# [Solution] Count the Number of Ideal Arrays solution leetcode

Count the Number of Ideal Arrays solution leetcode – You are given two integers `n` and `maxValue`, which are used to describe an ideal array.

## [Solution] Count the Number of Ideal Arrays solution leetcode

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`.

## [Solution] Count the Number of Ideal Arrays solution leetcode

```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.
```

## [Solution] Count the Number of Ideal Arrays solution leetcode

```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`