leetcode-problemset/leetcode-cn/originData/path-existence-queries-in-a-graph-i.json

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            "questionId": "3838",
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            "categoryTitle": "Algorithms",
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            "title": "Path Existence Queries in a Graph I",
            "titleSlug": "path-existence-queries-in-a-graph-i",
            "content": "<p>You are given an integer <code>n</code> representing the number of nodes in a graph, labeled from 0 to <code>n - 1</code>.</p>\n\n<p>You are also given an integer array <code>nums</code> of length <code>n</code> sorted in <strong>non-decreasing</strong> order, and an integer <code>maxDiff</code>.</p>\n\n<p>An <strong>undirected </strong>edge exists between nodes <code>i</code> and <code>j</code> if the <strong>absolute</strong> difference between <code>nums[i]</code> and <code>nums[j]</code> is <strong>at most</strong> <code>maxDiff</code> (i.e., <code>|nums[i] - nums[j]| &lt;= maxDiff</code>).</p>\n\n<p>You are also given a 2D integer array <code>queries</code>. For each <code>queries[i] = [u<sub>i</sub>, v<sub>i</sub>]</code>, determine whether there exists a path between nodes <code>u<sub>i</sub></code> and <code>v<sub>i</sub></code>.</p>\n\n<p>Return a boolean array <code>answer</code>, where <code>answer[i]</code> is <code>true</code> if there exists a path between <code>u<sub>i</sub></code> and <code>v<sub>i</sub></code> in the <code>i<sup>th</sup></code> query and <code>false</code> otherwise.</p>\n\n<p>&nbsp;</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\">n = 2, nums = [1,3], maxDiff = 1, queries = [[0,0],[0,1]]</span></p>\n\n<p><strong>Output:</strong> <span class=\"example-io\">[true,false]</span></p>\n\n<p><strong>Explanation:</strong></p>\n\n<ul>\n\t<li>Query <code>[0,0]</code>: Node 0 has a trivial path to itself.</li>\n\t<li>Query <code>[0,1]</code>: There is no edge between Node 0 and Node 1 because <code>|nums[0] - nums[1]| = |1 - 3| = 2</code>, which is greater than <code>maxDiff</code>.</li>\n\t<li>Thus, the final answer after processing all the queries is <code>[true, false]</code>.</li>\n</ul>\n</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\">n = 4, nums = [2,5,6,8], maxDiff = 2, queries = [[0,1],[0,2],[1,3],[2,3]]</span></p>\n\n<p><strong>Output:</strong> <span class=\"example-io\">[false,false,true,true]</span></p>\n\n<p><strong>Explanation:</strong></p>\n\n<p>The resulting graph is:</p>\n\n<p><img alt=\"\" src=\"https://assets.leetcode.com/uploads/2025/03/25/screenshot-2025-03-26-at-122249.png\" style=\"width: 300px; height: 170px;\" /></p>\n\n<ul>\n\t<li>Query <code>[0,1]</code>: There is no edge between Node 0 and Node 1 because <code>|nums[0] - nums[1]| = |2 - 5| = 3</code>, which is greater than <code>maxDiff</code>.</li>\n\t<li>Query <code>[0,2]</code>: There is no edge between Node 0 and Node 2 because <code>|nums[0] - nums[2]| = |2 - 6| = 4</code>, which is greater than <code>maxDiff</code>.</li>\n\t<li>Query <code>[1,3]</code>: There is a path between Node 1 and Node 3 through Node 2 since <code>|nums[1] - nums[2]| = |5 - 6| = 1</code> and <code>|nums[2] - nums[3]| = |6 - 8| = 2</code>, both of which are within <code>maxDiff</code>.</li>\n\t<li>Query <code>[2,3]</code>: There is an edge between Node 2 and Node 3 because <code>|nums[2] - nums[3]| = |6 - 8| = 2</code>, which is equal to <code>maxDiff</code>.</li>\n\t<li>Thus, the final answer after processing all the queries is <code>[false, false, true, true]</code>.</li>\n</ul>\n</div>\n\n<p>&nbsp;</p>\n<p><strong>Constraints:</strong></p>\n\n<ul>\n\t<li><code>1 &lt;= n == nums.length &lt;= 10<sup>5</sup></code></li>\n\t<li><code>0 &lt;= nums[i] &lt;= 10<sup>5</sup></code></li>\n\t<li><code>nums</code> is sorted in <strong>non-decreasing</strong> order.</li>\n\t<li><code>0 &lt;= maxDiff &lt;= 10<sup>5</sup></code></li>\n\t<li><code>1 &lt;= queries.length &lt;= 10<sup>5</sup></code></li>\n\t<li><code>queries[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; n</code></li>\n</ul>\n",
