<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>

class Solution:
    def minMalwareSpread(self, graph: List[List[int]], initial: List[int]) -> int:
        n = len(graph)
        initial_set = set(initial)
        # List to keep track of initial nodes that can reach each node
        infected_by = [set() for _ in range(n)]

        for node in initial:
            visited = [False] * n
            queue = [node]
            visited[node] = True
            while queue:
                u = queue.pop()
                for v in range(n):
                    if graph[u][v] == 1 and not visited[v]:
                        if v in initial_set:
                            continue  # Skip other initial nodes
                        infected_by[v].add(node)
                        visited[v] = True
                        queue.append(v)
        
        # Count unique infections for each initial node
        contribution = [0] * n
        for v in range(n):
            if len(infected_by[v]) == 1:
                u = infected_by[v].pop()
                contribution[u] += 1
        
        # Select the node to remove
        max_contrib = -1
        res = min(initial)
        for node in sorted(initial):
            if contribution[node] > max_contrib:
                max_contrib = contribution[node]
                res = node
        return res

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