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<div id="main-splitpane-left" class="coding-question__left-pane"><section class="question-view__title-wrapper"><div class="beta-icon-editor beta-desc">BETA</div><span class="question-view__switch-theme__wrapper">Can’t read the text? <button class="ui-btn ui-btn-normal ui-btn-plain btn-as-link question-view__switch-theme"><div class="ui-content align-icon-right"><span class="ui-text" aria-hidden="false">Switch</span></div></button> theme</span><h1 class="question-view__title">1. Optimizing Box Weights (example question)</h1></section><section class="question-view__instruction"><div class="candidate-rich-text"><div id="24i33a0pf0l-instruction"><p>An Amazon Fulfillment Associate has a set of items that need to be packed into two boxes. Given an integer array of the item weights (<code>arr</code>) to be packed, divide the item weights into two subsets, A and B, for packing into the associated boxes, while respecting the following conditions: </p>
<p> </p>
<div class="ps-content-wrapper-v0">
<ul>
<li><span style="font-family:"Whitney SSm A" , "Whitney SSm B" , AvenirNext-Regular , "Segoe UI" , Ubuntu , "Helvetica Neue" , Helvetica , Arial , sans-serif;font-size:1em;font-weight:normal;">The intersection of A and B is null.</span></li>
<li><span style="font-family:"Whitney SSm A" , "Whitney SSm B" , AvenirNext-Regular , "Segoe UI" , Ubuntu , "Helvetica Neue" , Helvetica , Arial , sans-serif;font-size:1em;font-weight:normal;">The union A and B is equal to the original array.</span></li>
<li><span style="font-family:"Whitney SSm A" , "Whitney SSm B" , AvenirNext-Regular , "Segoe UI" , Ubuntu , "Helvetica Neue" , Helvetica , Arial , sans-serif;font-size:1em;font-weight:normal;">The number of elements in subset A is minimal.</span></li>
<li><span style="font-family:"Whitney SSm A" , "Whitney SSm B" , AvenirNext-Regular , "Segoe UI" , Ubuntu , "Helvetica Neue" , Helvetica , Arial , sans-serif;font-size:1em;font-weight:normal;">The sum of A's weights is greater than the sum of B's weights.</span></li>
</ul>
<p> </p>
<p>Return the subset A in increasing order where the sum of A's weights is greater than the sum of B's weights. If more than one subset A exists, return the one with the maximal total weight.</p>
<p> </p>
<p><strong>Example</strong></p>
<p><em>n = 5</em></p>
<p><span style="font-family:"Whitney SSm A" , "Whitney SSm B" , AvenirNext-Regular , "Segoe UI" , Ubuntu , "Helvetica Neue" , Helvetica , Arial , sans-serif;font-size:1em;font-weight:normal;"><em>arr = [3, 7, 5, 6, 2]</em></span></p>
<p> </p>
<p>The 2 subsets in <em>arr</em> that satisfy the conditions for <em>A </em>are<em> [5, 7]</em> and <em> [6, 7]</em> :</p>
<ul>
<li>A is minimal (size 2)</li>
<li>Sum(A) = (5 + 7) = 12 > Sum(B) = (2 + 3 + 6) = 11</li>
<li>Sum(A) = (6 + 7) = 13 > Sum(B) = (2 + 3 + 5) = 10</li>
<li>The intersection of A and B is null and their union is equal to <em>arr</em>.</li>
<li>The subset A where the sum of its weight is maximal is [6, 7].</li>
</ul>
<p> </p>
<p class="section-title"><strong>Function Description</strong></p>
<p>Complete the <em>minimalHeaviestSetA</em> function in the editor below.</p>
<p> </p>
<p><em>minimalHeaviestSetA </em><strong>has the following parameter(s):</strong></p>
<p> <em>int arr[]:</em> an integer array of the weights of each item in the set</p>
<p> </p>
<p><strong>Returns:</strong></p>
<p> <b id="docs-internal-guid-50c4b635-9349-999b-5712-a2bba90c0934"><em>int[]</em> : an integer array with the values of subset A</b></p>
<p> </p>
<p class="section-title"><strong>Constraints</strong></p>
<ul>
<li><em>1 ≤ n ≤ 10<sup>5 </sup></em></li>
<li>
<em>1 ≤ arr[i] ≤ 10<sup>5 </sup></em><b><em>(</em>where<em> 0 ≤ i < n)</em></b>
</li>
</ul>
<p> </p>
<!-- <StartOfInputFormat> DO NOT REMOVE THIS LINE-->
<details><summary class="section-title"><strong>Input Format For Custom Testing</strong></summary>
<div class="collapsable-details">
<p dir="ltr"><b>The first line contains an integer, <em>n,</em> denoting the number of elements in the array.</b></p>
<p dir="ltr"><b>Each line <em>i</em> of the <em>n</em> subsequent lines contains an integer, which is an element of <em>arr.</em></b></p>
<p dir="ltr"> </p>
</div>
</details>
<!-- </StartOfInputFormat> DO NOT REMOVE THIS LINE-->
<details><summary class="section-title"><strong>Sample Case 0</strong></summary>
<div class="collapsable-details">
<p class="section-title">Sample Input For Custom Testing</p>
<pre>STDIN Function
----- --------
<b>6 </b>→ <i> arr</i>[] size n = 6<b>
5 </b>→ <i> arr</i>[] = <b>[5, 3, 2, 4, 1, 2]</b><b>
3
2
4
1
2</b></pre>
<p class="section-title">Sample Output</p>
<pre>4
5</pre>
<p class="section-title">Explanation</p>
<p dir="ltr"><b id="docs-internal-guid-30cb3446-934e-0ddb-63fe-13120270e31b"><em>n = 6</em></b></p>
<p dir="ltr"><b><em>arr = [5, 3, 2, 4, 1, 2]</em></b></p>
<p dir="ltr"> </p>
<p>The subset of A that satisfies the conditions is [4, 5] :</p>
<ul>
<li>A is minimal (size 2)</li>
<li>Sum(A) = (4 + 5) = 9 > Sum(B) = (1 + 2 + 2 + 3) = 8</li>
<li>The intersection of A and B is null and their union is equal to <em>arr.</em>
</li>
<li>The subset A with the maximal sum is [4, 5].</li>
</ul>
<p dir="ltr"> </p>
</div>
</details>
<details><summary class="section-title"><strong>Sample Case 1</strong></summary>
<div class="collapsable-details">
<p class="section-title">Sample Input For Custom Testing</p>
<pre>STDIN Function
----- --------
<b>5 </b>→ arr[] size n = 5<b>
4 </b>→ arr[] = <b>[4, 2, 5, 1, 6]
2
5
1
6</b></pre>
<p class="section-title">Sample Output</p>
<pre>5
6</pre>
<p class="section-title">Explanation</p>
<p dir="ltr"><b id="docs-internal-guid-30cb3446-934e-0ddb-63fe-13120270e31b"><em>n = 5</em></b></p>
<p dir="ltr"><b><em>arr = [4, 2, 5, 1, 6]</em></b></p>
<p dir="ltr"> </p>
<p>The subset of A that satisfies the conditions is [5, 6]:</p>
<ul>
<li>A is minimal (size 2)</li>
<li>Sum(A) = (5 + 6) = 11 > Sum(B) = (1 + 2 + 4) = 7</li>
<li>Sum(A) = (4 + 6) = 10 > Sum(B) = (1 + 2 + 5) = 8</li>
<li>The intersection of A and B is null and their union is equal to <em>arr</em>.</li>
<li>The subset A with the maximal sum is [5, 6].</li>
</ul>
</div>
</details>
</div>
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