<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 {
public:
    int minMalwareSpread(vector<vector<int>>& graph, vector<int>& initial) {
        int n = graph.size();
        int minInfections = n; // initialize with the maximum possible infections
        int nodeToRemove = initial[0]; // initialize with the first infected node

        sort(initial.begin(), initial.end()); // sort for deterministic output

        for (int removedNode : initial) {
            int infectionCount = 0; // count of infected nodes for this simulation
            queue<int> q;
            unordered_set<int> visited; // track visited nodes during BFS

            // add initially infected nodes to the queue (except the removed node)
            for (int infectedNode : initial) {
                if (infectedNode != removedNode) {
                    q.push(infectedNode);
                    visited.insert(infectedNode);
                }
            }

            // perform bfs to simulate malware spread
            while (!q.empty()) {
                int currNode = q.front(); 
                q.pop();
                infectionCount++;

                // explore neighbors
                for (int neighbor = 0; neighbor < n; neighbor++) {
                    // if connected, not visited, and not the removed node
                    if (graph[currNode][neighbor] && !visited.count(neighbor) && neighbor != removedNode) { 
                        visited.insert(neighbor);
                        q.push(neighbor);
                    }
                }
            }

            // update minInfections and nodeToRemove if we find a better result
            if (infectionCount < minInfections) {
                minInfections = infectionCount;
                nodeToRemove = removedNode;
            }
        }

        return nodeToRemove; // return the node to remove
    }
};
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