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<p>Given an array <em>task_memory</em> of <em>n</em> positive integers representing the amount of memory required to process each task, an array <em>task_type</em> of <em>n</em> positive integers representing the type of each task, and an integer <em>max_memory</em>, find the minimum amount of time required for the server to process all the tasks.</p>

<p>&nbsp;</p>

<p>Each task takes 1 unit of time to process. The server can process at most two tasks in parallel only if they are of the same type and together require no more than <em>max_memory</em> units of memory.</p>

<p>&nbsp;</p>

<p><strong>Example</strong></p>

<p>Suppose <em>n</em> = 4, <em>task_memory</em> = [7, 2, 3, 9], <em>task_type</em> = [1, 2, 1, 3], and <em>max_memory</em> = 10.</p>

<p>&nbsp;</p>

<p>One efficient schedule is shown.</p>

<table>
	<thead>
		<tr>
			<th>Task Pair</th>
			<th>Task 1</th>
			<th>Task 2</th>
			<th>Task Type</th>
			<th>Memory Requirement</th>
			<th>Within Max Memory</th>
			<th>Can Process in Parallel</th>
		</tr>
	</thead>
	<tbody>
		<tr>
			<td>1</td>
			<td>0</td>
			<td>2</td>
			<td>Same</td>
			<td>7 + 3 = 10</td>
			<td>Yes</td>
			<td>Yes</td>
		</tr>
		<tr>
			<td>2</td>
			<td>1</td>
			<td>3</td>
			<td>Different</td>
			<td>9 + 2 = 11</td>
			<td>No</td>
			<td>No</td>
		</tr>
	</tbody>
</table>

<p>&nbsp;</p>

<p>Tasks 0 and 2 are processed concurrently, but the other two must be processed separately due to their memory requirements and because they are not the same type. The minimum amount of time required to process all the tasks is 3 units.</p>
&nbsp;

<p class="section-title">Function Description</p>

<p>Complete the function <em>getMinTime</em> in the editor below.</p>

<p>&nbsp;</p>

<p><em>getMinTime</em> has the following parameter(s):</p>

<p>&nbsp;&nbsp;&nbsp;&nbsp;<em>int task_memory[n]:</em> the memory required by the tasks</p>

<p>&nbsp;&nbsp;&nbsp;&nbsp;<em>int task_type[n]:</em> the type of the tasks</p>

<p>&nbsp;&nbsp;&nbsp;&nbsp;<em>int max_memory:</em> the maximum total memory that can be allocated to the tasks</p>

<p>&nbsp;</p>

<p><strong>Returns</strong></p>

<p>&nbsp;&nbsp;&nbsp;&nbsp;<em>int:</em> the minimum time required to process all tasks</p>

<p>&nbsp;</p>

<p class="section-title">Constraints</p>

<ul>
	<li>1 ≤&nbsp;<em>n</em>&nbsp;≤ 2*10<sup>5</sup>
</li>
	<li>1 ≤&nbsp;<em>max_memory</em>&nbsp;≤ 10<sup>9</sup>
</li>
	<li>1 ≤&nbsp;<em>task_memory[i]</em>&nbsp;≤&nbsp;<em>max_memory</em>
</li>
	<li>1 ≤&nbsp;<em>task_type[i]</em>&nbsp;≤ 10<sup>9</sup>
</li>
</ul>

<p>&nbsp;</p>
<!-- <StartOfInputFormat> DO NOT REMOVE THIS LINE-->

<details open=""><summary class="section-title">Input Format For Custom Testing</summary>

<div class="collapsable-details">
<p>The first line contains an integer, <em>n</em>, the number of elements in <em>task_memory</em>.</p>

<p>The following <em>n</em> lines contain an integer, <em>task_memory[i]</em>.</p>

<p>The next line contains an integer, <em>n</em>, the number of elements in <em>task_type</em>.</p>

<p>The following <em>n</em> lines contain an integer, <em>task_type[i]</em>.</p>

<p>The last line contains an integer, <em>max_memory</em>.</p>
</div>
</details>
<!-- </StartOfInputFormat> DO NOT REMOVE THIS LINE-->

<details open=""><summary class="section-title">Sample Case 0</summary>

<div class="collapsable-details">
<p class="section-title">Sample Input For Custom Testing</p>

<pre>STDIN          FUNCTION
-----          --------
5        →     n = 5
1        →     task_memory = [1, 2, 3, 4, 2]
2
3
4
2
5        →     n = 5
1        →     <em>task_type</em> = [1, 2, 1, 2, 3]
2
1
2
3
4        →     max_memory = 4</pre>

<p class="section-title">Sample Output</p>

<pre>4</pre>

<p class="section-title">Explanation</p>

<p>The first and the third tasks are processed in parallel. The other three tasks need to be processed individually. The second and fourth use too much memory together, and the fifth is a unique type.</p>
</div>
</details>

<details open=""><summary class="section-title">Sample Case 1</summary>

<div class="collapsable-details">
<p class="section-title">Sample Input For Custom Testing</p>

<pre>STDIN          FUNCTION
-----          --------
3        →     n = 3
1        →     task_memory = [1, 2, 5]
2
5
3        →     n = 3
1        →     type = [1, 2, 3]
2
3
6        →     max_memory = 6</pre>

<p class="section-title">Sample Output</p>

<pre>3</pre>

<p class="section-title">Explanation</p>

<p>All the tasks are of different types and must be processed separately.&nbsp;</p>
</div>
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