Problems

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Total results1,786 problems

Title	Level	Topics	Solved	Time limit	Memory limit	Judge
Counting four cyclesCount ordered 4-vertex cycles in an undirected graph given as an N by N adjacency matrix with N up to 250.	Medium5	GraphCombinatorics+1	No attempts yet	2s	128 MB	Judgeable
Dreary DesignCount RGB triples with components from 0 to K whose largest pairwise difference is at most V.	Medium5	CombinatoricsMath	No attempts yet	5s	512 MB	Judgeable
Password Attacker (Large)Count length-N strings over M symbols that use every symbol at least once, modulo 1e9+7.	Medium5	CombinatoricsMath	No attempts yet	5s	512 MB	Judgeable
Parentheses Order (Small)Print the k-th valid parentheses string of n pairs in lexicographic order for each test case, or report that it does not exist.	Medium5	Dynamic programmingCombinatorics	No attempts yet	5s	512 MB	Judgeable
Parentheses Order (Large)Given n and k, output the k-th valid parentheses string of n pairs in lexicographic order, or Doesn't Exist! when fewer than k exist.	Medium5	Dynamic programmingCombinatorics+1	No attempts yet	5s	512 MB	Judgeable
Trie Sharding (Small)Split up to 8 strings across labeled servers to maximize the summed trie node counts and count the optimal splits.	Medium5	Brute forceTrie+1	No attempts yet	5s	512 MB	Judgeable
Consonants (Large)Count the substrings of each given name that contain at least n consecutive consonants.	Medium5	StringCombinatorics	No attempts yet	5s	512 MB	Judgeable
Arithmetic Digit Numbers 2Count the integers from 1 to N, with N up to 10^18, whose decimal digits form an arithmetic sequence.	Medium5	BacktrackingCombinatorics+1	No attempts yet	0.5s	512 MB	Judgeable
Handing out candiesFor every K, count the ways to choose one candy of each brand 1 through K, and print the total over all K.	Medium5	Dynamic programmingCombinatorics	No attempts yet	2s	512 MB	Judgeable
Trees and Path Lengths 2Find leaf counts p, q, r on a fixed 4-vertex path so the tree has exactly S length-3 paths, minimizing N then (p,q,r).	Medium5	MathImplementation+2	No attempts yet	2s	512 MB	Judgeable
pqrCount index triples p<q<r whose product A[p]A[q]A[r] is divisible by K, for N up to 2000.	Medium5	CombinatoricsNumber theory+1	No attempts yet	2s	512 MB	Judgeable
Counting Music ScoresCount scores over two pitches and two durations with n seconds total, balanced pitch counts, at least as many long notes as short, and alternating pitches starting low.	Medium5	CombinatoricsDynamic programming+1	No attempts yet	2s	512 MB	Judgeable
Distinct rational numbersCount distinct values of a/b with 0 <= a <= b <= N, i.e. fractions in [0,1] with reduced denominator at most N.	Medium5	MathNumber theory+2	No attempts yet	2s	512 MB	Judgeable
WindowPick a uniformly random axis-aligned subrectangle of an H by W grid; find the expected number of cells times 9, modulo 1e9+7.	Medium5	MathCombinatorics+2	No attempts yet	1s	512 MB	Judgeable
Lucky TicketsCount digit strings of length 2N whose first N digits sum to the same value as the last N digits, modulo 1e9+7.	Medium5	Dynamic programmingCombinatorics+2	No attempts yet	2s	512 MB	Judgeable
EcologyCompute the probability that exactly M of N birds wear a tracker after D days of catching C random birds each day.	Medium5	Dynamic programmingProbability+1	No attempts yet	2s	512 MB	Judgeable
Fibonacci ChickenGiven N, split it into Fibonacci-derived (people, chicken) pairs whose people counts sum to N, and report the minimum and maximum total chickens.	Medium5	Dynamic programmingMath+2	No attempts yet	1s	128 MB	Judgeable
