number theory

Count Primes

Count all prime numbers less than a given integer n using efficient array and math-based enumeration techniques.

Add Digits

Add Digits involves repeatedly summing digits of a number until a single digit is obtained.

Mirror Reflection

Given a square room with mirrors, find which receptor a laser ray will hit first based on two integers, p and q.

Prime Palindrome

The Prime Palindrome problem asks for the smallest prime palindrome greater than or equal to a given integer.

X of a Kind in a Deck of Cards

Solve the problem of determining if a deck can be partitioned into groups with equal occurrences of card values.

Largest Component Size by Common Factor

Find the largest connected component in an array where edges exist between numbers sharing a common factor greater than …

Ugly Number III

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

Check If It Is a Good Array

Determine if a given array of positive integers can generate 1 using integer multiples of any subset, leveraging number …

Simplified Fractions

Generate simplified fractions between 0 and 1 with denominators up to a given integer n.

The kth Factor of n

Find the kth factor of n by scanning divisors carefully or using factor pairs to skip unnecessary checks.

Graph Connectivity With Threshold

In 'Graph Connectivity With Threshold,' determine if cities are connected based on common divisors exceeding a threshold…

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…

Tree of Coprimes

Determine the closest coprime ancestor for each node in a tree using efficient traversal and state tracking of node valu…

Maximize Score After N Operations

Maximize the score after n operations by selecting pairs from the array and using their GCD with dynamic programming or …

Maximize Number of Nice Divisors

Solve Maximize Number of Nice Divisors by splitting primeFactors into mostly 3s and using fast modular exponentiation.

Number of Different Subsequences GCDs

Given an array of positive integers, find the number of different subsequences' GCDs.

Three Divisors

Determine if a given integer has exactly three positive divisors.

Find Greatest Common Divisor of Array

Find the greatest common divisor of the smallest and largest numbers in an integer array.

The Number of Good Subsets

Find the number of good subsets in an integer array, where each subset's product is the product of distinct primes.

GCD Sort of an Array

The GCD Sort problem challenges you to sort an array using a specific gcd-based swap method.

Number of Pairs of Interchangeable Rectangles

Count all pairs of rectangles that share the exact width-to-height ratio using efficient array scanning and hash lookup.

Count Array Pairs Divisible by K

Count Array Pairs Divisible by K requires counting index pairs whose products are divisible by a given number k.

Replace Non-Coprime Numbers in Array

Replace Non-Coprime Numbers in Array uses stack-based state management to iteratively merge adjacent non-coprime integer…

Minimum Lines to Represent a Line Chart

Determine the fewest lines needed to accurately connect stock price points in a line chart using array and math reasonin…