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"data": {
"question": {
"questionId": "3809",
"questionFrontendId": "3493",
"categoryTitle": "Algorithms",
"boundTopicId": 3623281,
"title": "Properties Graph",
"titleSlug": "properties-graph",
"content": "<p>You are given a 2D integer array <code>properties</code> having dimensions <code>n x m</code> and an integer <code>k</code>.</p>\n\n<p>Define a function <code>intersect(a, b)</code> that returns the <strong>number of distinct integers</strong> common to both arrays <code>a</code> and <code>b</code>.</p>\n\n<p>Construct an <strong>undirected</strong> graph where each index <code>i</code> corresponds to <code>properties[i]</code>. There is an edge between node <code>i</code> and node <code>j</code> if and only if <code>intersect(properties[i], properties[j]) &gt;= k</code>, where <code>i</code> and <code>j</code> are in the range <code>[0, n - 1]</code> and <code>i != j</code>.</p>\n\n<p>Return the number of <strong>connected components</strong> in the resulting graph.</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\">properties = [[1,2],[1,1],[3,4],[4,5],[5,6],[7,7]], k = 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>The graph formed has 3 connected components:</p>\n\n<p><img height=\"171\" src=\"https://assets.leetcode.com/uploads/2025/02/27/image.png\" width=\"279\" /></p>\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\">properties = [[1,2,3],[2,3,4],[4,3,5]], k = 2</span></p>\n\n<p><strong>Output:</strong> <span class=\"example-io\">1</span></p>\n\n<p><strong>Explanation:</strong></p>\n\n<p>The graph formed has 1 connected component:</p>\n\n<p><img alt=\"\" src=\"https://assets.leetcode.com/uploads/2025/02/27/screenshot-from-2025-02-27-23-58-34.png\" style=\"width: 219px; height: 171px;\" /></p>\n</div>\n\n<p><strong class=\"example\">Example 3:</strong></p>\n\n<div class=\"example-block\">\n<p><strong>Input:</strong> <span class=\"example-io\">properties = [[1,1],[1,1]], k = 2</span></p>\n\n<p><strong>Output:</strong> <span class=\"example-io\">2</span></p>\n\n<p><strong>Explanation:</strong></p>\n\n<p><code>intersect(properties[0], properties[1]) = 1</code>, which is less than <code>k</code>. This means there is no edge between <code>properties[0]</code> and <code>properties[1]</code> in the graph.</p>\n</div>\n\n<p>&nbsp;</p>\n<p><strong>Constraints:</strong></p>\n\n<ul>\n\t<li><code>1 &lt;= n == properties.length &lt;= 100</code></li>\n\t<li><code>1 &lt;= m == properties[i].length &lt;= 100</code></li>\n\t<li><code>1 &lt;= properties[i][j] &lt;= 100</code></li>\n\t<li><code>1 &lt;= k &lt;= m</code></li>\n</ul>\n",
"translatedTitle": "属性图",
"translatedContent": "<p>给你一个二维整数数组 <code>properties</code>,其维度为 <code>n x m</code>,以及一个整数 <code>k</code>。</p>\n\n<p>定义一个函数 <code>intersect(a, b)</code>,它返回数组 <code>a</code> 和 <code>b</code> 中<strong> 共有的不同整数的数量 </strong>。</p>\n\n<p>构造一个 <strong>无向图</strong>,其中每个索引 <code>i</code> 对应 <code>properties[i]</code>。如果且仅当 <code>intersect(properties[i], properties[j]) &gt;= k</code>(其中 <code>i</code> 和 <code>j</code> 的范围为 <code>[0, n - 1]</code> 且 <code>i != j</code>),节点 <code>i</code> 和节点 <code>j</code> 之间有一条边。</p>\n\n<p>返回结果图中<strong> 连通分量 </strong>的数量。</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\">properties = [[1,2],[1,1],[3,4],[4,5],[5,6],[7,7]], k = 1</span></p>\n\n<p><strong>输出:</strong> <span class=\"example-io\">3</span></p>\n\n<p><strong>解释:</strong></p>\n\n<p>生成的图有 3 个连通分量:</p>\n\n<p><img src=\"https://pic.leetcode.cn/1742665594-CDVPWz-image.png\" style=\"width: 279px; height: 171px;\" /></p>\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\">properties = [[1,2,3],[2,3,4],[4,3,5]], k = 2</span></p>\n\n<p><strong>输出:</strong> <span class=\"example-io\">1</span></p>\n\n<p><strong>解释:</strong></p>\n\n<p>生成的图有 1 个连通分量:</p>\n\n<p><img alt=\"\" src=\"https://pic.leetcode.cn/1742665565-NzYlYH-screenshot-from-2025-02-27-23-58-34.png\" style=\"width: 219px; height: 171px;\" /></p>\n</div>\n\n<p><strong class=\"example\">示例 3</strong></p>\n\n<div class=\"example-block\">\n<p><strong>输入:</strong> <span class=\"example-io\">properties = [[1,1],[1,1]], k = 2</span></p>\n\n<p><strong>输出:</strong> <span class=\"example-io\">2</span></p>\n\n<p><strong>解释:</strong></p>\n\n<p><code>intersect(properties[0], properties[1]) = 1</code>,小于 <code>k</code>。因此在图中 <code>properties[0]</code> 和 <code>properties[1]</code> 之间没有边。</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 == properties.length &lt;= 100</code></li>\n\t<li><code>1 &lt;= m == properties[i].length &lt;= 100</code></li>\n\t<li><code>1 &lt;= properties[i][j] &lt;= 100</code></li>\n\t<li><code>1 &lt;= k &lt;= m</code></li>\n</ul>\n",
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"How can we optimally find the intersection of two arrays? One way is to use <code>len(set(a) & set(b))</code>.",
"For connected components, think about using DFS, BFS, or DSU."
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