Hamming EllipsesCount words of length n over a q-symbol alphabet whose Hamming distances to two given words sum to exactly D.	Medium5	CombinatoricsMath+2	No attempts yet	5s	512 MB	Judgeable
Fleecing the RaffleAdd k slips with your name to a box of n slips so the chance your name is drawn exactly once among p draws is maximized.	Medium5	MathCombinatorics+2	No attempts yet	2s	512 MB	Judgeable
Jewelry StoreWith unlimited gems of each of N kinds, list all total values obtainable by choosing exactly K gems.	Medium5	Dynamic programmingCombinatorics	No attempts yet	5s	512 MB	Judgeable
Winner of the Bubble GameTwo players alternately swap adjacent out-of-order pairs until the permutation is sorted; the one who cannot move loses. Decide the winner.	Medium5	CombinatoricsGame theory+1	No attempts yet	2s	512 MB	Judgeable
Sum Decomposition 2Count ordered K-tuples of integers between 0 and N whose sum is N, modulo 1,000,000,000.	Medium5	Dynamic programmingCombinatorics+1	No attempts yet	1s	512 MB	Judgeable
Good Positions in a PermutationCount permutations of 1..N whose number of positions i with \|P_i - i\| = 1 equals a given K, modulo 1e9+7.	Medium5	CombinatoricsDynamic programming+1	No attempts yet	2s	512 MB	Judgeable
LettersGiven index i, return the uppercase letter at position i in the concatenation of all uppercase strings ordered by length then lexicographically.	Medium5	CombinatoricsMath	No attempts yet	0.2s	256 MB	Judgeable
m-ary PartitionsCount the partitions of n into powers of m, for up to 1000 queries with n up to 10000.	Medium5	Dynamic programmingMath+2	No attempts yet	2s	512 MB	Judgeable
PasswordCount n-digit strings over 0-9 that contain every one of the m given digits at least once.	Medium5	CombinatoricsMath	No attempts yet	1s	64 MB	Judgeable
Binomial coefficient queriesGiven M pairs N and K, print the binomial coefficient C(N, K) modulo 1,000,000,007.	Medium5	CombinatoricsMath+1	No attempts yet	1s	512 MB	Judgeable
Cities and StatesGiven up to 200,000 cities with names and two-letter state codes, count unordered pairs whose first two name letters match the other city's state code and vice versa, with different states.	Medium5	Hash mapString+2	No attempts yet	2s	512 MB	Judgeable
Vote (Large)Given N supporters of A and M of B in random arrival order, find the probability A leads after every vote; a ballot-problem computation.	Medium5	CombinatoricsProbability+2	No attempts yet	5s	512 MB	Judgeable
Codejamon Cipher (Small)For each enciphered string, count the sentences of vocabulary words whose letter multisets concatenate to it, modulo 1e9+7.	Medium5	Dynamic programmingHash map+1	No attempts yet	5s	512 MB	Judgeable
Sherlock and Parentheses (Small)Given L left and R right parentheses, arrange all of them to maximize the count of balanced non-empty substrings, counted by position.	Medium5	GreedyMath+2	No attempts yet	5s	512 MB	Judgeable
Slides! (Small)Given B up to 6 and M up to 20, decide if exactly M paths from building 1 to B exist, and print the fixed-rule matrix when possible.	Medium5	CombinatoricsDynamic programming+1	No attempts yet	5s	512 MB	Judgeable
What Is Dynamic Programming?Count paths from the top-left cell to the bottom-right cell of an n by m grid when each step moves right, down, or diagonally down-right, printed modulo 1e9+7.	Medium5	Dynamic programmingMatrix+1	No attempts yet	2s	512 MB	Judgeable
Tiling a 2 by N wallCount the ways to tile a 2 by N wall with 2x1, 1x2, and 1x1 tiles, modulo 1e9+7.	Medium5	Dynamic programmingCombinatorics	No attempts yet	2s	512 MB	Judgeable
DespojadosCount the divisors of N that are squarefree and have at least two prime factors.	Medium5	Number theoryCombinatorics+1	No attempts yet	1s	1024 MB	Judgeable
