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<div id="main-splitpane-left" class="coding-question__left-pane"><section class="question-view__title-wrapper"><h1 class="question-view__title">4. Maximizing Task Priority</h1></section><section class="question-view__instruction"><div class="candidate-rich-text"><div id="2mbl80d86og-instruction"><style type="text/css">.ps-content-wrapper-v0 div { margin: 0 auto; overflow: auto; } .ps-content-wrapper-v0 div.preheader { display: none; } .ps-content-wrapper-v0 p { white-space: pre-wrap; padding-left: 4px; padding-right: 4px; padding-top: 0px; padding-bottom: 2px; } .ps-content-wrapper-v0 p.section-title { font-weight: bold; padding-bottom: 0px; } .ps-content-wrapper-v0 ol.plain-list, .ps-content-wrapper-v0 ul.plain-list { list-style-type: none; padding: 4px; } .ps-content-wrapper-v0 li { white-space: normal; margin-top: 4px; margin-bottom: 4px; } .ps-content-wrapper-v0 code { color: black; } .ps-content-wrapper-v0 pre { background-color: #f4faff; border: 0; border-radius: 2px; margin: 8px; padding: 10px; } .ps-content-wrapper-v0 pre.scrollable-full-json { overflow-x: scroll; white-space: pre; } .ps-content-wrapper-v0 pre.scrollable-json { height: 300px; 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</style>
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<div class="ps-content-wrapper-v0">
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<p>ByteDance is working on a new algorithm that operates on a special CPU that can handle <em>n</em> types of tasks, and the priority of the<em> i<sup>th</sup></em> task is represented by the array<em> priority[i]</em>. The CPU will run for <em>y</em> seconds and you can choose any task to perform which follows the given conditions:</p>
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<ul>
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<li>In each second, you&nbsp;user can choose to perform any available task from the <em>n</em> types (if there are any tasks to perform).</li>
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<li>It is allowed to perform multiple tasks of the same type within the given time frame, but there is a time constraint that there must be at least <em>x</em> seconds between any two consecutive tasks of the same type.</li>
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<li>It is not allowed to perform more than one task at any second.</li>
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</ul>
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<p>&nbsp;</p>
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<p>Given <em>n</em> tasks, an array <em>priority, </em>and<em> </em>an integer<em> x</em> and <i>y</i>, find the maximum possible sum of the priority of tasks performed during the <em>y</em> seconds.</p>
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<p>&nbsp;</p>
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<p class="section-title">Example</p>
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<p>Given, <em>n</em> = 3, <em>priority = </em>[3, 1, 2], <em>x =</em> 5, and <em>y = </em>7.</p>
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<p>&nbsp;</p>
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<table border="1" cellpadding="1" cellspacing="1" style="width:500px;">
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<thead>
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<tr>
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<th scope="col">Seconds</th>
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<th scope="col">Task Performed</th>
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<th scope="col">Sum of priority</th>
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</tr>
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</thead>
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<tbody>
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<tr>
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<td>
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<strong>&nbsp; &nbsp; &nbsp; </strong>1<span style="font-size:12.5px;">.&nbsp;</span>
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</td>
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<td>Perform a task of the 1<sup>st</sup> type</td>
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<td>3</td>
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</tr>
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<tr>
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<td>&nbsp; &nbsp; &nbsp; 2.&nbsp;</td>
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<td>Perform a task of the 3<sup>rd</sup> type</td>
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<td>3 + 2 = 5</td>
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</tr>
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<tr>
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<td>&nbsp; &nbsp; &nbsp; 3.&nbsp;</td>
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<td>Perform a task of the 2<sup>nd</sup> type</td>
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<td>3 + 2 +1 = 6</td>
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</tr>
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<tr>
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<td>&nbsp; &nbsp; &nbsp; 4.&nbsp;</td>
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<td>No task perfomed</td>
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<td>3 + 2 + 1 = 6</td>
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</tr>
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<tr>
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<td>&nbsp; &nbsp; &nbsp; 5.&nbsp;</td>
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<td>No task perfomed</td>
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<td>3 + 2 + 1 = 6</td>
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</tr>
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<tr>
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<td>&nbsp; &nbsp; &nbsp; 6.&nbsp;</td>
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<td>Perform a task of the 1<sup>st</sup> type</td>
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<td>3 + 2 + 1 + 3 = 9</td>
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</tr>
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<tr>
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<td>&nbsp; &nbsp; &nbsp; 7.&nbsp;</td>
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<td>Perform a task of the 3<sup>rd</sup> type</td>
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<td>3 + 2 + 1 + 3 + 2 = 11</td>
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</tr>
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</tbody>
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</table>
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<p>Hence, the maximum sum of priority of tasks we can get is equal to 11. We performed the task of the 1<sup>st</sup> type then till the second 5 we cannot perform the task of the 1<sup>st</sup> type again because of the time constraint x, from the 6th second we can perform the task of the 1<sup>st</sup> type. The same applies to the task of the 3<sup>rd</sup>&nbsp;type as we once performed it in the 2<sup>nd</sup> second, and then till the 6<sup>th</sup> second, we cannot perform the task of the 3<sup>rd</sup> type.</p>
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<p>&nbsp;</p>
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<p class="section-title">Function Description</p>
