No attempts yet
Time limit
40s
Memory limit
1024 MB
Judgeable
Broken Device 2
Hard8
Math, Bit manipulation+1
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Sprinkler
Hard8
Tree, DFS+2
No attempts yet
Time limit
4s
Memory limit
1024 MB
Judgeable
Genealogy of Puppets
Hard8
Dynamic programming, Tree+1
No attempts yet
Time limit
2s
Memory limit
1024 MB
Judgeable
Pair Programming
Hard8
Dynamic programming, Combinatorics+1
No attempts yet
Time limit
2s
Memory limit
1024 MB
Judgeable
Joyful KMP
Hard8
String matching, Combinatorics+1
No attempts yet
Time limit
1s
Memory limit
1024 MB
Judgeable
The Locked Box
Hard8
Segment tree, Matrix+1
No attempts yet
Time limit
3s
Memory limit
1024 MB
Judgeable
Radar
Hard8
Geometry, Sorting+1
No attempts yet
Time limit
2s
Memory limit
256 MB
Judgeable
Systematic salesman
Hard8
Divide and conquer, Dynamic programming+1
No attempts yet
Time limit
6s
Memory limit
256 MB
Judgeable
Integer Lines
Hard8
Geometry, Math+1
No attempts yet
Time limit
5s
Memory limit
1024 MB
Judgeable
Dawn Detective Game
Hard8
Game theory, BFS+1
No attempts yet
Time limit
1s
Memory limit
1024 MB
Judgeable
Cake Slices (Hard)
Hard8
Dynamic programming, Combinatorics+1
No attempts yet
Time limit
3s
Memory limit
1024 MB
Judgeable
Bi-ing Lottery Treekets
Hard8
Tree, Dynamic programming+1
No attempts yet
Time limit
1s
Memory limit
1024 MB
Judgeable
Double Sort
Hard8
Combinatorics, Probability+1
No attempts yet
Time limit
1.5s
Memory limit
1024 MB
Judgeable
Triangular Logs
Hard8
Segment tree, Sorting+1
No attempts yet
Time limit
12s
Memory limit
1024 MB
Judgeable
Decrypting Zodiac
Hard8
String matching, Math+1
No attempts yet
Time limit
8s
Memory limit
1024 MB
Judgeable
Saving the Jelly
Hard8
Graph, Geometry+1
No attempts yet
Time limit
Not set
Memory limit
1024 MB
Judgeable
Dao and the Triple Mex Game
Hard8
Array, Greedy+1
No attempts yet
Time limit
1s
Memory limit
1024 MB
Judgeable
Fancy Stack
Hard8
Dynamic programming, Combinatorics+1
No attempts yet
Time limit
3s
Memory limit
512 MB
Judgeable
Sum of Subarray Sums Under Range Assignment Queries
Hard8
Segment tree, Combinatorics+1
No attempts yet
Time limit
4s
Memory limit
1024 MB
Judgeable
Semiconductor Fabrication
Hard8
Graph, Shortest path+1
No attempts yet
Time limit
4s
Memory limit
1024 MB
Judgeable
Numbers on a Board: Expected Sum and Product
Hard8
Combinatorics, Math
No attempts yet
Time limit
4s
Memory limit
1024 MB
Judgeable
Lagrange's Theorem Has Subtraction Too
Hard8
Number theory, Math+1
No attempts yet
Time limit
1s
Memory limit
512 MB
Judgeable
Prisoners' Challenge
Hard8
Math, Implementation
No attempts yet
Time limit
1s
Memory limit
1024 MB
Judgeable
Kingdom
Hard8
Dynamic programming, Binary search+1
No attempts yet
Time limit
1s
Memory limit
1024 MB
Judgeable
Lord of the Characteristic Polynomials (2)
Hard8
Matrix, Math+1
No attempts yet
Time limit
5s
Memory limit
1024 MB
Judgeable
No More Headaches from Mental Math!