TilingCount the ways to tile a 3 by W rectangle with 2 by 1 dominoes, printing the result modulo 1e9+7.	Medium5	Dynamic programmingCombinatorics+2	No attempts yet	2s	512 MB	Judgeable
Birthday CakeGiven up to 50 candle points and up to 15 cuts, decide whether the cuts carve the cake so that every resulting piece holds exactly one candle.	Medium5	GeometryBit manipulation+2	No attempts yet	2s	512 MB	Judgeable
Counting a^i b^j c^k subsequencesCount subsequences of a string of a, b, c that read as some positive number of a's, then b's, then c's, modulo 1e9+7.	Medium5	Dynamic programmingString+1	No attempts yet	2s	512 MB	Judgeable
Xayahh-Rakann at Moloco (Hard)Given n jars with m inseparable pairs, decide whether exactly k jars can be placed in one building so that no inseparable pair is split across the two buildings.	Medium5	GraphUnion-find+2	No attempts yet	2s	512 MB	Judgeable
DunglishGiven a Dutch sentence and per-word dictionary options marked correct or incorrect, output the unique translation and its status, or counts of correct and incorrect translations.	Medium5	ImplementationMath+1	No attempts yet	2s	512 MB	Judgeable
Drain PipesCount the number of ways to pick quantities of each pipe type, within the given stock, so the chosen pipes sum to exactly x.	Medium5	Dynamic programmingArray+2	No attempts yet	1s	128 MB	Judgeable
Uks Is an Apple Fan!!Count the number of paths on an N by M grid where each cell directs movement right, down, or both, and every path must end at cell (N, M).	Medium5	Dynamic programmingCombinatorics+1	No attempts yet	2s	512 MB	Judgeable
1, 2, 3 Sum 5Count the ordered sums of 1, 2, and 3 that add to n, with no equal value adjacent, modulo 1,000,000,009.	Medium5	Dynamic programmingMath+2	No attempts yet	1s	512 MB	Judgeable
1, 2, 3 Addition 7Count ordered compositions of n into exactly m parts, where each part is 1, 2, or 3, modulo 1,000,000,009.	Medium5	Dynamic programmingCombinatorics+2	No attempts yet	0.25s	512 MB	Judgeable
Adding 1, 2, 3 (9)Count ordered compositions of n into parts 1, 2, and 3 that use at most m terms, and output each count modulo 1,000,000,009.	Medium5	Dynamic programmingCombinatorics+2	No attempts yet	1s	512 MB	Judgeable
Magic WeaponCount triples of details, one per color, where the red number's first and last digits match the green's last digit and the blue's first digit, and all three model numbers differ.	Medium5	CombinatoricsMath+2	No attempts yet	2s	512 MB	Judgeable
Building a Symmetric StairGiven n unit cubes, build a symmetric stair (Ferrers diagram symmetric across the diagonal) using all n cubes, or report it is impossible.	Medium5	MathImplementation+2	No attempts yet	3s	512 MB	Judgeable
Making the Number NCount how many digit-by-digit sequences build the number N when each new digit is attached to the left or right end.	Medium5	Dynamic programmingString+2	No attempts yet	1s	256 MB	Judgeable
League of Legends (Large)Count the sequences of skills A (1 second) and B (M seconds) that fill exactly N seconds with no idle time, modulo 1e9+7.	Medium5	Dynamic programmingCombinatorics+1	No attempts yet	3s	256 MB	Judgeable
Tribal WarGiven N tribes where listed pairs are allied and all other pairs are hostile, count the number of triples that are all allied or all hostile.	Medium5	CombinatoricsMath+2	No attempts yet	3s	512 MB	Judgeable
Code WordCount length-l digit sequences on an r by c grid where no two consecutive presses are orthogonally or diagonally adjacent, mod 1e9+7.	Medium5	Dynamic programmingMatrix+2	No attempts yet	1s	512 MB	Judgeable
