Given a range [L, R] where 0 ≤ L ≤ R ≤ 108. The task is to find the count of integers from the given range that can be represented as (2x) * (3y).
Input: L = 1, R = 10
The numbers are 1, 2, 3, 4, 6, 8 and 9
Input: L = 100, R = 200
The numbers are 108, 128, 144, 162 and 192
Approach: Since the numbers, which are powers of two and three, quickly grow, you can use the following algorithm. For all the numbers of the form (2x) * (3y) in the range [1, 108] store them in a vector. Later sort the vector. Then the required answer can be calculated using an upper bound. Pre-calculating these integers will be helpful when there are a number of queries of the form [L, R].
Below is the implementation of the above approach:
- Ways to form an array having integers in given range such that total sum is divisible by 2
- Count integers in the range [A, B] that are not divisible by C and D
- Count integers in a range which are divisible by their euler totient value
- Queries to count integers in a range [L, R] such that their digit sum is prime and divisible by K
- Count of integers in a range which have even number of odd digits and odd number of even digits
- Represent (2 / N) as the sum of three distinct positive integers of the form (1 / m)
- Most frequent factor in a range of integers
- Given an array and two integers l and r, find the kth largest element in the range [l, r]
- Integers from the range that are composed of a single distinct digit
- Count of integers of length N and value less than K such that they contain digits only from the given set
- Count of m digit integers that are divisible by an integer n
- Count number of integers less than or equal to N which has exactly 9 divisors
- Count of integers that divide all the elements of the given array
- Count ways to express even number ‘n’ as sum of even integers
- Count of all possible pairs of disjoint subsets of integers from 1 to N
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