Number of Possible Sets of Closing Branches
<p>There is a company with <code>n</code> branches across the country, some of which are connected by roads. Initially, all branches are reachable from each other by traveling some roads.</p>

<p>The company has realized that they are spending an excessive amount of time traveling between their branches. As a result, they have decided to close down some of these branches (<strong>possibly none</strong>). However, they want to ensure that the remaining branches have a distance of at most <code>maxDistance</code> from each other.</p>

<p>The <strong>distance</strong> between two branches is the <strong>minimum</strong> total traveled length needed to reach one branch from another.</p>

<p>You are given integers <code>n</code>, <code>maxDistance</code>, and a <strong>0-indexed</strong> 2D array <code>roads</code>, where <code>roads[i] = [u<sub>i</sub>, v<sub>i</sub>, w<sub>i</sub>]</code> represents the <strong>undirected</strong> road between branches <code>u<sub>i</sub></code> and <code>v<sub>i</sub></code> with length <code>w<sub>i</sub></code>.</p>

<p>Return <em>the number of possible sets of closing branches, so that any branch has a distance of at most </em><code>maxDistance</code><em> from any other</em>.</p>

<p><strong>Note</strong> that, after closing a branch, the company will no longer have access to any roads connected to it.</p>

<p><strong>Note</strong> that, multiple roads are allowed.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="" src="https://fastly.jsdelivr.net/gh/doocs/leetcode@main/solution/2900-2999/2959.Number%20of%20Possible%20Sets%20of%20Closing%20Branches/images/example11.png" style="width: 221px; height: 191px;" />
<pre>
<strong>Input:</strong> n = 3, maxDistance = 5, roads = [[0,1,2],[1,2,10],[0,2,10]]
<strong>Output:</strong> 5
<strong>Explanation:</strong> The possible sets of closing branches are:
- The set [2], after closing, active branches are [0,1] and they are reachable to each other within distance 2.
- The set [0,1], after closing, the active branch is [2].
- The set [1,2], after closing, the active branch is [0].
- The set [0,2], after closing, the active branch is [1].
- The set [0,1,2], after closing, there are no active branches.
It can be proven, that there are only 5 possible sets of closing branches.
</pre>

<p><strong class="example">Example 2:</strong></p>
<img alt="" src="https://fastly.jsdelivr.net/gh/doocs/leetcode@main/solution/2900-2999/2959.Number%20of%20Possible%20Sets%20of%20Closing%20Branches/images/example22.png" style="width: 221px; height: 241px;" />
<pre>
<strong>Input:</strong> n = 3, maxDistance = 5, roads = [[0,1,20],[0,1,10],[1,2,2],[0,2,2]]
<strong>Output:</strong> 7
<strong>Explanation:</strong> The possible sets of closing branches are:
- The set [], after closing, active branches are [0,1,2] and they are reachable to each other within distance 4.
- The set [0], after closing, active branches are [1,2] and they are reachable to each other within distance 2.
- The set [1], after closing, active branches are [0,2] and they are reachable to each other within distance 2.
- The set [0,1], after closing, the active branch is [2].
- The set [1,2], after closing, the active branch is [0].
- The set [0,2], after closing, the active branch is [1].
- The set [0,1,2], after closing, there are no active branches.
It can be proven, that there are only 7 possible sets of closing branches.
</pre>

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

<pre>
<strong>Input:</strong> n = 1, maxDistance = 10, roads = []
<strong>Output:</strong> 2
<strong>Explanation:</strong> The possible sets of closing branches are:
- The set [], after closing, the active branch is [0].
- The set [0], after closing, there are no active branches.
It can be proven, that there are only 2 possible sets of closing branches.
</pre>

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

<ul>
	<li><code>1 &lt;= n &lt;= 10</code></li>
	<li><code>1 &lt;= maxDistance &lt;= 10<sup>5</sup></code></li>
	<li><code>0 &lt;= roads.length &lt;= 1000</code></li>
	<li><code>roads[i].length == 3</code></li>
	<li><code>0 &lt;= u<sub>i</sub>, v<sub>i</sub> &lt;= n - 1</code></li>
	<li><code>u<sub>i</sub> != v<sub>i</sub></code></li>
	<li><code>1 &lt;= w<sub>i</sub> &lt;= 1000</code></li>
	<li>All branches are reachable from each other by traveling some roads.</li>
</ul>
Bit Manipulation; Graph; Enumeration; Shortest Path; Heap (Priority Queue)
func numberOfSets(n int, maxDistance int, roads [][]int) (ans int) {
	for mask := 0; mask < 1<<n; mask++ {
		g := make([][]int, n)
		for i := range g {
			g[i] = make([]int, n)
			for j := range g[i] {
				g[i][j] = 1 << 29
			}
		}
		for _, e := range roads {
			u, v, w := e[0], e[1], e[2]
			if mask>>u&1 == 1 && mask>>v&1 == 1 {
				g[u][v] = min(g[u][v], w)
				g[v][u] = min(g[v][u], w)
			}
		}
		for k := 0; k < n; k++ {
			if mask>>k&1 == 1 {
				g[k][k] = 0
				for i := 0; i < n; i++ {
					for j := 0; j < n; j++ {
						g[i][j] = min(g[i][j], g[i][k]+g[k][j])
					}
				}
			}
		}
		ok := 1
		for i := 0; i < n && ok == 1; i++ {
			for j := 0; j < n && ok == 1; j++ {
				if mask>>i&1 == 1 && mask>>j&1 == 1 && g[i][j] > maxDistance {
					ok = 0
				}
			}
		}
		ans += ok
	}
	return
}