combinatorics

Unique Paths

Calculate the number of unique paths for a robot to move on an m x n grid with only right and down movements.

Poor Pigs

Find the minimum number of pigs required to determine the poisonous bucket within a set time using state transition dyna…

Number of Music Playlists

Solve the Number of Music Playlists problem with dynamic programming, focusing on state transitions and combinatorics to…

Ugly Number III

Find the nth positive integer divisible by a, b, or c using binary search over the answer space efficiently and accurate…

Count All Valid Pickup and Delivery Options

Count all valid pickup and delivery sequences for n orders where deliveries occur after pickups using dynamic programmin…

Probability of a Two Boxes Having The Same Number of Distinct Balls

Compute the probability that two boxes contain the same number of distinct balls using careful combinatorial and DP meth…

Number of Ways to Reorder Array to Get Same BST

Determine the number of ways to reorder an array to get the same binary search tree (BST) from its insertion order.

Number of Sets of K Non-Overlapping Line Segments

Count all valid arrangements of k non-overlapping line segments on n points using state transition dynamic programming.

Count Sorted Vowel Strings

Calculate the number of length-n strings with vowels only that are sorted lexicographically using state transitions.

Kth Smallest Instructions

Find the kth smallest lexicographic instruction sequence for reaching a destination in a grid using state transition dyn…

Count Ways to Make Array With Product

Determine the number of arrays of size n where the product equals k using prime factorization and combinatorial DP techn…

Minimum Number of Operations to Make String Sorted

Calculate the minimum operations to sort a string using combinatorial math and string manipulation techniques efficientl…

Sum of All Subset XOR Totals

Compute the sum of all subset XOR totals using a backtracking search with pruning for arrays of small size.

Number of Ways to Rearrange Sticks With K Sticks Visible

Calculate the number of arrangements of n uniquely-sized sticks so exactly k sticks are visible using dynamic programmin…

Count Ways to Build Rooms in an Ant Colony

Solve the problem of counting distinct ways to build rooms in an ant colony using dynamic programming and topological or…

Vowels of All Substrings

Compute the total number of vowels in all substrings of a given string using efficient state transition dynamic programm…

Find Triangular Sum of an Array

The problem asks for calculating the triangular sum of an array through repeated pairwise summation.

Count the Number of Ideal Arrays

This problem involves counting the number of ideal arrays of a given length under certain conditions using state transit…

Number of Ways to Reach a Position After Exactly k Steps

Find the number of ways to reach a position after exactly k steps on an infinite number line using dynamic programming.

Count Anagrams

Learn to count distinct anagrams for a multi-word string using hash tables, math, and combinatorics efficiently.

The Number of Beautiful Subsets

Count all non-empty subsets of an array where no two numbers have an absolute difference equal to k, using array scannin…

Count K-Subsequences of a String With Maximum Beauty

Determine the number of k-length unique subsequences in a string that maximize the sum of character frequencies efficien…

Distribute Candies Among Children I

Given two integers n and limit, find the number of ways to distribute n candies among 3 children, with no child receivin…

Distribute Candies Among Children II

Determine how to distribute n candies among 3 children without exceeding a limit on individual candies.