leetcode-problemset/leetcode-cn/originData/find-minimum-diameter-after-merging-two-trees.json

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        "question": {
            "questionId": "3439",
            "questionFrontendId": "3203",
            "categoryTitle": "Algorithms",
            "boundTopicId": 2824508,
            "title": "Find Minimum Diameter After Merging Two Trees",
            "titleSlug": "find-minimum-diameter-after-merging-two-trees",
            "content": "<p>There exist two <strong>undirected </strong>trees with <code>n</code> and <code>m</code> nodes, numbered from <code>0</code> to <code>n - 1</code> and from <code>0</code> to <code>m - 1</code>, respectively. You are given two 2D integer arrays <code>edges1</code> and <code>edges2</code> of lengths <code>n - 1</code> and <code>m - 1</code>, respectively, where <code>edges1[i] = [a<sub>i</sub>, b<sub>i</sub>]</code> indicates that there is an edge between nodes <code>a<sub>i</sub></code> and <code>b<sub>i</sub></code> in the first tree and <code>edges2[i] = [u<sub>i</sub>, v<sub>i</sub>]</code> indicates that there is an edge between nodes <code>u<sub>i</sub></code> and <code>v<sub>i</sub></code> in the second tree.</p>\n\n<p>You must connect one node from the first tree with another node from the second tree with an edge.</p>\n\n<p>Return the <strong>minimum </strong>possible <strong>diameter </strong>of the resulting tree.</p>\n\n<p>The <strong>diameter</strong> of a tree is the length of the <em>longest</em> path between any two nodes in the tree.</p>\n\n<p>&nbsp;</p>\n<p><strong class=\"example\">Example 1:</strong><img alt=\"\" src=\"https://assets.leetcode.com/uploads/2024/04/22/example11-transformed.png\" /></p>\n\n<div class=\"example-block\">\n<p><strong>Input:</strong> <span class=\"example-io\">edges1 = [[0,1],[0,2],[0,3]], edges2 = [[0,1]]</span></p>\n\n<p><strong>Output:</strong> <span class=\"example-io\">3</span></p>\n\n<p><strong>Explanation:</strong></p>\n\n<p>We can obtain a tree of diameter 3 by connecting node 0 from the first tree with any node from the second tree.</p>\n</div>\n\n<p><strong class=\"example\">Example 2:</strong></p>\n<img alt=\"\" src=\"https://assets.leetcode.com/uploads/2024/04/22/example211.png\" />\n<div class=\"example-block\">\n<p><strong>Input:</strong> <span class=\"example-io\">edges1 = [[0,1],[0,2],[0,3],[2,4],[2,5],[3,6],[2,7]], edges2 = [[0,1],[0,2],[0,3],[2,4],[2,5],[3,6],[2,7]]</span></p>\n\n<p><strong>Output:</strong> <span class=\"example-io\">5</span></p>\n\n<p><strong>Explanation:</strong></p>\n\n<p>We can obtain a tree of diameter 5 by connecting node 0 from the first tree with node 0 from the second tree.</p>\n</div>\n\n<p>&nbsp;</p>\n<p><strong>Constraints:</strong></p>\n\n<ul>\n\t<li><code>1 &lt;= n, m &lt;= 10<sup>5</sup></code></li>\n\t<li><code>edges1.length == n - 1</code></li>\n\t<li><code>edges2.length == m - 1</code></li>\n\t<li><code>edges1[i].length == edges2[i].length == 2</code></li>\n\t<li><code>edges1[i] = [a<sub>i</sub>, b<sub>i</sub>]</code></li>\n\t<li><code>0 &lt;= a<sub>i</sub>, b<sub>i</sub> &lt; n</code></li>\n\t<li><code>edges2[i] = [u<sub>i</sub>, v<sub>i</sub>]</code></li>\n\t<li><code>0 &lt;= u<sub>i</sub>, v<sub>i</sub> &lt; m</code></li>\n\t<li>The input is generated such that <code>edges1</code> and <code>edges2</code> represent valid trees.</li>\n</ul>\n",
            "translatedTitle": "合并两棵树后的最小直径",
