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51 lines
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51 lines
2.3 KiB
HTML
<p>Given <code>n</code> <code>cuboids</code> where the dimensions of the <code>i<sup>th</sup></code> cuboid is <code>cuboids[i] = [width<sub>i</sub>, length<sub>i</sub>, height<sub>i</sub>]</code> (<strong>0-indexed</strong>). Choose a <strong>subset</strong> of <code>cuboids</code> and place them on each other.</p>
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<p>You can place cuboid <code>i</code> on cuboid <code>j</code> if <code>width<sub>i</sub> <= width<sub>j</sub></code> and <code>length<sub>i</sub> <= length<sub>j</sub></code> and <code>height<sub>i</sub> <= height<sub>j</sub></code>. You can rearrange any cuboid's dimensions by rotating it to put it on another cuboid.</p>
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<p>Return <em>the <strong>maximum height</strong> of the stacked</em> <code>cuboids</code>.</p>
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<p> </p>
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<p><strong class="example">Example 1:</strong></p>
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<p><strong><img alt="" src="https://assets.leetcode.com/uploads/2019/10/21/image.jpg" style="width: 420px; height: 299px;" /></strong></p>
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<pre>
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<strong>Input:</strong> cuboids = [[50,45,20],[95,37,53],[45,23,12]]
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<strong>Output:</strong> 190
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<strong>Explanation:</strong>
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Cuboid 1 is placed on the bottom with the 53x37 side facing down with height 95.
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Cuboid 0 is placed next with the 45x20 side facing down with height 50.
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Cuboid 2 is placed next with the 23x12 side facing down with height 45.
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The total height is 95 + 50 + 45 = 190.
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</pre>
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<p><strong class="example">Example 2:</strong></p>
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<pre>
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<strong>Input:</strong> cuboids = [[38,25,45],[76,35,3]]
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<strong>Output:</strong> 76
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<strong>Explanation:</strong>
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You can't place any of the cuboids on the other.
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We choose cuboid 1 and rotate it so that the 35x3 side is facing down and its height is 76.
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</pre>
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<p><strong class="example">Example 3:</strong></p>
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<pre>
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<strong>Input:</strong> cuboids = [[7,11,17],[7,17,11],[11,7,17],[11,17,7],[17,7,11],[17,11,7]]
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<strong>Output:</strong> 102
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<strong>Explanation:</strong>
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After rearranging the cuboids, you can see that all cuboids have the same dimension.
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You can place the 11x7 side down on all cuboids so their heights are 17.
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The maximum height of stacked cuboids is 6 * 17 = 102.
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</pre>
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<p> </p>
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<p><strong>Constraints:</strong></p>
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<ul>
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<li><code>n == cuboids.length</code></li>
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<li><code>1 <= n <= 100</code></li>
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<li><code>1 <= width<sub>i</sub>, length<sub>i</sub>, height<sub>i</sub> <= 100</code></li>
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</ul>
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