Hard8
Math, Number theory+1
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Keep in Touch
Hard8
Binary search, Geometry+1
No attempts yet
Time limit
1s
Memory limit
1024 MB
Judgeable
Strange Number 2
Hard8
Number theory, Math+1
No attempts yet
Time limit
2s
Memory limit
1024 MB
Judgeable
Counting Sequence
Hard8
Dynamic programming, Math+1
No attempts yet
Time limit
16s
Memory limit
1024 MB
Judgeable
Just Another Number Theory Problem
Hard8
Number theory, Math+1
No attempts yet
Time limit
1s
Memory limit
1024 MB
Judgeable
Two-dimensional array
Hard8
Math, Implementation
No attempts yet
Time limit
1s
Memory limit
512 MB
Judgeable
Rectangle Placement
Hard8
Combinatorics, Math+1
No attempts yet
Time limit
1s
Memory limit
1024 MB
Judgeable
X-Sums Sudoku
Hard8
Math, Bit manipulation+1
No attempts yet
Time limit
4s
Memory limit
1024 MB
Judgeable
Squirrel Game
Hard8
Game theory, Dynamic programming+1
No attempts yet
Time limit
3s
Memory limit
1024 MB
Judgeable
Two Paths
Hard8
Tree, Dynamic programming+1
No attempts yet
Time limit
5s
Memory limit
1024 MB
Judgeable
The Beauty of Cycles
Hard8
Number theory, Math
No attempts yet
Time limit
2s
Memory limit
1024 MB
Judgeable
K-Item Shopping Spree
Hard8
Math, Dynamic programming+1
No attempts yet
Time limit
10s
Memory limit
1024 MB
Judgeable
Kermode Bear's Salmon Hunt
Hard8
Game theory, Graph+2
No attempts yet
Time limit
1s
Memory limit
1024 MB
Judgeable
Prime Arrangement
Hard8
Combinatorics, Sorting+1
No attempts yet
Time limit
1s
Memory limit
1024 MB
Judgeable
Longest Shortest Paths
Hard8
Geometry, Graph+2
No attempts yet
Time limit
2s
Memory limit
1024 MB
Judgeable
Formula Flatland
Hard8
Graph, BFS+1
No attempts yet
Time limit
3s
Memory limit
1024 MB
Judgeable
GomGom and Tetris
Hard8
Game theory, Bit manipulation+1
No attempts yet
Time limit
2s
Memory limit
1024 MB
Judgeable
Card Game
Hard8
Game theory, Dynamic programming+1
No attempts yet
Time limit
1s
Memory limit
1024 MB
Judgeable
Empty Quadrilaterals
Hard8
Geometry, Dynamic programming+2
No attempts yet
Time limit
2s
Memory limit
1024 MB
Judgeable
Linear Regression
Hard8
Geometry, Binary search+1
No attempts yet
Time limit
5s
Memory limit
1024 MB
Judgeable
SubsetMex
Hard8
Greedy, Dynamic programming+1
No attempts yet
Time limit
1s
Memory limit
1024 MB
Judgeable
Lego Wall
Hard8
Combinatorics, Dynamic programming+1
No attempts yet
Time limit
3s
Memory limit
1024 MB
Judgeable
Take On Meme
Hard8
Tree, Geometry+1
No attempts yet
Time limit
4s
Memory limit
1024 MB
Judgeable
Unbroken Spirit 2
Hard8
Greedy, Heap+1
No attempts yet
Time limit
1.5s
Memory limit
1024 MB
Judgeable
Faster Than Light
Hard8
Geometry, Sorting+1
No attempts yet
Time limit
10s
Memory limit
1024 MB
Judgeable
Mortgage
Hard8
Prefix sum, Divide and conquer+1
No attempts yet
Time limit
3s
Memory limit
1024 MB
Judgeable
Kalel, the Jumping Frog
Hard8
Dynamic programming, Matrix+1
No attempts yet
Time limit
18s
Memory limit
1024 MB
Judgeable
Silver Tree
Hard8
Tree, Math+1
No attempts yet
Time limit
2s
Memory limit
512 MB
Judgeable
Expected length of the minimum cycle
Hard8
Combinatorics, Math
No attempts yet
Time limit
2s
Memory limit
1024 MB
Judgeable
Flying Doors
Hard8
Sorting, Greedy+1
No attempts yet
Time limit
2s
Memory limit
1024 MB
Judgeable
Simple Math Problem
Hard8
Combinatorics, Math+1
No attempts yet
Time limit
1s
Memory limit
256 MB
Judgeable
Reimu's Teleportation Practice
Hard8
Tree, Dynamic programming+1
No attempts yet
Time limit
6s
Memory limit
1024 MB
Judgeable
BinCoin
Hard8
Tree, Probability+1
No attempts yet
Time limit
3s
Memory limit
1024 MB
Judgeable
Cactus Meets Torus
Hard8
Graph, DFS+1
No attempts yet
Time limit
3s
Memory limit
1024 MB
Judgeable
Game of Questions
Hard8
Dynamic programming, Bit manipulation+1
No attempts yet
Time limit
5s
Memory limit
1024 MB
Judgeable
Balanced Seesaw Array
Hard8
Segment tree, Math+1