            "translatedTitle": "针对图的路径存在性查询 I",
            "translatedContent": "<p>给你一个整数 <code>n</code>，表示图中的节点数量，这些节点按从 <code>0</code> 到 <code>n - 1</code>&nbsp;编号。</p>\n\n<p>同时给你一个长度为 <code>n</code> 的整数数组 <code>nums</code>，该数组按&nbsp;<strong>非递减&nbsp;</strong>顺序排序，以及一个整数 <code>maxDiff</code>。</p>\n\n<p>如果满足 <code>|nums[i] - nums[j]| &lt;= maxDiff</code>（即 <code>nums[i]</code> 和 <code>nums[j]</code> 的&nbsp;<strong>绝对差&nbsp;</strong>至多为 <code>maxDiff</code>），则节点 <code>i</code> 和节点 <code>j</code> 之间存在一条&nbsp;<strong>无向边&nbsp;</strong>。</p>\n\n<p>此外，给你一个二维整数数组 <code>queries</code>。对于每个 <code>queries[i] = [u<sub>i</sub>, v<sub>i</sub>]</code>，需要判断节点 <code>u<sub>i</sub></code> 和 <code>v<sub>i</sub></code> 之间是否存在路径。</p>\n\n<p>返回一个布尔数组 <code>answer</code>，其中 <code>answer[i]</code> 等于 <code>true</code> 表示在第 <code>i</code> 个查询中节点 <code>u<sub>i</sub></code> 和 <code>v<sub>i</sub></code> 之间存在路径，否则为 <code>false</code>。</p>\n\n<p>&nbsp;</p>\n\n<p><strong class=\"example\">示例 1：</strong></p>\n\n<div class=\"example-block\">\n<p><strong>输入:</strong> <span class=\"example-io\">n = 2, nums = [1,3], maxDiff = 1, queries = [[0,0],[0,1]]</span></p>\n\n<p><strong>输出:</strong> <span class=\"example-io\">[true,false]</span></p>\n\n<p><strong>解释:</strong></p>\n\n<ul>\n\t<li>查询 <code>[0,0]</code>：节点 0 有一条到自己的显然路径。</li>\n\t<li>查询 <code>[0,1]</code>：节点 0 和节点 1 之间没有边，因为 <code>|nums[0] - nums[1]| = |1 - 3| = 2</code>，大于 <code>maxDiff</code>。</li>\n\t<li>因此，在处理完所有查询后，最终答案为 <code>[true, false]</code>。</li>\n</ul>\n</div>\n\n<p><strong class=\"example\">示例 2：</strong></p>\n\n<div class=\"example-block\">\n<p><strong>输入:</strong> <span class=\"example-io\">n = 4, nums = [2,5,6,8], maxDiff = 2, queries = [[0,1],[0,2],[1,3],[2,3]]</span></p>\n\n<p><strong>输出:</strong> <span class=\"example-io\">[false,false,true,true]</span></p>\n\n<p><strong>解释:</strong></p>\n\n<p>生成的图如下：</p>\n\n<p><img alt=\"\" src=\"https://pic.leetcode.cn/1745660506-eNVQtC-screenshot-2025-03-26-at-122249.png\" style=\"width: 300px; height: 170px;\" /></p>\n\n<ul>\n\t<li>查询 <code>[0,1]</code>：节点 0 和节点 1 之间没有边，因为 <code>|nums[0] - nums[1]| = |2 - 5| = 3</code>，大于 <code>maxDiff</code>。</li>\n\t<li>查询 <code>[0,2]</code>：节点 0 和节点 2 之间没有边，因为 <code>|nums[0] - nums[2]| = |2 - 6| = 4</code>，大于 <code>maxDiff</code>。</li>\n\t<li>查询 <code>[1,3]</code>：节点 1 和节点 3 之间存在路径通过节点 2，因为 <code>|nums[1] - nums[2]| = |5 - 6| = 1</code> 和 <code>|nums[2] - nums[3]| = |6 - 8| = 2</code>，都小于等于 <code>maxDiff</code>。</li>\n\t<li>查询 <code>[2,3]</code>：节点 2 和节点 3 之间有一条边，因为 <code>|nums[2] - nums[3]| = |6 - 8| = 2</code>，等于 <code>maxDiff</code>。</li>\n\t<li>因此，在处理完所有查询后，最终答案为 <code>[false, false, true, true]</code>。</li>\n</ul>\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 == nums.length &lt;= 10<sup>5</sup></code></li>\n\t<li><code>0 &lt;= nums[i] &lt;= 10<sup>5</sup></code></li>\n\t<li><code>nums</code> 按&nbsp;<strong>非递减&nbsp;</strong>顺序排序。</li>\n\t<li><code>0 &lt;= maxDiff &lt;= 10<sup>5</sup></code></li>\n\t<li><code>1 &lt;= queries.length &lt;= 10<sup>5</sup></code></li>\n\t<li><code>queries[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; n</code></li>\n</ul>\n",
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