<p>You are given a network of <code>n</code> nodes represented as an <code>n x n</code> adjacency matrix <code>graph</code>, where the <code>i<sup>th</sup></code> node is directly connected to the <code>j<sup>th</sup></code> node if <code>graph[i][j] == 1</code>.</p>

<p>Some nodes <code>initial</code> are initially infected by malware. Whenever two nodes are directly connected, and at least one of those two nodes is infected by malware, both nodes will be infected by malware. This spread of malware will continue until no more nodes can be infected in this manner.</p>

<p>Suppose <code>M(initial)</code> is the final number of nodes infected with malware in the entire network after the spread of malware stops.</p>

<p>We will remove <strong>exactly one node</strong> from <code>initial</code>, <strong>completely removing it and any connections from this node to any other node</strong>.</p>

<p>Return the node that, if removed, would minimize <code>M(initial)</code>. If multiple nodes could be removed to minimize <code>M(initial)</code>, return such a node with <strong>the smallest index</strong>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<pre><strong>Input:</strong> graph = [[1,1,0],[1,1,0],[0,0,1]], initial = [0,1]
<strong>Output:</strong> 0
</pre><p><strong class="example">Example 2:</strong></p>
<pre><strong>Input:</strong> graph = [[1,1,0],[1,1,1],[0,1,1]], initial = [0,1]
<strong>Output:</strong> 1
</pre><p><strong class="example">Example 3:</strong></p>
<pre><strong>Input:</strong> graph = [[1,1,0,0],[1,1,1,0],[0,1,1,1],[0,0,1,1]], initial = [0,1]
<strong>Output:</strong> 1
</pre>
<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>n == graph.length</code></li>
	<li><code>n == graph[i].length</code></li>
	<li><code>2 &lt;= n &lt;= 300</code></li>
	<li><code>graph[i][j]</code> is <code>0</code> or <code>1</code>.</li>
	<li><code>graph[i][j] == graph[j][i]</code></li>
	<li><code>graph[i][i] == 1</code></li>
	<li><code>1 &lt;= initial.length &lt;&nbsp;n</code></li>
	<li><code>0 &lt;= initial[i] &lt;= n - 1</code></li>
	<li>All the integers in <code>initial</code> are <strong>unique</strong>.</li>
</ul>

from typing import List

class Solution:
    def minMalwareSpread(self, graph: List[List[int]], initial: List[int]) -> int:
        def dfs(node: int, visited: set, excluded_node: int):
            for neighbor, is_connected in enumerate(graph[node]):
                if is_connected == 1 and neighbor not in visited and neighbor != excluded_node:
                    visited.add(neighbor)
                    dfs(neighbor, visited, excluded_node)
        
        # Sort the initial list to ensure smallest index is preferred in case of ties
        initial.sort()
        min_infected = float('inf')
        best_node = initial[0]
        
        for node_to_remove in initial:
            visited = set()
            for start_node in initial:
                if start_node == node_to_remove:
                    continue
                if start_node not in visited:
                    visited.add(start_node)
                    dfs(start_node, visited, node_to_remove)
            infected_count = len(visited)
            if infected_count < min_infected:
                min_infected = infected_count
                best_node = node_to_remove
        
        return best_node
22200