No attempts yet
Time limit
3s
Memory limit
1024 MB
Judgeable
Invitation
Hard8
Combinatorics, Sorting+1
No attempts yet
Time limit
3s
Memory limit
1024 MB
Judgeable
Under Construction Forever
Hard8
Graph, Dynamic programming+1
No attempts yet
Time limit
1s
Memory limit
1024 MB
Judgeable
Knightmare
Hard8
Segment tree, Sorting+1
No attempts yet
Time limit
5s
Memory limit
1024 MB
Judgeable
Gold Rush
Hard8
Divide and conquer, Dynamic programming+2
No attempts yet
Time limit
1s
Memory limit
1024 MB
Judgeable
Knight Moves: Black Edition
Hard8
Math, Implementation
No attempts yet
Time limit
1s
Memory limit
1024 MB
Judgeable
Who is closer
Hard8
Bit manipulation, Divide and conquer+1
No attempts yet
Time limit
1s
Memory limit
1024 MB
Judgeable

Title	Level	Topics	Solved	Time limit	Memory limit	Judge
Circle BounceA ball thrown from (-1,0) with rational slope a/b bounces perfectly inside a unit circle n times; output the x-coordinate of the n-th impact point modulo 1e9+7.	Hard8	MathGeometry+2	No attempts yet	1s	1024 MB	Judgeable
Rise and FallGiven a huge decimal string, find the largest number no greater than it whose digits split into a nondecreasing prefix and a nonincreasing suffix.	Hard8	GreedyString+2	No attempts yet	1s	1024 MB	Judgeable
Redistributing GiftsGiven each cow's preference permutation and breed strings, count the gift reassignments per string where every cow keeps her gift or gets a preferred one within her breed.	Hard8	Dynamic programmingBit manipulation+1	No attempts yet	2s	1024 MB	Judgeable
Cow CampWith up to K submissions that always pass the sample and guess the other T-1 cases fairly, find the maximum expected final score under optimal stopping.	Hard8	ProbabilityDynamic programming+1	No attempts yet	2s	1024 MB	Judgeable
Robot InstructionsGiven up to 40 vectors, count for each K how many K-subsets sum to a target point, using meet-in-the-middle over the two halves.	Hard8	Divide and conquerHash map+2	No attempts yet	4s	1024 MB	Judgeable
Substrings and SubsequencesCharacterize strings whose distinct substrings equal their distinct subsequences, then print the n-th such string in length-then-lexicographic order for n up to 1e6.	Hard8	StringCombinatorics+2	No attempts yet	1s	512 MB	Judgeable
If We Add Them Up...Given n integers a_i greater than 1, choose positive rational exponents b_i so that the sum of a_i^(b_i) is an integer, and print the smallest such integer.	Hard8	MathNumber theory+1	No attempts yet	1s	512 MB	Judgeable
Cactus EaterGiven a cactus, find the expected total energy released when a random vertex is repeatedly eaten and each remaining component is processed, modulo 998244353.	Hard8	GraphDFS+2	No attempts yet	2s	512 MB	Judgeable
Extreme ProblemGiven Yes/No flags for multiple local maxima, minima, and plateaus, print an RPN expression for a grid function with the requested properties.	Hard8	MathImplementation+1	No attempts yet	2s	512 MB	Judgeable
Journey in FogGiven Jane's equally likely speeds, find the minimum expected time for Julia to meet Jane on a street of length L and return home.	Hard8	ProbabilityGreedy+1	No attempts yet	2s	512 MB	Judgeable
Destructive GameEach pile is an independent subtraction game where you may remove b^k stones; determine the winner of the sum under optimal play.	Hard8	Game theoryMath+2	No attempts yet	2s	1024 MB	Judgeable
Math StringSum the values of all length-N strings over digits 1-9 and the operators + and * that form valid expressions, modulo 998244353, with N up to 1e18.	Hard8	Dynamic programmingMath+2	No attempts yet	2s	1024 MB	Judgeable
Two TreesGiven two trees on the same n vertices, compute the sum over all vertex pairs of the squared sum of their distances in both trees, modulo 2^32.	Hard8	TreeDivide and conquer+1	No attempts yet	8s	256 MB	Judgeable
