leetcode-problemset/leetcode-cn/problem (English)/最多 K 个元素的子数组的最值之和(English) [maximum-and-minimum-sums-of-at-most-size-k-subarrays].html

<p>You are given an integer array <code>nums</code> and a <strong>positive</strong> integer <code>k</code>. Return the sum of the <strong>maximum</strong> and <strong>minimum</strong> elements of all <span data-keyword="subarray-nonempty">subarrays</span> with <strong>at most</strong> <code>k</code> elements.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<div class="example-block">
<p><strong>Input:</strong> <span class="example-io">nums = [1,2,3], k = 2</span></p>

<p><strong>Output:</strong> <span class="example-io">20</span></p>

<p><strong>Explanation:</strong></p>

<p>The subarrays of <code>nums</code> with at most 2 elements are:</p>

<table style="border: 1px solid black;">
	<tbody>
		<tr>
			<th style="border: 1px solid black;"><b>Subarray</b></th>
			<th style="border: 1px solid black;">Minimum</th>
			<th style="border: 1px solid black;">Maximum</th>
			<th style="border: 1px solid black;">Sum</th>
		</tr>
		<tr>
			<td style="border: 1px solid black;"><code>[1]</code></td>
			<td style="border: 1px solid black;">1</td>
			<td style="border: 1px solid black;">1</td>
			<td style="border: 1px solid black;">2</td>
		</tr>
		<tr>
			<td style="border: 1px solid black;"><code>[2]</code></td>
			<td style="border: 1px solid black;">2</td>
			<td style="border: 1px solid black;">2</td>
			<td style="border: 1px solid black;">4</td>
		</tr>
		<tr>
			<td style="border: 1px solid black;"><code>[3]</code></td>
			<td style="border: 1px solid black;">3</td>
			<td style="border: 1px solid black;">3</td>
			<td style="border: 1px solid black;">6</td>
		</tr>
		<tr>
			<td style="border: 1px solid black;"><code>[1, 2]</code></td>
			<td style="border: 1px solid black;">1</td>
			<td style="border: 1px solid black;">2</td>
			<td style="border: 1px solid black;">3</td>
		</tr>
		<tr>
			<td style="border: 1px solid black;"><code>[2, 3]</code></td>
			<td style="border: 1px solid black;">2</td>
			<td style="border: 1px solid black;">3</td>
			<td style="border: 1px solid black;">5</td>
		</tr>
		<tr>
			<td style="border: 1px solid black;"><strong>Final Total</strong></td>
			<td style="border: 1px solid black;">&nbsp;</td>
			<td style="border: 1px solid black;">&nbsp;</td>
			<td style="border: 1px solid black;">20</td>
		</tr>
	</tbody>
</table>

<p>The output would be 20.</p>
</div>

<p><strong class="example">Example 2:</strong></p>

<div class="example-block">
<p><strong>Input:</strong> <span class="example-io">nums = [1,-3,1], k = 2</span></p>

<p><strong>Output:</strong> <span class="example-io">-6</span></p>

<p><strong>Explanation:</strong></p>

<p>The subarrays of <code>nums</code> with at most 2 elements are:</p>

<table style="border: 1px solid black;">
	<tbody>
		<tr>
			<th style="border: 1px solid black;"><b>Subarray</b></th>
			<th style="border: 1px solid black;">Minimum</th>
			<th style="border: 1px solid black;">Maximum</th>
			<th style="border: 1px solid black;">Sum</th>
		</tr>
		<tr>
			<td style="border: 1px solid black;"><code>[1]</code></td>
			<td style="border: 1px solid black;">1</td>
			<td style="border: 1px solid black;">1</td>
			<td style="border: 1px solid black;">2</td>
		</tr>
		<tr>
			<td style="border: 1px solid black;"><code>[-3]</code></td>
			<td style="border: 1px solid black;">-3</td>
			<td style="border: 1px solid black;">-3</td>
			<td style="border: 1px solid black;">-6</td>
		</tr>
		<tr>
			<td style="border: 1px solid black;"><code>[1]</code></td>
			<td style="border: 1px solid black;">1</td>
			<td style="border: 1px solid black;">1</td>
			<td style="border: 1px solid black;">2</td>
		</tr>
		<tr>
			<td style="border: 1px solid black;"><code>[1, -3]</code></td>
			<td style="border: 1px solid black;">-3</td>
			<td style="border: 1px solid black;">1</td>
			<td style="border: 1px solid black;">-2</td>
		</tr>
		<tr>
			<td style="border: 1px solid black;"><code>[-3, 1]</code></td>
			<td style="border: 1px solid black;">-3</td>
			<td style="border: 1px solid black;">1</td>
			<td style="border: 1px solid black;">-2</td>
		</tr>
		<tr>
			<td style="border: 1px solid black;"><strong>Final Total</strong></td>
			<td style="border: 1px solid black;">&nbsp;</td>
			<td style="border: 1px solid black;">&nbsp;</td>
			<td style="border: 1px solid black;">-6</td>
		</tr>
	</tbody>
</table>

<p>The output would be -6.</p>
</div>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= nums.length &lt;= 80000</code></li>
	<li><code>1 &lt;= k &lt;= nums.length</code></li>
	<li><code>-10<sup>6</sup> &lt;= nums[i] &lt;= 10<sup>6</sup></code></li>
</ul>