mirror of
https://gitee.com/coder-xiaomo/leetcode-problemset
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201 lines
28 KiB
JSON
201 lines
28 KiB
JSON
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"title": "Maximum Genetic Difference Query",
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"content": "<p>There is a rooted tree consisting of <code>n</code> nodes numbered <code>0</code> to <code>n - 1</code>. Each node's number denotes its <strong>unique genetic value</strong> (i.e. the genetic value of node <code>x</code> is <code>x</code>). The <strong>genetic difference</strong> between two genetic values is defined as the <strong>bitwise-</strong><strong>XOR</strong> of their values. You are given the integer array <code>parents</code>, where <code>parents[i]</code> is the parent for node <code>i</code>. If node <code>x</code> is the <strong>root</strong> of the tree, then <code>parents[x] == -1</code>.</p>\n\n<p>You are also given the array <code>queries</code> where <code>queries[i] = [node<sub>i</sub>, val<sub>i</sub>]</code>. For each query <code>i</code>, find the <strong>maximum genetic difference</strong> between <code>val<sub>i</sub></code> and <code>p<sub>i</sub></code>, where <code>p<sub>i</sub></code> is the genetic value of any node that is on the path between <code>node<sub>i</sub></code> and the root (including <code>node<sub>i</sub></code> and the root). More formally, you want to maximize <code>val<sub>i</sub> XOR p<sub>i</sub></code>.</p>\n\n<p>Return <em>an array </em><code>ans</code><em> where </em><code>ans[i]</code><em> is the answer to the </em><code>i<sup>th</sup></code><em> query</em>.</p>\n\n<p> </p>\n<p><strong class=\"example\">Example 1:</strong></p>\n<img alt=\"\" src=\"https://assets.leetcode.com/uploads/2021/06/29/c1.png\" style=\"width: 118px; height: 163px;\" />\n<pre>\n<strong>Input:</strong> parents = [-1,0,1,1], queries = [[0,2],[3,2],[2,5]]\n<strong>Output:</strong> [2,3,7]\n<strong>Explanation: </strong>The queries are processed as follows:\n- [0,2]: The node with the maximum genetic difference is 0, with a difference of 2 XOR 0 = 2.\n- [3,2]: The node with the maximum genetic difference is 1, with a difference of 2 XOR 1 = 3.\n- [2,5]: The node with the maximum genetic difference is 2, with a difference of 5 XOR 2 = 7.\n</pre>\n\n<p><strong class=\"example\">Example 2:</strong></p>\n<img alt=\"\" src=\"https://assets.leetcode.com/uploads/2021/06/29/c2.png\" style=\"width: 256px; height: 221px;\" />\n<pre>\n<strong>Input:</strong> parents = [3,7,-1,2,0,7,0,2], queries = [[4,6],[1,15],[0,5]]\n<strong>Output:</strong> [6,14,7]\n<strong>Explanation: </strong>The queries are processed as follows:\n- [4,6]: The node with the maximum genetic difference is 0, with a difference of 6 XOR 0 = 6.\n- [1,15]: The node with the maximum genetic difference is 1, with a difference of 15 XOR 1 = 14.\n- [0,5]: The node with the maximum genetic difference is 2, with a difference of 5 XOR 2 = 7.