Fancy ArraysCount length-n arrays whose elements all divide m and whose neighboring elements share a prime factor, modulo 1e9+7, for up to 150 queries.	Hard8	Dynamic programmingNumber theory+2	No attempts yet	2.5s	256 MB	Judgeable
Restricted ArraysCount the moduli M up to n for which some integer array satisfies a[x]+1 = a[y] (mod M) for every given pair, and list them.	Hard8	GraphUnion-find+2	No attempts yet	4s	256 MB	Judgeable
Stone Pile Game 1Three piles; a move takes one stone from two nonempty piles and adds one to the third. The player unable to move wins, so determine the optimal winner with R moving first.	Hard8	Game theoryMath+2	No attempts yet	1s	1024 MB	Judgeable
Pentagons Filling the PlaneGiven the square centers of two pentagons in a plane tiling, find the shortest graph distance between them for up to 100,000 test cases.	Hard8	MathNumber theory+1	No attempts yet	2s	1024 MB	Judgeable
Interesting SubsegmentsGiven n and k, build the lexicographically smallest array of 0, 1, and 2 of length n with exactly k subsegments whose sum is divisible by 3, or print -1.	Hard8	Prefix sumMath+2	No attempts yet	1s	512 MB	Judgeable
Lucky TicketsGiven n, s, and a prime q, find the sum of luckiness over all q-digit base-n tickets whose digit sum plus digit product is s mod n, modulo q.	Hard8	Dynamic programmingNumber theory+2	No attempts yet	2s	512 MB	Judgeable
DisbalanceEach minute one bacterium is picked at random to divide among n dishes; output the expected sum of the imbalance d over k minutes modulo 998244353.	Hard8	ProbabilityDynamic programming+1	No attempts yet	1s	512 MB	Judgeable
GachaponGiven item frequencies and per-level round counts, compute for each star count the expected number of such items in a legal top-level rolling, times its legality probability, modulo 998244353.	Hard8	Dynamic programmingProbability+1	No attempts yet	5s	512 MB	Judgeable
Build a CityGiven settlements and a per-move wall budget m, decide whether some order of acquiring them keeps each move's new wall length within m.	Hard8	GeometryGreedy+1	No attempts yet	3s	1024 MB	Judgeable
Three CountriesFind the area of the convex hull of the union of three given circles.	Hard8	GeometryMath+1	No attempts yet	1s	512 MB	Judgeable
RadioStations on frequencies 1 to n switch on and off, and each query asks whether two active frequencies in [l, r] share a common factor above 1.	Hard8	Segment treeNumber theory+1	No attempts yet	1.5s	512 MB	Judgeable
XOR-ABCCount triples A < B < C with A xor B = C, all within 1 to 2^K - 1, for K up to 10^18, modulo 1000003.	Hard8	Bit manipulationCombinatorics+1	No attempts yet	1s	1024 MB	Judgeable
Three Spheres and a TetrahedronGiven tetrahedron OABC, find the center and radius of the sphere through A, B, C that touches the inscribed sphere and the four exspheres.	Hard8	GeometryMath+1	No attempts yet	1s	1024 MB	Judgeable
Yurik and Woodwork LessonCount the ways to cut cells from an N by M board so that the top-left and bottom-right cells stay, the rest is connected, and each row and column is one contiguous segment, modulo 998244353.	Hard8	MathCombinatorics	No attempts yet	1s	512 MB	Judgeable
BirthdayGiven n double-sided cards, sum over all segments [l, r] the largest achievable total not divisible by k, modulo 1e9+7.	Hard8	Prefix sumStack+2	No attempts yet	2s	512 MB	Judgeable
A+BCount the column permutations of three n-digit rows that make a+b=c hold with no leading zeros, modulo 10^9+7.	Hard8	Dynamic programmingCombinatorics+1	No attempts yet	1s	512 MB	Judgeable
Sorting FractionsGiven two sets of distinct integers, sort all reduced fractions a_i/b_j and output the c-th fraction in the sorted list for each query.	Hard8	Binary searchSorting+2	No attempts yet	1s	512 MB	Judgeable
DartGiven a convex polygon dartboard and two lists of dart throws, compute each player's total score modulo 1e9+7 and report the winner.	Hard8	GeometryBinary search+1	No attempts yet	2s	1024 MB	Judgeable