Summer TripGiven a string of event types, count contiguous substrings of length at least two whose first and last characters are distinct and each appears only once in the substring.	Medium5	StringTwo pointers+2	No attempts yet	3s	1024 MB	Judgeable
Rainbow StringsCount subsequences of a string in which no letter repeats, distinguishing them by position, modulo 11092019.	Medium5	Dynamic programmingMath+2	No attempts yet	1s	512 MB	Judgeable
Managing DifficultiesCount triples of increasing indices i < j < k where a[j] - a[i] equals a[k] - a[j], so a[i] + a[k] = 2*a[j].	Medium5	Hash mapCombinatorics+2	No attempts yet	2s	512 MB	Judgeable
Big ChangesOn N labeled cities, count the spanning trees whose maximum degree is as large as possible, i.e. the star trees.	Medium5	CombinatoricsTree+2	No attempts yet	2s	512 MB	Judgeable
Number Baseball FGuess a secret N-digit number with distinct digits by asking strike/ball queries, for up to 5040 games.	Medium5	Brute forceImplementation+1	No attempts yet	2s	512 MB	Judgeable
Stacking Blocks TogetherEach of N students offers a set of distinct block sizes, at most one block per student is used, and we count subsets of students whose chosen blocks sum to exactly H modulo 10007.	Medium5	Dynamic programmingPrefix sum+2	No attempts yet	1s	256 MB	Judgeable
BinomialGiven a sequence, count ordered pairs (i, j) where the binomial coefficient C(a_i, a_j) is odd, using the Lucas theorem bit condition.	Medium5	CombinatoricsBit manipulation+2	No attempts yet	5s	512 MB	Judgeable
Keep On MovinGiven counts of several character types, split all characters into palindromic strings so that the shortest palindrome is as long as possible.	Medium5	GreedyMath+2	No attempts yet	1s	64 MB	Judgeable
MountainsCount triples x < y < z where the middle mountain y is strictly taller than both mountain x and mountain z.	Medium5	ArrayCombinatorics+2	No attempts yet	2s	256 MB	Judgeable
Mysterious EquationCount ordered pairs of non-negative integers (x, y) with x + y + xy = n, where n can be as large as 10^9.	Medium5	MathNumber theory+2	No attempts yet	2s	512 MB	Judgeable
BarbellsSplit the weights 1 through n into three groups of equal total weight, or report that no such split exists.	Medium5	MathGreedy+2	No attempts yet	2s	512 MB	Judgeable
Decreasing NumberGiven N, find the N-th smallest non-negative integer whose digits strictly decrease from left to right, or output -1 if none exists.	Medium6	CombinatoricsGreedy+2	No attempts yet	1s	512 MB	Judgeable
Park Seongwon's ProbabilityCount permutations of up to 15 numbers whose concatenation is divisible by K, and output the probability as a reduced fraction.	Medium6	Dynamic programmingBit manipulation+2	No attempts yet	2s	128 MB	Judgeable
Card Organization 1Each box lists counts per card color; find the minimum number of box-to-box transfers so at most one mixed box remains and every other color sits in a single box.	Medium6	GreedyImplementation+2	No attempts yet	2s	128 MB	Judgeable
Zigzag LineupCount permutations of N distinct heights where adjacent comparisons strictly alternate, modulo 1,000,000.	Medium6	Dynamic programmingCombinatorics+1	No attempts yet	2s	128 MB	Judgeable
Student ShuffleCount permutations of up to 16 students so that every pair of adjacent heights differs by more than a given value K.	Medium6	Dynamic programmingBit manipulation+2	No attempts yet	2s	128 MB	Judgeable
Code CollectionGiven N possible codes and target K distinct codes, compute the expected number of independent uniform draws needed to collect at least K distinct codes, with N up to 10^18.	Medium6	ProbabilityMath+1	No attempts yet	2s	256 MB	Judgeable
