count-ways-to-make-array-with-product

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Algorithms

You are given a 2D integer array, <code>queries</code>. For each <code>queries[i]</code>, where <code>queries[i] = [ni, ki]</code>, find the number of different ways you can place positive integers into an array of size <code>ni</code> such that the product of the integers is <code>ki</code>. As the number of ways may be too large, the answer to the <code>ith</code> query is the number of ways modulo <code>109 + 7</code>.

Return an integer array <code>answer</code> where <code>answer.length == queries.length</code>, and <code>answer[i]</code> is the answer to the <code>ith</code> query.

&nbsp;
Example 1:

<pre>
Input: queries = [[2,6],[5,1],[73,660]]
Output: [4,1,50734910]
Explanation:&nbsp;Each query is independent.
[2,6]: There are 4 ways to fill an array of size 2 that multiply to 6: [1,6], [2,3], [3,2], [6,1].
[5,1]: There is 1 way to fill an array of size 5 that multiply to 1: [1,1,1,1,1].
[73,660]: There are 1050734917 ways to fill an array of size 73 that multiply to 660. 1050734917 modulo 109 + 7 = 50734910.
</pre>

Example 2:

<pre>
Input: queries = [[1,1],[2,2],[3,3],[4,4],[5,5]]
Output: [1,2,3,10,5]
</pre>

&nbsp;
Constraints:

<ul>
	<li><code>1 &lt;= queries.length &lt;= 104 </code></li>
	<li><code>1 &lt;= ni, ki &lt;= 104</code></li>
</ul>

waysToFillArray

Count Ways to Make Array With Product

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count-the-number-of-ideal-arrays

统计理想数组的数目

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smallest-value-after-replacing-with-sum-of-prime-factors

使用质因数之和替换后可以取到的最小值

Closest Prime Numbers in Range

closest-prime-numbers-in-range

范围内最接近的两个质数

Array

Math

Dynamic Programming

Combinatorics

Number Theory

给你一个二维整数数组 <code>queries</code> ，其中 <code>queries[i] = [ni, ki]</code> 。第 <code>i</code> 个查询 <code>queries[i]</code> 要求构造长度为 <code>ni</code> 、每个元素都是正整数的数组，且满足所有元素的乘积为 <code>ki</code> ，请你找出有多少种可行的方案。由于答案可能会很大，方案数需要对 <code>109 + 7</code> 取余 。

请你返回一个整数数组 <code>answer</code>，满足 <code>answer.length == queries.length</code> ，其中 <code>answer[i]</code>是第 <code>i</code> 个查询的结果。

 

示例 1：

<pre>
输入：queries = [[2,6],[5,1],[73,660]]
输出：[4,1,50734910]
解释：每个查询之间彼此独立。
[2,6]：总共有 4 种方案得到长度为 2 且乘积为 6 的数组：[1,6]，[2,3]，[3,2]，[6,1]。
[5,1]：总共有 1 种方案得到长度为 5 且乘积为 1 的数组：[1,1,1,1,1]。
[73,660]：总共有 1050734917 种方案得到长度为 73 且乘积为 660 的数组。1050734917 对 109 + 7 取余得到 50734910 。
</pre>

示例 2 ：

<pre>
输入：queries = [[1,1],[2,2],[3,3],[4,4],[5,5]]
输出：[1,2,3,10,5]
</pre>

 

提示：

<ul>
	<li><code>1 <= queries.length <= 104 </code></li>
	<li><code>1 <= ni, ki <= 104</code></li>
</ul>