\n</pre>\n\n<p> </p>\n<p><strong>Constraints:</strong></p>\n\n<ul>\n\t<li><code>2 <= parents.length <= 10<sup>5</sup></code></li>\n\t<li><code>0 <= parents[i] <= parents.length - 1</code> for every node <code>i</code> that is <strong>not</strong> the root.</li>\n\t<li><code>parents[root] == -1</code></li>\n\t<li><code>1 <= queries.length <= 3 * 10<sup>4</sup></code></li>\n\t<li><code>0 <= node<sub>i</sub> <= parents.length - 1</code></li>\n\t<li><code>0 <= val<sub>i</sub> <= 2 * 10<sup>5</sup></code></li>\n</ul>\n",
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"translatedTitle": "查询最大基因差",
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"translatedContent": "<p>给你一棵 <code>n</code> 个节点的有根树，节点编号从 <code>0</code> 到 <code>n - 1</code> 。每个节点的编号表示这个节点的 <strong>独一无二的基因值</strong> （也就是说节点 <code>x</code> 的基因值为 <code>x</code>）。两个基因值的 <strong>基因差</strong> 是两者的 <strong>异或和</strong> 。给你整数数组 <code>parents</code> ，其中 <code>parents[i]</code> 是节点 <code>i</code> 的父节点。如果节点 <code>x</code> 是树的 <strong>根</strong> ，那么 <code>parents[x] == -1</code> 。</p>\n\n<p>给你查询数组 <code>queries</code> ，其中 <code>queries[i] = [node<sub>i</sub>, val<sub>i</sub>]</code> 。对于查询 <code>i</code> ，请你找到 <code>val<sub>i</sub></code> 和 <code>p<sub>i</sub></code> 的 <strong>最大基因差</strong> ，其中 <code>p<sub>i</sub></code> 是节点 <code>node<sub>i</sub></code> 到根之间的任意节点（包含 <code>node<sub>i</sub></code> 和根节点）。更正式的，你想要最大化 <code>val<sub>i</sub> XOR p<sub>i</sub></code><sub> </sub>。</p>\n\n<p>请你返回数组<em> </em><code>ans</code> ，其中 <code>ans[i]</code> 是第 <code>i</code> 个查询的答案。</p>\n\n<p> </p>\n\n<p><strong>示例 1：</strong></p>\n<img alt=\"\" src=\"https://assets.leetcode.com/uploads/2021/06/29/c1.png\" style=\"width: 118px; height: 163px;\">\n<pre><b>输入：</b>parents = [-1,0,1,1], queries = [[0,2],[3,2],[2,5]]\n<b>输出：</b>[2,3,7]\n<strong>解释：</strong>查询数组处理如下：\n- [0,2]：最大基因差的对应节点为 0 ，基因差为 2 XOR 0 = 2 。\n- [3,2]：最大基因差的对应节点为 1 ，基因差为 2 XOR 1 = 3 。\n- [2,5]：最大基因差的对应节点为 2 ，基因差为 5 XOR 2 = 7 。\n</pre>\n\n<p><strong>示例 2：</strong></p>\n<img alt=\"\" src=\"https://assets.leetcode.com/uploads/2021/06/29/c2.png\" style=\"width: 256px; height: 221px;\">\n<pre><b>输入：</b>parents = [3,7,-1,2,0,7,0,2], queries = [[4,6],[1,15],[0,5]]\n<b>输出：</b>[6,14,7]\n<strong>解释：</strong>查询数组处理如下：\n- [4,6]：最大基因差的对应节点为 0 ，基因差为 6 XOR 0 = 6 。\n- [1,15]：最大基因差的对应节点为 1 ，基因差为 15 XOR 1 = 14 。\n- [0,5]：最大基因差的对应节点为 2 ，基因差为 5 XOR 2 = 7 。\n</pre>\n\n<p> </p>\n\n<p><strong>提示：</strong></p>\n\n<ul>\n\t<li><code>2 <= parents.length <= 10<sup>5</sup></code></li>\n\t<li>对于每个 <strong>不是</strong> 根节点的 <code>i</code> ，有 <code>0 <= parents[i] <= parents.length - 1</code> 。</li>\n\t<li><code>parents[root] == -1</code></li>\n\t<li><code>1 <= queries.length <= 3 * 10<sup>4</sup></code></li>\n\t<li><code>0 <= node<sub>i</sub> <= parents.length - 1</code></li>\n\t<li><code>0 <= val<sub>i</sub> <= 2 * 10<sup>5</sup></code></li>\n</ul>\n",
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