Forest GameCount the non-empty sets of trees where B wins the stone game, with each turn moving a stone 1 to K unused branches, modulo 998244353.	Hard8	TreeGame theory+2	No attempts yet	2s	1024 MB	Judgeable
Inventor OutlastingTwo players take turns building attractions on free X cells, where each build fills diagonal sign runs; count the first moves that let the first player win.	Hard8	Game theorySimulation+1	No attempts yet	40s	1024 MB	Judgeable
Broken Device 2Anna must encode an integer up to 10^18 into 0/1 arrays sent through a riffle-shuffle device so Bruno can recover it exactly.	Hard8	MathBit manipulation+1	No attempts yet	2s	512 MB	Judgeable
SprinklerGiven a tree of lands with millet heights, multiply every height within distance D of a land by W modulo L, and answer height queries for single lands.	Hard8	TreeDFS+2	No attempts yet	4s	1024 MB	Judgeable
Genealogy of PuppetsCount the ordered binary trees on n puppets that respect each puppet's child-count limits and require a later-released child under every parent with children, modulo 1e9+7.	Hard8	Dynamic programmingTree+1	No attempts yet	2s	1024 MB	Judgeable
Pair ProgrammingCount the distinct expressions formed by interleaving two programs of N instructions each, modulo 10^9+7.	Hard8	Dynamic programmingCombinatorics+1	No attempts yet	2s	1024 MB	Judgeable
Joyful KMPCount the lowercase strings that have the same failure function as the given string, and print the K-th one in lexicographic order or OVER.	Hard8	String matchingCombinatorics+1	No attempts yet	1s	1024 MB	Judgeable
The Locked BoxMaintain the value of a continued fraction built from a W/E operation string under append, flip, and reverse updates, printing it modulo 998244353.	Hard8	Segment treeMatrix+1	No attempts yet	3s	1024 MB	Judgeable
RadarEach radius and ray direction gives one scanned point. For each query point, output the distance to the nearest scanned point.	Hard8	GeometrySorting+1	No attempts yet	2s	256 MB	Judgeable
Systematic salesmanFind the shortest path through all cities when the route must alternate left/right and lower/upper splits of the point set, and print the visiting order.	Hard8	Divide and conquerDynamic programming+1	No attempts yet	6s	256 MB	Judgeable
Integer LinesCount integer lines y = ax + b that split the n peppers into two equal groups without touching any pepper, or print -1 if there are infinitely many.	Hard8	GeometryMath+1	No attempts yet	5s	1024 MB	Judgeable
Dawn Detective GameOn a grid with walls, the detective and thief move in turns, and the task is to find the fewest moves for the detective to lock the thief in prison, or print -1.	Hard8	Game theoryBFS+1	No attempts yet	1s	1024 MB	Judgeable
Cake Slices (Hard)Count the subsets of cake slices, where slice i is 1/c_i of a cake, whose total falls between 0.99 and 1.01 of a whole cake, modulo 10^9+7.	Hard8	Dynamic programmingCombinatorics+1	No attempts yet	3s	1024 MB	Judgeable
Bi-ing Lottery TreeketsCount the distinct winning tickets produced by dropping K numbered balls into a rooted binary tree of N nodes, modulo 1e9+7.	Hard8	TreeDynamic programming+1	No attempts yet	1s	1024 MB	Judgeable
Double SortFor a uniformly random n-element subset of 1..m, find the expected final sequence after sorting its positive gaps and taking prefix sums.	Hard8	CombinatoricsProbability+1	No attempts yet	1.5s	1024 MB	Judgeable
Triangular LogsFor each rectangle query, decide whether three trees inside it have heights that form a non-degenerate triangle.	Hard8	Segment treeSorting+1	No attempts yet	12s	1024 MB	Judgeable
Decrypting ZodiacGiven an encrypted string and a guessed plaintext, find the minimum letter mismatches over all Caesar shifts and cyclic splits used during encryption.	Hard8	String matchingMath+1	No attempts yet	8s	1024 MB	Judgeable