NMKConstruct a permutation of 1..N whose longest increasing subsequence is exactly M and longest decreasing subsequence is exactly K, or report impossible.	Medium6	CombinatoricsGreedy+2	No attempts yet	2s	128 MB	Judgeable
Christmas TreeCount the ways to decorate an N-level tree where level k needs k ornaments split evenly among chosen colors, given limited red, green and blue ornaments.	Medium6	Dynamic programmingCombinatorics+1	No attempts yet	2s	128 MB	Judgeable
Problem AssignmentGiven an N x N matrix of student-problem times, find the minimum-cost perfect matching assigning one distinct problem to each student.	Medium6	Dynamic programmingGraph+2	No attempts yet	5s	128 MB	Judgeable
Restricted PermutationsCount permutations of 1..N where every element differs from its index by at most K, using a bitmask DP over a sliding window.	Medium6	Dynamic programmingBit manipulation+2	No attempts yet	2s	128 MB	Judgeable
TheaterConstruct the longest sequence of distinct nonempty actor subsets where consecutive scenes differ by exactly one actor and the play starts and ends with a single actor.	Medium6	Bit manipulationCombinatorics+2	No attempts yet	2s	128 MB	Judgeable
PokerCompute the exact probability of each of 12 six-card poker hand rankings, including custom back straight and royal straight flush definitions, as reduced fractions.	Medium6	CombinatoricsBrute force+2	No attempts yet	2s	128 MB	Judgeable
Guitar ChordGiven each guitar string's open note and a target chord, choose which chord note each string plays to minimize the pressed-fret range needed to cover all chord notes.	Medium6	MathGreedy+2	No attempts yet	2s	128 MB	Judgeable
CandyGiven candy prices, count the distinct ways to pick a multiset of candies whose price sum is a prime number.	Medium6	Dynamic programmingNumber theory+2	No attempts yet	2s	128 MB	Judgeable
Counting Divisible NumbersCount integers in a range that are divisible by at least one element of a given array using inclusion-exclusion over subsets and LCM.	Medium6	CombinatoricsMath+2	No attempts yet	2s	128 MB	Judgeable
Anti-PalindromeRearrange all characters of a string to form the lexicographically smallest anti-palindrome, where each pair of symmetric positions must differ, or report impossible.	Medium6	GreedyString+2	No attempts yet	2s	128 MB	Judgeable
Making PrimesCombine all N (up to 6) given numbers with +,-,*,/ and parentheses in every possible way to find the smallest and largest prime value obtainable.	Medium6	BacktrackingBrute force+2	No attempts yet	2s	128 MB	Judgeable
Tree EncodingGiven N and an index, find the k-th lexicographically smallest preorder traversal string among all binary search trees built from the first N letters, using Catalan number counting.	Medium6	CombinatoricsMath+2	No attempts yet	2s	128 MB	Judgeable
Sequences of 1 and -1Given M sequences of 1 and -1 of even length N, construct for each one a partner sequence whose elementwise product sums to zero, using at most N distinct partner sequences overall.	Medium6	CombinatoricsPrefix sum+2	No attempts yet	2s	128 MB	Judgeable
Tiling a GridCount the ways to fully tile an N by M grid (N, M up to 14) with 2x1 dominoes, modulo 9901.	Medium6	Dynamic programmingBit manipulation+2	No attempts yet	2s	128 MB	Judgeable
Resident Registration NumberGiven a 19-digit ID pattern with some digits erased, count completions that form a valid birth date and satisfy the modular checksum rule for the last digit.	Medium6	CombinatoricsMath+2	No attempts yet	2s	128 MB	Judgeable
Tile CodesCount distinct tilings of a 2xN board using 1x2, 2x1, and 2x2 tiles, where mirror-image tilings under left-right flip count as one.	Medium6	Dynamic programmingCombinatorics+1	No attempts yet	2s	128 MB	Judgeable
