mirror of
https://gitee.com/coder-xiaomo/leetcode-problemset
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181 lines
21 KiB
JSON
181 lines
21 KiB
JSON
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"title": "Maximize the Number of Target Nodes After Connecting Trees II",
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"titleSlug": "maximize-the-number-of-target-nodes-after-connecting-trees-ii",
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"content": "<p>There exist two <strong>undirected </strong>trees with <code>n</code> and <code>m</code> nodes, labeled from <code>[0, n - 1]</code> and <code>[0, m - 1]</code>, respectively.</p>\n\n<p>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>Node <code>u</code> is <strong>target</strong> to node <code>v</code> if the number of edges on the path from <code>u</code> to <code>v</code> is even. <strong>Note</strong> that a node is <em>always</em> <strong>target</strong> to itself.</p>\n\n<p>Return an array of <code>n</code> integers <code>answer</code>, where <code>answer[i]</code> is the <strong>maximum</strong> possible number of nodes that are <strong>target</strong> to node <code>i</code> of the first tree if you had to connect one node from the first tree to another node in the second tree.</p>\n\n<p><strong>Note</strong> that queries are independent from each other. That is, for every query you will remove the added edge before proceeding to the next query.</p>\n\n<p> </p>\n<p><strong class=\"example\">Example 1:</strong></p>\n\n<div class=\"example-block\">\n<p><strong>Input:</strong> <span class=\"example-io\">edges1 = [[0,1],[0,2],[2,3],[2,4]], edges2 = [[0,1],[0,2],[0,3],[2,7],[1,4],[4,5],[4,6]]</span></p>\n\n<p><strong>Output:</strong> <span class=\"example-io\">[8,7,7,8,8]</span></p>\n\n<p><strong>Explanation:</strong></p>\n\n<ul>\n\t<li>For <code>i = 0</code>, connect node 0 from the first tree to node 0 from the second tree.</li>\n\t<li>For <code>i = 1</code>, connect node 1 from the first tree to node 4 from the second tree.</li>\n\t<li>For <code>i = 2</code>, connect node 2 from the first tree to node 7 from the second tree.</li>\n\t<li>For <code>i = 3</code>, connect node 3 from the first tree to node 0 from the second tree.</li>\n\t<li>For <code>i = 4</code>, connect node 4 from the first tree to node 4 from the second tree.</li>\n</ul>\n<img alt=\"\" src=\"https://assets.leetcode.com/uploads/2024/09/24/3982-1.png\" style=\"width: 600px; height: 169px;\" /></div>\n\n<p><strong class=\"example\">Example 2:</strong></p>\n\n<div class=\"example-block\">\n<p><strong>Input:</strong> <span class=\"example-io\">edges1 = [[0,1],[0,2],[0,3],[0,4]], edges2 = [[0,1],[1,2],[2,3]]</span></p>\n\n<p><strong>Output:</strong> <span class=\"example-io\">[3,6,6,6,6]</span></p>\n\n<p><strong>Explanation:</strong></p>\n\n<p>For every <code>i</code>, connect node <code>i</code> of the first tree with any node of the second tree.</p>\n<img alt=\"\" src=\"https://assets.leetcode.com/uploads/2024/09/24/3928-2.png\" style=\"height: 281px; width: 500px;\" /></div>\n\n<p> </p>\n<p><strong>Constraints:</strong></p>\n\n<ul>\n\t<li><code>2 <= n, m <= 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 <= a<sub>i</sub>, b<sub>i</sub> < n</code></li>\n\t<li><code>edges2[i] = [u<sub>i</sub>, v<sub>i</sub>]</code></li>\n\t<li><code>0 <= u<sub>i</sub>, v<sub>i</sub> < 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",
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"Compute an array <code>even</code> where <code>even[u]</code> is the number of nodes at an even distance from node <code>u</code>, for every <code>u</code> of the first tree.",
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"Compute an array <code>odd</code> where <code>odd[u]</code> is the number of nodes at an odd distance from node <code>u</code>, for every <code>u</code> of the second tree.",
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"<code>answer[i] = even[i]+ max(odd[1], odd[2], …, odd[m - 1])</code>"
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