Saving the JellyGiven N children and N+1 sweets, decide if calling the children in some order can leave the blueberry jelly uneaten, and output that order.	Hard8	GraphGeometry+1	No attempts yet	Not set	1024 MB	Judgeable
Dao and the Triple Mex GameGiven array A, pick subsequences to build array B of mex values, then pick subarrays of B to build C. Find the maximum possible sum of C.	Hard8	ArrayGreedy+1	No attempts yet	1s	1024 MB	Judgeable
Fancy StackCount the stacks that use all n blocks in a zigzag order where even positions strictly increase, modulo 998244353.	Hard8	Dynamic programmingCombinatorics+1	No attempts yet	3s	512 MB	Judgeable
Sum of Subarray Sums Under Range Assignment QueriesGiven N cells and Q range-assign queries, sum every subarray sum over all query windows [U, D], modulo 998244353.	Hard8	Segment treeCombinatorics+1	No attempts yet	4s	1024 MB	Judgeable
Semiconductor FabricationChoose vertex potentials and edge energies, with E1=1.0 and EN=-1.0 fixed, to minimize total transfer cost, or print HAPPY if the cost can drop below zero.	Hard8	GraphShortest path+1	No attempts yet	4s	1024 MB	Judgeable
Numbers on a Board: Expected Sum and ProductGiven N integers, find for each k the expected final sum after k product merges and the expected final product after k sum merges, modulo 998244353.	Hard8	CombinatoricsMath	No attempts yet	4s	1024 MB	Judgeable
Lagrange's Theorem Has Subtraction TooGiven an integer N with \|N\| up to 10^12, find the fewest distinct positive squares whose signed sum equals N and print each signed term.	Hard8	Number theoryMath+1	No attempts yet	1s	512 MB	Judgeable
Prisoners' ChallengeDesign a prisoner strategy that uses one blackboard integer to pass information, so the group can find the bag with fewer coins when each bag holds at most N coins.	Hard8	MathImplementation	No attempts yet	1s	1024 MB	Judgeable
KingdomChoose K castles, including both endpoints on the x-axis, to maximize the area of their convex hull.	Hard8	Dynamic programmingBinary search+1	No attempts yet	1s	1024 MB	Judgeable
Lord of the Characteristic Polynomials (2)Given an n by n matrix whose entries are a + bsqrt(D), find each coefficient of its characteristic polynomial as p + qsqrt(D), reduced modulo M.	Hard8	MatrixMath+1	No attempts yet	5s	1024 MB	Judgeable
No More Headaches from Mental Math!Given N and M called numbers (duplicates allowed, N up to 1e9), find the product of the uncalled integers from 1 to N modulo 1e9+7.	Hard8	MathNumber theory+1	No attempts yet	2s	512 MB	Judgeable
Keep in TouchGiven two polylines, find the minimum distance d such that agents A and B can walk their routes together while never being farther apart than d.	Hard8	Binary searchGeometry+1	No attempts yet	1s	1024 MB	Judgeable
Strange Number 2Given N up to 1e9, sum f(A,B) over all pairs 1 to N, where f counts C whose GCD with A and LCM with B match the stated values.	Hard8	Number theoryMath+1	No attempts yet	2s	1024 MB	Judgeable
Counting SequenceCount sequences of positive integers with adjacent differences of 1 and sum n, weighting each by c raised to the number of descents, modulo 998244353.	Hard8	Dynamic programmingMath+1	No attempts yet	16s	1024 MB	Judgeable
Just Another Number Theory ProblemGiven n primes below 10^18 with the smallest under 100, sum the squared gaps between consecutive numbers in [0, product] divisible by at least one prime, modulo 998244353.	Hard8	Number theoryMath+1	No attempts yet	1s	1024 MB	Judgeable
Two-dimensional arrayPlace 1 to N^2 in an N by N grid so that the smallest ratio p/q between two values sharing a row or column is as large as possible.	Hard8	MathImplementation	No attempts yet	1s	512 MB	Judgeable
Rectangle PlacementCount the ways to draw two rectangles on a grid of W vertical and H horizontal lines so that their boundaries share no point, modulo 998244353.	Hard8	CombinatoricsMath+1	No attempts yet	1s	1024 MB	Judgeable