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<p>Complete the function <i>maximumPrioritySum</i> in the editor below.</p>
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<p><i>maximumPrioritySum</i> has the following parameters:</p>
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<ul>
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<li>
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<em>int priority[n]:</em>&nbsp; an array of integers representing the priorities of each task.</li>
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<li>
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<em>int x</em>: an integer&nbsp;denoting the minimum time constraint between every <em>2</em>&nbsp;tasks of the same type to be performed.</li>
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<li>
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<em>int y</em>: an integer&nbsp;denoting the number of seconds the CPU will run.</li>
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</ul>
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<p>&nbsp;</p>
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<p><strong>Returns</strong></p>
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<p><em>int:</em> the maximum possible sum of the priority of tasks performed during the <em>y</em> seconds.</p>
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<p>&nbsp;</p>
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<p class="section-title">Constraints</p>
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<ul>
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<li>1&nbsp;≤<em> n&nbsp;</em>≤ 10<sup>5</sup>
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</li>
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<li>1&nbsp;≤<em> priority<span style="font-size:12px;">[i]&nbsp;</span></em>≤&nbsp;10<sup>5</sup>
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</li>
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<li>1&nbsp;≤<em> x&nbsp;</em>≤ 10<sup>9</sup>
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</li>
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<li>1&nbsp;≤<em> y&nbsp;</em>≤ 10<sup>9</sup>
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</li>
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</ul>
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<p>&nbsp;</p>
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<!-- <StartOfInputFormat> DO NOT REMOVE THIS LINE-->
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<details open=""><summary class="section-title">Input Format For Custom Testing</summary>
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<div class="collapsable-details">
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<p>The first line contains an integer <em>n, </em>the number of types of tasks present.</p>
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<p>Each of the next <em>n</em> lines contains an integer <em>priority[i]</em>.</p>
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<p>The next line contains an integer <em>x, </em>the minimum time constraint between every <em>2</em>&nbsp;tasks of the same type to be performed.</p>
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<p>The next line contains an integer <em>y, </em>the number of seconds the CPU will run.</p>
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</div>
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</details>
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<!-- </StartOfInputFormat> DO NOT REMOVE THIS LINE-->
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<details open=""><summary class="section-title">Sample Case 0</summary>
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<div class="collapsable-details">
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<p class="section-title">Sample Input For Custom Testing</p>
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<pre>STDIN Function
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----- --------
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3 ⇒ priority[] size n = 3
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2 ⇒ priority = [2, 1, 3]
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1
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3
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2 ⇒ x = 2
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3 ⇒ y = 3</pre>
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<p class="section-title">Sample Output</p>
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<pre>8</pre>
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<p class="section-title">Explanation</p>
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<table border="1" cellpadding="1" cellspacing="1" style="width:500px;">
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<thead>
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<tr>
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<th scope="col">Seconds</th>
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<th scope="col">Tasks Performed</th>
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<th scope="col">Sum of priority</th>
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</tr>
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</thead>
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<tbody>
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<tr>
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<td>
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<strong>&nbsp; &nbsp; &nbsp; &nbsp;</strong> 1<span style="font-size:12.5px;">.&nbsp;</span>
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</td>
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<td>Perform a task of the 3<sup>rd </sup>type</td>
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<td>3</td>
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</tr>
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<tr>
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<td>
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<strong>&nbsp; &nbsp; &nbsp; &nbsp;</strong> 2<span style="font-size:12.5px;">.&nbsp;</span>
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</td>
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<td>Perform a task of the 1<sup>st</sup> type</td>
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<td>3 + 2 =5</td>
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</tr>
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<tr>
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<td>
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<strong>&nbsp; </strong>&nbsp; &nbsp; &nbsp; 3<span style="font-size:12.5px;">.&nbsp;</span>
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</td>
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<td>Perform a task of the 3<sup>rd</sup> type</td>
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<td>3 + 2 + 3 =8</td>
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</tr>
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</tbody>
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</table>
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<p>Hence, the maximum sum of priority we can get is equal to 8.</p>
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</div>
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</details>
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<details><summary class="section-title">Sample Case 1</summary>
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<div class="collapsable-details">
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<p class="section-title">Sample Input For Custom Testing</p>