            "translatedContent": "<p>给你两棵 <strong>无向</strong>&nbsp;树，分别有&nbsp;<code>n</code> 和&nbsp;<code>m</code>&nbsp;个节点，节点编号分别为&nbsp;<code>0</code>&nbsp;到&nbsp;<code>n - 1</code>&nbsp;和&nbsp;<code>0</code>&nbsp;到&nbsp;<code>m - 1</code>&nbsp;。给你两个二维整数数组&nbsp;<code>edges1</code> 和&nbsp;<code>edges2</code>&nbsp;，长度分别为&nbsp;<code>n - 1</code> 和&nbsp;<code>m - 1</code>&nbsp;，其中&nbsp;<code>edges1[i] = [a<sub>i</sub>, b<sub>i</sub>]</code>&nbsp;表示在第一棵树中节点&nbsp;<code>a<sub>i</sub></code> 和&nbsp;<code>b<sub>i</sub></code>&nbsp;之间有一条边，<code>edges2[i] = [u<sub>i</sub>, v<sub>i</sub>]</code>&nbsp;表示在第二棵树中节点&nbsp;<code>u<sub>i</sub></code> 和&nbsp;<code>v<sub>i</sub></code>&nbsp;之间有一条边。</p>\n\n<p>你必须在第一棵树和第二棵树中分别选一个节点，并用一条边连接它们。</p>\n\n<p>请你返回添加边后得到的树中，<strong>最小直径</strong>&nbsp;为多少。</p>\n\n<p>一棵树的 <strong>直径</strong>&nbsp;指的是树中任意两个节点之间的最长路径长度。</p>\n\n<p>&nbsp;</p>\n\n<p><b>示例 1：</b><img alt=\"\" src=\"https://assets.leetcode.com/uploads/2024/04/22/example11-transformed.png\" style=\"width: 1000px; height: 494px;\" /></p>\n\n<div class=\"example-block\">\n<p><span class=\"example-io\"><b>输入：</b>edges1 = [[0,1],[0,2],[0,3]], edges2 = [[0,1]]</span></p>\n\n<p><span class=\"example-io\"><b>输出：</b>3</span></p>\n\n<p><strong>解释：</strong></p>\n\n<p>将第一棵树中的节点 0 与第二棵树中的任意节点连接，得到一棵直径为 3 的树。</p>\n</div>\n\n<p><strong class=\"example\">示例 2：<img alt=\"\" src=\"https://assets.leetcode.com/uploads/2024/04/22/example211.png\" style=\"width: 1000px; height: 492px;\" /></strong></p>\n\n<div class=\"example-block\">\n<p><span class=\"example-io\"><b>输入：</b>edges1 = [[0,1],[0,2],[0,3],[2,4],[2,5],[3,6],[2,7]], edges2 = [[0,1],[0,2],[0,3],[2,4],[2,5],[3,6],[2,7]]</span></p>\n\n<p><span class=\"example-io\"><b>输出：</b>5</span></p>\n\n<p><strong>解释：</strong></p>\n\n<p>将第一棵树中的节点 0 和第二棵树中的节点 0 连接，可以得到一棵直径为 5 的树。</p>\n</div>\n\n<p>&nbsp;</p>\n\n<p><strong>提示：</strong></p>\n\n<ul>\n\t<li><code>1 &lt;= n, m &lt;= 10<sup>5</sup></code></li>\n\t<li><code>edges1.length == n - 1</code></li>\n\t<li><code>edges2.length == m - 1</code></li>\n\t<li><code>edges1[i].length == edges2[i].length == 2</code></li>\n\t<li><code>edges1[i] = [a<sub>i</sub>, b<sub>i</sub>]</code></li>\n\t<li><code>0 &lt;= a<sub>i</sub>, b<sub>i</sub> &lt; n</code></li>\n\t<li><code>edges2[i] = [u<sub>i</sub>, v<sub>i</sub>]</code></li>\n\t<li><code>0 &lt;= u<sub>i</sub>, v<sub>i</sub> &lt; m</code></li>\n\t<li>输入保证&nbsp;<code>edges1</code> 和&nbsp;<code>edges2</code>&nbsp;分别表示一棵合法的树。</li>\n</ul>\n",
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                "Suppose that we connected node <code>a</code> in tree1 with node <code>b</code> in tree2. The diameter length of the resulting tree will be the largest of the following 3 values: \r\n<ol>\r\n<li>The diameter of tree 1.</li>\r\n<li>The diameter of tree 2.</li>\r\n<li>The length of the longest path that starts at node <code>a</code> and that is completely within Tree 1 + The length of the longest path that starts at node <code>b</code> and that is completely within Tree 2 + 1.</li>\r\n</ol> \r\nThe added one in the third value is due to the additional edge that we have added between trees 1 and 2.",
                "Values 1 and 2 are constant regardless of our choice of <code>a</code> and <code>b</code>. Therefore, we need to pick <code>a</code> and <code>b</code> in such a way that minimizes value 3.",
                "If we pick <code>a</code> and <code>b</code> optimally, they will be in the diameters of Tree 1 and Tree 2, respectively. Exactly which nodes of the diameter should we pick?",
                "<code>a</code> is the center of the diameter of tree 1, and <code>b</code> is the center of the diameter of tree 2."
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