Package g2301_2400.s2338_count_the_number_of_ideal_arrays

Class Solution

  • public class Solution
extends 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 Detail

      • Solution

        public Solution()

    • Method Detail

      • idealArrays

        public int idealArrays​(int n,
                       int maxValue)