<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:
    void dfs(int node, vector<vector<int>> &adjList, vector<bool> &visited, int &infectionCount) {
        visited[node] = true; // mark the current node as visited
        infectionCount++; 

        // explore all neighbors of the current node
        for (int neighbor : adjList[node]) {
            if (!visited[neighbor]) { // if the neighbor is not visited
                dfs(neighbor, adjList, visited, infectionCount);
            }
        }
    }

    int minMalwareSpread(vector<vector<int>>& graph, vector<int>& initial) {
        int n = graph.size();
        int minInfected = n + 1; // initialize with a value greater than the maximum possible
        int nodeToRemove = 0; // initialize the node to remove

        vector<vector<int>> adjList(n); // adjacency list representation of the graph
        // build the adjacency list
        for (int i = 0; i < n; i++) {
            for (int j = i + 1; j < n; j++) {
                if (graph[i][j]) {
                    adjList[i].push_back(j);
                    adjList[j].push_back(i);
                }
            }
        }

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

        // simulate removing each infected node
        for (int removedNode : initial) {
            vector<bool> visited(n, false); // track visited nodes during dfs
            visited[removedNode] = true; // mark the removed node as visited
            int infectionCount = 0; 

            // perform dfs from each remaining initially infected node
            for (int infectedNode : initial) {
                if (infectedNode != removedNode && !visited[infectedNode]) {
                    dfs(infectedNode, adjList, visited, infectionCount);
                }
            }

            // update minInfected and nodeToRemove if a smaller count is found
            if (infectionCount < minInfected) {
                minInfected = infectionCount;
                nodeToRemove = removedNode;
            }
        }
        
        return nodeToRemove; 
    }
};
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