Properties Graph
<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>

<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>

<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>

<p>Return the number of <strong>connected components</strong> in the resulting graph.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<div class="example-block">
<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>

<p><strong>Output:</strong> <span class="example-io">3</span></p>

<p><strong>Explanation:</strong></p>

<p>The graph formed has 3 connected components:</p>

<p><img height="171" src="https://fastly.jsdelivr.net/gh/doocs/leetcode@main/solution/3400-3499/3493.Properties%20Graph/images/image.png" width="279" /></p>
</div>

<p><strong class="example">Example 2:</strong></p>

<div class="example-block">
<p><strong>Input:</strong> <span class="example-io">properties = [[1,2,3],[2,3,4],[4,3,5]], k = 2</span></p>

<p><strong>Output:</strong> <span class="example-io">1</span></p>

<p><strong>Explanation:</strong></p>

<p>The graph formed has 1 connected component:</p>

<p><img alt="" src="https://fastly.jsdelivr.net/gh/doocs/leetcode@main/solution/3400-3499/3493.Properties%20Graph/images/screenshot-from-2025-02-27-23-58-34.png" style="width: 219px; height: 171px;" /></p>
</div>

<p><strong class="example">Example 3:</strong></p>

<div class="example-block">
<p><strong>Input:</strong> <span class="example-io">properties = [[1,1],[1,1]], k = 2</span></p>

<p><strong>Output:</strong> <span class="example-io">2</span></p>

<p><strong>Explanation:</strong></p>

<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>
</div>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= n == properties.length &lt;= 100</code></li>
	<li><code>1 &lt;= m == properties[i].length &lt;= 100</code></li>
	<li><code>1 &lt;= properties[i][j] &lt;= 100</code></li>
	<li><code>1 &lt;= k &lt;= m</code></li>
</ul>
Depth-First Search; Breadth-First Search; Union Find; Graph; Array; Hash Table
class Solution:
    def numberOfComponents(self, properties: List[List[int]], k: int) -> int:
        def dfs(i: int) -> None:
            vis[i] = True
            for j in g[i]:
                if not vis[j]:
                    dfs(j)

        n = len(properties)
        ss = list(map(set, properties))
        g = [[] for _ in range(n)]
        for i, s1 in enumerate(ss):
            for j in range(i):
                s2 = ss[j]
                if len(s1 & s2) >= k:
                    g[i].append(j)
                    g[j].append(i)
        ans = 0
        vis = [False] * n
        for i in range(n):
            if not vis[i]:
                dfs(i)
                ans += 1
        return ans
