leetcode-problemset/leetcode-cn/originData/maximum-height-by-stacking-cuboids.json

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            "title": "Maximum Height by Stacking Cuboids ",
            "titleSlug": "maximum-height-by-stacking-cuboids",
            "content": "<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>\n\n<p>You can place cuboid <code>i</code> on cuboid <code>j</code> if <code>width<sub>i</sub> &lt;= width<sub>j</sub></code> and <code>length<sub>i</sub> &lt;= length<sub>j</sub></code> and <code>height<sub>i</sub> &lt;= height<sub>j</sub></code>. You can rearrange any cuboid&#39;s dimensions by rotating it to put it on another cuboid.</p>\n\n<p>Return <em>the <strong>maximum height</strong> of the stacked</em> <code>cuboids</code>.</p>\n\n<p>&nbsp;</p>\n<p><strong class=\"example\">Example 1:</strong></p>\n\n<p><strong><img alt=\"\" src=\"https://assets.leetcode.com/uploads/2019/10/21/image.jpg\" style=\"width: 420px; height: 299px;\" /></strong></p>\n\n<pre>\n<strong>Input:</strong> cuboids = [[50,45,20],[95,37,53],[45,23,12]]\n<strong>Output:</strong> 190\n<strong>Explanation:</strong>\nCuboid 1 is placed on the bottom with the 53x37 side facing down with height 95.\nCuboid 0 is placed next with the 45x20 side facing down with height 50.\nCuboid 2 is placed next with the 23x12 side facing down with height 45.\nThe total height is 95 + 50 + 45 = 190.\n</pre>\n\n<p><strong class=\"example\">Example 2:</strong></p>\n\n<pre>\n<strong>Input:</strong> cuboids = [[38,25,45],[76,35,3]]\n<strong>Output:</strong> 76\n<strong>Explanation:</strong>\nYou can&#39;t place any of the cuboids on the other.\nWe choose cuboid 1 and rotate it so that the 35x3 side is facing down and its height is 76.\n</pre>\n\n<p><strong class=\"example\">Example 3:</strong></p>\n\n<pre>\n<strong>Input:</strong> cuboids = [[7,11,17],[7,17,11],[11,7,17],[11,17,7],[17,7,11],[17,11,7]]\n<strong>Output:</strong> 102\n<strong>Explanation:</strong>\nAfter rearranging the cuboids, you can see that all cuboids have the same dimension.\nYou can place the 11x7 side down on all cuboids so their heights are 17.\nThe maximum height of stacked cuboids is 6 * 17 = 102.\n</pre>\n\n<p>&nbsp;</p>\n<p><strong>Constraints:</strong></p>\n\n<ul>\n\t<li><code>n == cuboids.length</code></li>\n\t<li><code>1 &lt;= n &lt;= 100</code></li>\n\t<li><code>1 &lt;= width<sub>i</sub>, length<sub>i</sub>, height<sub>i</sub> &lt;= 100</code></li>\n</ul>\n",
            "translatedTitle": "堆叠长方体的最大高度",
            "translatedContent": "<p>给你 <code>n</code> 个长方体 <code>cuboids</code> ，其中第 <code>i</code> 个长方体的长宽高表示为 <code>cuboids[i] = [width<sub>i</sub>, length<sub>i</sub>, height<sub>i</sub>]</code>（<strong>下标从 0 开始</strong>）。请你从 <code>cuboids</code> 选出一个 <strong>子集</strong> ，并将它们堆叠起来。</p>\n\n<p>如果 <code>width<sub>i</sub> <= width<sub>j</sub></code> 且 <code>length<sub>i</sub> <= length<sub>j</sub></code> 且 <code>height<sub>i</sub> <= height<sub>j</sub></code> ，你就可以将长方体 <code>i</code> 堆叠在长方体 <code>j</code> 上。你可以通过旋转把长方体的长宽高重新排列，以将它放在另一个长方体上。</p>\n\n<p>返回 <strong>堆叠长方体</strong> <code>cuboids</code> 可以得到的 <strong>最大高度</strong> 。</p>\n\n<p> </p>\n\n<p><strong>示例 1：</strong></p>\n\n<p><strong><img alt=\"\" src=\"https://assets.leetcode-cn.com/aliyun-lc-upload/uploads/2020/12/12/image.jpg\" style=\"width: 420px; height: 299px;\" /></strong></p>\n\n<pre>\n<strong>输入：</strong>cuboids = [[50,45,20],[95,37,53],[45,23,12]]\n<strong>输出：</strong>190\n<strong>解释：</strong>\n第 1 个长方体放在底部，53x37 的一面朝下，高度为 95 。\n第 0 个长方体放在中间，45x20 的一面朝下，高度为 50 。\n第 2 个长方体放在上面，23x12 的一面朝下，高度为 45 。\n总高度是 95 + 50 + 45 = 190 。\n</pre>\n\n<p><strong>示例 2：</strong></p>\n\n<pre>\n<strong>输入：</strong>cuboids = [[38,25,45],[76,35,3]]\n<strong>输出：</strong>76\n<strong>解释：</strong>\n无法将任何长方体放在另一个上面。\n选择第 1 个长方体然后旋转它，使 35x3 的一面朝下，其高度为 76 。\n</pre>\n\n<p><strong>示例 3：</strong></p>\n\n<pre>\n<strong>输入：</strong>cuboids = [[7,11,17],[7,17,11],[11,7,17],[11,17,7],[17,7,11],[17,11,7]]\n<strong>输出：</strong>102\n<strong>解释：</strong>\n重新排列长方体后，可以看到所有长方体的尺寸都相同。\n你可以把 11x7 的一面朝下，这样它们的高度就是 17 。\n堆叠长方体的最大高度为 6 * 17 = 102 。\n</pre>\n\n<p> </p>\n\n<p><strong>提示：</strong></p>\n\n<ul>\n\t<li><code>n == cuboids.length</code></li>\n\t<li><code>1 <= n <= 100</code></li>\n\t<li><code>1 <= width<sub>i</sub>, length<sub>i</sub>, height<sub>i</sub> <= 100</code></li>\n</ul>\n",
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