Count Selections with GCD 1Given up to 50 integers, count non-empty subsets whose greatest common divisor equals 1, modulo 10,000,003.	Medium6	Number theoryCombinatorics+1	No attempts yet	2s	128 MB	Judgeable
Mirror NumbersCount how many numbers between A and B (up to 10^18) read the same when reflected in a mirror, using only digits 0,1,2,5,8 with 2 and 5 swapped.	Medium6	CombinatoricsString+2	No attempts yet	1s	64 MB	Judgeable
Counting Ordered Pairs with a Given GCDCount ordered pairs (x, y) with x <= a, y <= b and gcd(x, y) = d for up to 50,000 queries.	Medium6	Number theoryMath+1	No attempts yet	2s	128 MB	Judgeable
Making a RectangleGiven up to 16 sticks, choose four disjoint groups forming two equal-length pairs of sides to maximize the rectangle's area, or return -1 if impossible.	Medium6	Bit manipulationDynamic programming+2	No attempts yet	2s	256 MB	Judgeable
Partitioning for Fun and ProfitGiven m, n and k, output the k-th lexicographically smallest partition of m into n non-decreasing positive parts.	Medium6	CombinatoricsDynamic programming+2	No attempts yet	2s	128 MB	Judgeable
Counting Full Binary TreesCount full binary trees with exactly n nodes and height exactly k, modulo 9901, using a height-bounded DP and subtraction trick.	Medium6	Dynamic programmingTree+2	No attempts yet	2s	128 MB	Judgeable
Cow PizzaCount subsets of up to 20 toppings that avoid containing every topping of any given forbidden constraint set, using inclusion-exclusion or bitmask enumeration.	Medium6	Bit manipulationCombinatorics+1	No attempts yet	2s	128 MB	Judgeable
Rock-Paper-ScissorsCompute, as a reduced fraction, the probability that Hangseung reaches K round wins before Dongju in at most N rounds of rock-paper-scissors with ties possible.	Medium6	Dynamic programmingProbability+1	No attempts yet	2s	128 MB	Judgeable
Trailing Zeros in a CombinationCompute the count of trailing zeros in C(n, m) for n up to 2 billion using prime factor exponents of 2 and 5 via Legendre's formula.	Medium6	Number theoryMath+1	No attempts yet	2s	128 MB	Judgeable
Counting Grid TrianglesCount triangles with positive area formed by choosing three distinct lattice points from an (N+1) by (M+1) grid.	Medium6	CombinatoricsMath+1	No attempts yet	2s	128 MB	Judgeable
Baby Goat LineupGiven binary labels A through B, find the X-th label when ordered first by popcount then by numeric value.	Medium6	CombinatoricsBit manipulation+1	No attempts yet	2s	128 MB	Judgeable
Degree SequenceGiven a target degree sequence for N vertices, construct any simple graph's adjacency matrix matching it exactly, or report impossibility.	Medium6	GreedyGraph+2	No attempts yet	2s	128 MB	Judgeable
Number of MultisetsGiven multiplicities of values from 1 to T among A numbers, count multisets of size K for S≤K≤B modulo 1,000,000.	Medium6	Dynamic programmingCombinatorics+1	No attempts yet	2s	128 MB	Judgeable
Cactus GraphGiven a graph described by edge-paths, verify it is a cactus and count connected spanning subgraphs that remain cactus graphs.	Medium6	GraphDFS+1	No attempts yet	2s	128 MB	Judgeable
Find the K-th Pinary NumberGiven K up to 10^18, output the K-th smallest binary string with no leading zero and no two consecutive 1s, treated as a number by value order.	Medium6	Dynamic programmingCombinatorics+1	No attempts yet	2s	128 MB	Judgeable
Circular NetworkGiven a cycle of N nodes and P path requests, choose a direction for each request to minimize the total number of distinct cycle edges converted.	Medium6	GreedyBit manipulation+1	No attempts yet	2s	128 MB	Judgeable