mirror of
https://gitee.com/coder-xiaomo/leetcode-problemset
synced 2025-11-04 03:33:12 +08:00
36 lines
1.6 KiB
HTML
36 lines
1.6 KiB
HTML
<p>Given two <strong>positive</strong> integers <code>n</code> and <code>x</code>.</p>
|
|
|
|
<p>Return <em>the number of ways </em><code>n</code><em> can be expressed as the sum of the </em><code>x<sup>th</sup></code><em> power of <strong>unique</strong> positive integers, in other words, the number of sets of unique integers </em><code>[n<sub>1</sub>, n<sub>2</sub>, ..., n<sub>k</sub>]</code><em> where </em><code>n = n<sub>1</sub><sup>x</sup> + n<sub>2</sub><sup>x</sup> + ... + n<sub>k</sub><sup>x</sup></code><em>.</em></p>
|
|
|
|
<p>Since the result can be very large, return it modulo <code>10<sup>9</sup> + 7</code>.</p>
|
|
|
|
<p>For example, if <code>n = 160</code> and <code>x = 3</code>, one way to express <code>n</code> is <code>n = 2<sup>3</sup> + 3<sup>3</sup> + 5<sup>3</sup></code>.</p>
|
|
|
|
<p> </p>
|
|
<p><strong class="example">Example 1:</strong></p>
|
|
|
|
<pre>
|
|
<strong>Input:</strong> n = 10, x = 2
|
|
<strong>Output:</strong> 1
|
|
<strong>Explanation:</strong> We can express n as the following: n = 3<sup>2</sup> + 1<sup>2</sup> = 10.
|
|
It can be shown that it is the only way to express 10 as the sum of the 2<sup>nd</sup> power of unique integers.
|
|
</pre>
|
|
|
|
<p><strong class="example">Example 2:</strong></p>
|
|
|
|
<pre>
|
|
<strong>Input:</strong> n = 4, x = 1
|
|
<strong>Output:</strong> 2
|
|
<strong>Explanation:</strong> We can express n in the following ways:
|
|
- n = 4<sup>1</sup> = 4.
|
|
- n = 3<sup>1</sup> + 1<sup>1</sup> = 4.
|
|
</pre>
|
|
|
|
<p> </p>
|
|
<p><strong>Constraints:</strong></p>
|
|
|
|
<ul>
|
|
<li><code>1 <= n <= 300</code></li>
|
|
<li><code>1 <= x <= 5</code></li>
|
|
</ul>
|