X-Sums SudokuGiven n, m, a direction, and an index, find the X-sum of that row or column in the lexicographically smallest 2^n by 2^m sudoku.	Hard8	MathBit manipulation+1	No attempts yet	4s	1024 MB	Judgeable
Squirrel GameTwinkle and Nova alternately place acorns on empty stones left of some squirrel, and the player with no legal move loses. Find the winner.	Hard8	Game theoryDynamic programming+1	No attempts yet	3s	1024 MB	Judgeable
Two PathsGiven a weighted tree and queries (u, v, A, B), find vertex-disjoint paths from u and from v that maximize A times the first path weight plus B times the second.	Hard8	TreeDynamic programming+1	No attempts yet	5s	1024 MB	Judgeable
The Beauty of CyclesGiven n, m, and base k, count the distinct purely cyclic base-k reals that can be written as x/y with 1 <= x <= n and 1 <= y <= m.	Hard8	Number theoryMath	No attempts yet	2s	1024 MB	Judgeable
K-Item Shopping SpreeCount length-k sequences of item indices (repeats and order allowed) whose prices sum to each query target, modulo 997.	Hard8	MathDynamic programming+1	No attempts yet	10s	1024 MB	Judgeable
Kermode Bear's Salmon HuntTwo bears alternately place salmon on empty vertices that have a unique simple path from a salmon vertex. Find which bear is stuck when no move is left.	Hard8	Game theoryGraph+2	No attempts yet	1s	1024 MB	Judgeable
Prime ArrangementGiven RC distinct primes, count the ways to fill an R by C grid so that each row's product has a prescribed rank among all row products.	Hard8	CombinatoricsSorting+1	No attempts yet	1s	1024 MB	Judgeable
Longest Shortest PathsGiven rectangles and two vertical segments in the plane, find the largest shortest-path length between any point on S and any point on T.	Hard8	GeometryGraph+2	No attempts yet	2s	1024 MB	Judgeable
Formula FlatlandGiven a planar road network with crossing coordinates, find the fewest crossings that can form a simple closed cycle.	Hard8	GraphBFS+1	No attempts yet	3s	1024 MB	Judgeable
GomGom and TetrisTwo players alternately place Tetris pieces or 1x1 blocks on an N by M board to maximize their own score, and the task is to decide the winner with a 0.5 first-player penalty.	Hard8	Game theoryBit manipulation+1	No attempts yet	2s	1024 MB	Judgeable
Card GameAlice and Bob alternately pick a card on an N by M grid and remove its connected diagonal run by color. Determine whether the first player wins.	Hard8	Game theoryDynamic programming+1	No attempts yet	1s	1024 MB	Judgeable
Empty QuadrilateralsCount simple quadrilaterals on a point set with no three collinear whose interiors contain no other points, for up to 300 points.	Hard8	GeometryDynamic programming+2	No attempts yet	2s	1024 MB	Judgeable
Linear RegressionRemove k points, then find a line that minimizes the largest vertical distance to the remaining points, and print that distance.	Hard8	GeometryBinary search+1	No attempts yet	5s	1024 MB	Judgeable
SubsetMexGiven the counts f_i of each value below n in a multiset, find the fewest subset-and-mex operations needed to insert n.	Hard8	GreedyDynamic programming+1	No attempts yet	1s	1024 MB	Judgeable
Lego WallCount the connected, hole-free walls of width w and height h built from 1x1x1 and 2x1x1 bricks, modulo 1000000007.	Hard8	CombinatoricsDynamic programming+1	No attempts yet	3s	1024 MB	Judgeable
Take On MemeGiven a rooted vote tree where each child's (x, y) vector is added or subtracted at every node, find the largest squared length the root can reach.	Hard8	TreeGeometry+1	No attempts yet	4s	1024 MB	Judgeable
Unbroken Spirit 2For each prefix of N dragons with growth D_i and start height H_i, find the max total height a thief can cut with one arrow per day.	Hard8	GreedyHeap+1	No attempts yet	1.5s	1024 MB	Judgeable
Faster Than LightGiven n non-overlapping axis-aligned rectangles, decide whether a single infinite line touches every one of them.	Hard8	GeometrySorting+1	No attempts yet	10s	1024 MB	Judgeable