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<pre>STDIN &nbsp; &nbsp; &nbsp; &nbsp; Function
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----- &nbsp; &nbsp; &nbsp; &nbsp; --------
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1 &nbsp; ⇒ priority[] size n = 1
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1 ⇒ priority = [1]
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3 ⇒ x = 3
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10 ⇒ y = 10</pre>
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<p class="section-title">Sample Output</p>
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<pre>4</pre>
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<p class="section-title">Explanation</p>
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<table border="1" cellpadding="1" cellspacing="1" style="width:500px;">
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<thead>
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<tr>
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<th scope="col">Seconds</th>
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<th scope="col">Tasks Performed</th>
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<th scope="col">Sum of priority</th>
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</tr>
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</thead>
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<tbody>
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<tr>
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<td>
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<strong>&nbsp; </strong>&nbsp; &nbsp; &nbsp; &nbsp; 1<span style="font-size:12.5px;">.&nbsp;</span>
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</td>
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<td>Perform a task of the 1<sup>st</sup> type</td>
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<td>1</td>
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</tr>
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<tr>
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<td>
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<strong>&nbsp; </strong>&nbsp; &nbsp; &nbsp; &nbsp; 2<span style="font-size:12.5px;">.&nbsp;</span>
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</td>
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<td>No task perfomed</td>
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<td>1+0= 1</td>
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</tr>
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<tr>
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<td>
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<strong>&nbsp; </strong>&nbsp; &nbsp; &nbsp; &nbsp; 3<span style="font-size:12.5px;">.&nbsp;</span>
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</td>
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<td>No task perfomed</td>
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<td>1+0+0= 1</td>
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</tr>
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<tr>
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<td>
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<strong>&nbsp; </strong>&nbsp; &nbsp; &nbsp; &nbsp; 4<span style="font-size:12.5px;">.&nbsp;</span>
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</td>
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<td>Perform a task of the 1<sup>st</sup> type</td>
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<td>1+0+0+1= 2</td>
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</tr>
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<tr>
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<td>
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<strong>&nbsp; </strong>&nbsp; &nbsp; &nbsp; &nbsp; 5<span style="font-size:12.5px;">.&nbsp;</span>
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</td>
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<td>No task perfomed</td>
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<td>1+0+0+1+0= 2</td>
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</tr>
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<tr>
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<td>
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<strong>&nbsp; </strong>&nbsp; &nbsp; &nbsp; &nbsp; 6<span style="font-size:12.5px;">.&nbsp;</span>
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</td>
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<td>No task perfomed</td>
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<td>1+0+0+1+0+0= 2</td>
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</tr>
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<tr>
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<td>
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<strong>&nbsp; </strong>&nbsp; &nbsp; &nbsp; &nbsp; 7<span style="font-size:12.5px;">.&nbsp;</span>
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</td>
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<td>Perform a task of the 1<sup>st</sup> type</td>
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<td>1+0+0+1+0+0+1= 3</td>
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</tr>
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<tr>
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<td>
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<strong>&nbsp; </strong>&nbsp; &nbsp; &nbsp; &nbsp; 8<span style="font-size:12.5px;">&nbsp;</span>
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</td>
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<td>No task perfomed</td>
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<td>1+0+0+1+0+0+1+0= 3</td>
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</tr>
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<tr>
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<td>
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<strong>&nbsp; </strong>&nbsp; &nbsp; &nbsp; &nbsp; 9<span style="font-size:12.5px;">.&nbsp;</span>
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</td>
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<td>No task perfomed</td>
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<td>1+0+0+1+0+0+1+0+0= 3</td>
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</tr>
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<tr>
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<td>
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<strong>&nbsp; </strong>&nbsp; &nbsp; &nbsp; 10<span style="font-size:12.5px;">.&nbsp;</span>
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</td>
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<td>Perform a task of the 1<sup>st</sup> type</td>
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<td>1+0+0+1+0+0+1+0+0+1= 4</td>
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</tr>
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</tbody>
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</table>
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<p>Hence, the maximum possible sum of priority we can get is 4 by performing the task of 1<sup>st</sup>&nbsp;type in the interval of <em>x</em> seconds.</p>
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</div>
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</details>
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</div>
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</div></div></section></div>

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