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
func numberOfComponents(properties [][]int, k int) (ans int) {
	n := len(properties)
	ss := make([]map[int]struct{}, n)
	g := make([][]int, n)

	for i := 0; i < n; i++ {
		ss[i] = make(map[int]struct{})
		for _, x := range properties[i] {
			ss[i][x] = struct{}{}
		}
	}

	for i := 0; i < n; i++ {
		for j := 0; j < i; j++ {
			cnt := 0
			for x := range ss[i] {
				if _, ok := ss[j][x]; ok {
					cnt++
				}
			}
			if cnt >= k {
				g[i] = append(g[i], j)
				g[j] = append(g[j], i)
			}
		}
	}

	vis := make([]bool, n)
	var dfs func(int)
	dfs = func(i int) {
		vis[i] = true
		for _, j := range g[i] {
			if !vis[j] {
				dfs(j)
			}
		}
	}

	for i := 0; i < n; i++ {
		if !vis[i] {
			dfs(i)
			ans++
		}
	}
	return
}