MortgageGiven monthly incomes and several loan intervals, find for each interval the largest equal payment that can be covered month by month using only money saved inside that interval.	Hard8	Prefix sumDivide and conquer+1	No attempts yet	3s	1024 MB	Judgeable
Kalel, the Jumping FrogCount the jump sequences that take Kalel from stone 1 to stone N with total energy at most K, modulo 1e9, for jumps of length up to 10.	Hard8	Dynamic programmingMatrix+1	No attempts yet	18s	1024 MB	Judgeable
Silver TreeGiven K, H, and query pairs of keys, find the path length between the two blue nodes holding each pair in a silver tree, or -1 if a key is missing.	Hard8	TreeMath+1	No attempts yet	2s	512 MB	Judgeable
Expected length of the minimum cycleGiven N and a prime P, find the expected length of the shortest cycle in a random permutation of 1 to N, modulo P as a reduced fraction.	Hard8	CombinatoricsMath	No attempts yet	2s	1024 MB	Judgeable
Flying DoorsGiven n doors with ceiling heights a_i and velocities b_i, arrange them in an order that minimizes the probability Kostya can fly through all doors at a random starting height.	Hard8	SortingGreedy+1	No attempts yet	2s	1024 MB	Judgeable
Simple Math ProblemGiven N, K, and X, find the X-th lexicographically smallest length-K array over 1 to N that uses every value and balances each i-1 count around every i.	Hard8	CombinatoricsMath+1	No attempts yet	1s	256 MB	Judgeable
Reimu's Teleportation PracticeGiven a tree where K nodes are priests who can teleport to any priest with equal chance, find the minimum expected moves from A to B.	Hard8	TreeDynamic programming+1	No attempts yet	6s	1024 MB	Judgeable
BinCoinGiven k random signing sequences from a full binary tree, restore each employee's direct superior in that tree.	Hard8	TreeProbability+1	No attempts yet	3s	1024 MB	Judgeable
Cactus Meets TorusGiven a cactus as edge-disjoint paths, decide if it can be drawn on a torus so that cutting along any one cycle keeps the sheet in one piece.	Hard8	GraphDFS+1	No attempts yet	3s	1024 MB	Judgeable
Game of QuestionsGiven n questions answered correctly or not by m participants, find the probability that participant 1 is the last one left after all questions are asked in a random order.	Hard8	Dynamic programmingBit manipulation+1	No attempts yet	5s	1024 MB	Judgeable
Balanced Seesaw ArrayGiven an array with range add and range assign updates, answer whether a queried subarray is a balanced seesaw array.	Hard8	Segment treeMath+1	No attempts yet	3s	1024 MB	Judgeable
InvitationCount the groups of k leaders whose availability intervals share a common time slot, for every k from 1 to n, modulo 998244353.	Hard8	CombinatoricsSorting+1	No attempts yet	3s	1024 MB	Judgeable
Under Construction ForeverGiven a connected graph of buildings with costs, find the fewest buildings left after leaf-absorbing reconstructions, the minimum cost for that count, and the number of ways modulo 1,000,000,007.	Hard8	GraphDynamic programming+1	No attempts yet	1s	1024 MB	Judgeable
KnightmareCount the squares attacked by at least k knights, where each knight's reach is a symmetric set of offsets determined by its a and b values.	Hard8	Segment treeSorting+1	No attempts yet	5s	1024 MB	Judgeable
Gold RushCount the distinct win-loss records possible in an n-player single-elimination bracket with best-of-k matches, modulo 1,000,003.	Hard8	Divide and conquerDynamic programming+2	No attempts yet	1s	1024 MB	Judgeable
Knight Moves: Black EditionGiven an N by N board with N up to 1e15, find the fewest knight moves between two cells.	Hard8	MathImplementation	No attempts yet	1s	1024 MB	Judgeable
Who is closerFor each X from 0 to 2^N-1, count the cards Y where X is closer to Z = X xor Y than Y is, with ties won when X < Y.	Hard8	Bit manipulationDivide and conquer+1	No attempts yet	1s	1024 MB	Judgeable