Package g2301_2400.s2338_count_the_number_of_ideal_arrays

Class Solution

java.lang.Object
g2301_2400.s2338_count_the_number_of_ideal_arrays.Solution
public class Solution extends java.lang.Object
2338 - Count the Number of Ideal Arrays.

Hard

You are given two integers n and maxValue, which are used to describe an ideal array.

A 0-indexed integer array arr of length n is considered ideal if the following conditions hold:

  • Every arr[i] is a value from 1 to maxValue, for 0 <= i < n.
  • Every arr[i] is divisible by arr[i - 1], for 0 < i < n.

Return the number of distinct ideal arrays of length n. Since the answer may be very large, return it modulo 109 + 7.

Example 1:

Input: n = 2, maxValue = 5

Output: 10

Explanation: The following are the possible ideal arrays:

  • Arrays starting with the value 1 (5 arrays): [1,1], [1,2], [1,3], [1,4], [1,5]

  • Arrays starting with the value 2 (2 arrays): [2,2], [2,4]

  • Arrays starting with the value 3 (1 array): [3,3]

  • Arrays starting with the value 4 (1 array): [4,4]

  • Arrays starting with the value 5 (1 array): [5,5]

There are a total of 5 + 2 + 1 + 1 + 1 = 10 distinct ideal arrays.

Example 2:

Input: n = 5, maxValue = 3

Output: 11

Explanation: The following are the possible ideal arrays:

  • Arrays starting with the value 1 (9 arrays):

    • With no other distinct values (1 array): [1,1,1,1,1]

    • With 2nd distinct value 2 (4 arrays): [1,1,1,1,2], [1,1,1,2,2], [1,1,2,2,2], [1,2,2,2,2]

    • With 2nd distinct value 3 (4 arrays): [1,1,1,1,3], [1,1,1,3,3], [1,1,3,3,3], [1,3,3,3,3]

  • Arrays starting with the value 2 (1 array): [2,2,2,2,2]

  • Arrays starting with the value 3 (1 array): [3,3,3,3,3]

There are a total of 9 + 1 + 1 = 11 distinct ideal arrays.

Constraints:

  • 2 <= n <= 104
  • 1 <= maxValue <= 104

  • Constructor Summary

    Constructors
    Constructor
    Description
    Solution()
     

  • Method Summary

    Modifier and Type
    Method
    Description
    int
    idealArrays(int n, int maxValue)
     

    Methods inherited from class java.lang.Object

    clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

  • Constructor Details

    • Solution

      public Solution()

  • Method Details

    • idealArrays

      public int idealArrays(int n, int maxValue)