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 Object

2338 - Count the Number of Ideal Arrays.<p>Hard</p> <p>You are given two integers <code>n</code> and <code>maxValue</code>, which are used to describe an <strong>ideal</strong> array.</p> <p>A <strong>0-indexed</strong> integer array <code>arr</code> of length <code>n</code> is considered <strong>ideal</strong> if the following conditions hold:</p> <ul> <li>Every <code>arr[i]</code> is a value from <code>1</code> to <code>maxValue</code>, for <code>0 <= i < n</code>.</li> <li>Every <code>arr[i]</code> is divisible by <code>arr[i - 1]</code>, for <code>0 < i < n</code>.</li> </ul> <p>Return <em>the number of <strong>distinct</strong> ideal arrays of length</em> <code>n</code>. Since the answer may be very large, return it modulo <code>10⁹ + 7</code>.</p> <p><strong>Example 1:</strong></p> <p><strong>Input:</strong> n = 2, maxValue = 5</p> <p><strong>Output:</strong> 10</p> <p><strong>Explanation:</strong> The following are the possible ideal arrays:</p> <ul> <li> <p>Arrays starting with the value 1 (5 arrays): [1,1], [1,2], [1,3], [1,4], [1,5]</p> </li> <li> <p>Arrays starting with the value 2 (2 arrays): [2,2], [2,4]</p> </li> <li> <p>Arrays starting with the value 3 (1 array): [3,3]</p> </li> <li> <p>Arrays starting with the value 4 (1 array): [4,4]</p> </li> <li> <p>Arrays starting with the value 5 (1 array): [5,5]</p> </li> </ul> <p>There are a total of 5 + 2 + 1 + 1 + 1 = 10 distinct ideal arrays.</p> <p><strong>Example 2:</strong></p> <p><strong>Input:</strong> n = 5, maxValue = 3</p> <p><strong>Output:</strong> 11</p> <p><strong>Explanation:</strong> The following are the possible ideal arrays:</p> <ul> <li> <p>Arrays starting with the value 1 (9 arrays):</p> <ul> <li> <p>With no other distinct values (1 array): [1,1,1,1,1]</p> </li> <li> <p>With 2^nd 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]</p> </li> <li> <p>With 2^nd 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]</p> </li> </ul> </li> <li> <p>Arrays starting with the value 2 (1 array): [2,2,2,2,2]</p> </li> <li> <p>Arrays starting with the value 3 (1 array): [3,3,3,3,3]</p> </li> </ul> <p>There are a total of 9 + 1 + 1 = 11 distinct ideal arrays.</p> <p><strong>Constraints:</strong></p> <ul> <li><code>2 <= n <= 10⁴</code></li> <li><code>1 <= maxValue <= 10⁴</code></li> </ul>

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)