<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. We will remove <strong>exactly one node</strong> from <code>initial</code>.</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>Note that if a node was removed from the <code>initial</code> list of infected nodes, it might still be infected later due to the malware spread.</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 = [[1,0,0],[0,1,0],[0,0,1]], initial = [0,2]
<strong>Output:</strong> 0
</pre><p><strong class="example">Example 3:</strong></p>
<pre><strong>Input:</strong> graph = [[1,1,1],[1,1,1],[1,1,1]], initial = [1,2]
<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;= 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>

import collections

class Solution:
    def minMalwareSpread(self, graph: list[list[int]], initial: list[int]) -> int:
        colors = {}
        N = len(graph)
        def dfs(node, color):
            if node in colors:
                return
            # color the current node
            colors[node] = color
            # color neighbors
            # if didn't already color the node and the node is adjacent
            for nei, adj in enumerate(graph[node]):
                if nei not in colors and adj:
                    dfs(nei, color)

        # call dfs to fill out colors
        color = 0
        for node in range(N):
            if node not in colors:
                dfs(node, color)
            color += 1

        # count the size of each color
        # color_sizes = {color: count of that color}
        color_sizes = collections.Counter(colors.values())
        print(colors, color_sizes)

        # find the unique colors from initial array
        # if two nodes in the initial array have the same color, removing either will do nothing
        unique_colors_counter = collections.defaultdict(int)
        unique_colors_set = set()
        for node in initial:
            node_color = colors[node]
            unique_colors_counter[node_color] += 1
            if unique_colors_counter[node_color] == 1:
                unique_colors_set.add(node_color)
            elif unique_colors_counter[node_color] > 1 and node_color in unique_colors_set:
                unique_colors_set.remove(node_color)

        # if no unique colors, return the smallest index
        if len(unique_colors_set) == 0:
            return min(initial)

        res = -1
        maxSize = -1
        for node in initial:
            color = colors[node]
            if color not in unique_colors_set:
                continue
            size = color_sizes[color]
            if size > maxSize:
                maxSize = size
                res = node
            elif size == maxSize:
                res = min(res, node)

        return res
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