maximum-and-minimum-sums-of-at-most-size-k-subarrays

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Algorithms

You are given an integer array <code>nums</code> and a positive integer <code>k</code>. Return the sum of the maximum and minimum elements of all subarrays with at most <code>k</code> elements.

&nbsp;
Example 1:

<div class="example-block">
Input: nums = [1,2,3], k = 2

Output: 20

Explanation:

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

<table style="border: 1px solid black;">
	<tbody>
		<tr>
			<th style="border: 1px solid black;">Subarray</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;">Final Total</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>

The output would be 20.
</div>

Example 2:

<div class="example-block">
Input: nums = [1,-3,1], k = 2

Output: -6

Explanation:

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

<table style="border: 1px solid black;">
	<tbody>
		<tr>
			<th style="border: 1px solid black;">Subarray</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;">Final Total</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>

The output would be -6.
</div>

&nbsp;
Constraints:

<ul>
	<li><code>1 &lt;= nums.length &lt;= 80000</code></li>
	<li><code>1 &lt;= k &lt;= nums.length</code></li>
	<li><code>-106 &lt;= nums[i] &lt;= 106</code></li>
</ul>

Subarray	Minimum	Maximum	Sum
`[1]`	1	1	2
`[2]`	2	2	4
`[3]`	3	3	6
`[1, 2]`	1	2	3
`[2, 3]`	2	3	5
Final Total			20