In a network of nodes, each node i is directly connected to another node j if and only if graph[i][j] = 1.
Some nodes initial 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.
Suppose M(initial) is the final number of nodes infected with malware in the entire network, after the spread of malware stops.
We will remove one node from the initial list.  Return the node that if removed, would minimize M(initial).  If multiple nodes could be removed to minimize M(initial), return such a node with the smallest index.
Note that if a node was removed from the initial list of infected nodes, it may still be infected later as a result of the malware spread.
 


Example 1:
Input: graph = [[1,1,0],[1,1,0],[0,0,1]], initial = [0,1]
Output: 0

Example 2:
Input: graph = [[1,0,0],[0,1,0],[0,0,1]], initial = [0,2]
Output: 0

Example 3:
Input: graph = [[1,1,1],[1,1,1],[1,1,1]], initial = [1,2]
Output: 1

 
Note:

1 < graph.length = graph[0].length <= 300
0 <= graph[i][j] == graph[j][i] <= 1
graph[i][i] == 1
1 <= initial.length <= graph.length
0 <= initial[i] < graph.length

Source: leetcode | Difficulty: MEDIUM
Tags: Matrices

Data structures

Graph traversal

Spanning trees

Starter code: class Solution:
    def minMalwareSpread(self, graph: List[List[int]], initial: List[int]) -> int:
        

Solutions:
class Solution(object):

	def minMalwareSpread(self, graph, initial):
		N = len(graph)
		colors = {}
		c = 0

		def dfs(node, color):
			colors[node] = color
			for (nei, adj) in enumerate(graph[node]):
				if adj and nei not in colors:
					dfs(nei, color)
		for node in range(N):
			if node not in colors:
				dfs(node, c)
				c += 1
		size = collections.Counter(colors.values())
		color_count = collections.Counter()
		for node in initial:
			color_count[colors[node]] += 1
		ans = float('inf')
		for x in initial:
			c = colors[x]
			if color_count[c] == 1:
				if ans == float('inf'):
					ans = x
				elif size[c] > size[colors[ans]]:
					ans = x
				elif size[c] == size[colors[ans]] and x < ans:
					ans = x
		return ans if ans < float('inf') else min(initial)


class Solution:

	def minMalwareSpread(self, graph: List[List[int]], initial: List[int]) -> int:

		def dfs(node, vis):
			for connect in range(len(graph[node])):
				if graph[node][connect] == 1 and connect not in vis:
					vis.add(connect)
					dfs(connect, vis)
		init = set(initial)
		total_vis = set()
		(del_node, subgraph_len) = (min(initial), 0)
		for node in range(len(graph)):
			if node not in total_vis:
				vis = set([node])
				dfs(node, vis)
				infect = vis & init
				if len(infect) == 1:
					if len(vis) > subgraph_len or (len(vis) == subgraph_len and list(infect)[0] < del_node):
						(del_node, subgraph_len) = (list(infect)[0], len(vis))
				total_vis |= vis
		return del_node


class Solution:

	def minMalwareSpread(self, graph: List[List[int]], initial: List[int]) -> int:

		def dfs(node, vis):
			for v in range(len(graph[node])):
				if graph[node][v] == 1 and v not in vis:
					vis.add(v)
					dfs(v, vis)
		s = set(initial)
		t_vis = set()
		(del_node, subgraph_len) = (min(initial), 0)
		for node in range(len(graph)):
			if node not in t_vis:
				vis = set([node])
				dfs(node, vis)
				infect = vis & s
				if len(infect) == 1:
					if len(vis) > subgraph_len or (len(vis) == subgraph_len and list(infect)[0] < del_node):
						(del_node, subgraph_len) = (list(infect)[0], len(vis))
				t_vis |= vis
		return del_node


from itertools import count
from collections import Counter

class Solution:

	def minMalwareSpread(self, graph: List[List[int]], initial: List[int]) -> int:
		colors = dict()
		c = count()

		def dfs(node, color):
			colors[node] = color
			for (nei, adj) in enumerate(graph[node]):
				if adj and nei not in colors:
					dfs(nei, color)
		for node in range(len(graph)):
			if node not in colors:
				dfs(node, next(c))
		size = Counter(list(colors.values()))
		malware_count = Counter()
		for node in initial:
			malware_count[colors[node]] += 1
		ans = None
		ans_nodes = 0
		for x in initial:
			c = colors[x]
			if malware_count[c] != 1:
				continue
			if size[c] > ans_nodes:
				ans = x
				ans_nodes = size[c]
			elif size[c] == ans_nodes:
				ans = min(ans, x)
		return ans if ans else min(initial)


class Solution:

	def minMalwareSpread(self, graph: List[List[int]], initial: List[int]) -> int:
		if len(graph) == 0:
			return 0
		g = dict()
		for i in range(len(graph)):
			for j in range(len(graph[i])):
				if graph[i][j]:
					if i in g:
						g[i].append(j)
					else:
						g[i] = [j]
		groups = []
		initialSet = set(initial)
		numOfNodes = [0] * len(graph)
		for (v, e) in list(g.items()):
			if v not in initialSet:
				continue
			num = 1
			initialSet.remove(v)
			group = [v]
			stack = e
			visited = {v}
			while len(stack) != 0:
				vertex = stack.pop()
				if vertex not in visited:
					if vertex in initialSet:
						initialSet.remove(vertex)
						group.append(vertex)
					stack.extend(g[vertex])
					visited.add(vertex)
					num += 1
			groups.append(group)
			numOfNodes[v] = num
		canRemove = set([group[0] for group in groups if len(group) == 1])
		if len(canRemove) == 0:
			return min(initial)
		result = -1
		for vertex in initial:
			if vertex in canRemove and (result == -1 or numOfNodes[vertex] > numOfNodes[result]):
				result = vertex
			elif vertex in canRemove and numOfNodes[vertex] == numOfNodes[result] and (vertex < result):
				result = vertex
		return result


class Solution:

	def minMalwareSpread(self, graph, initial):

		def dfs(i):
			nodes.add(i)
			for j in range(len(graph[i])):
				if graph[i][j] and j not in nodes:
					dfs(j)
		rank = {}
		initial = set(initial)
		for node in sorted(initial):
			nodes = set()
			dfs(node)
			rank[node] = nodes
		print(rank)
		passed = []
		for (k, v) in list(rank.items()):
			count = 0
			for i in initial:
				if i in v:
					count += 1
			if count <= 1:
				passed.append((k, len(v)))
		passed.sort(key=lambda x: x[1], reverse=True)
		if len(passed) == 0:
			return min(initial)
		else:
			return passed[0][0]


class Solution:

	def minMalwareSpread(self, graph: List[List[int]], initial: List[int]) -> int:

		def dfs(i):
			nodes.add(i)
			for j in range(len(graph[i])):
				if graph[i][j] and j not in nodes:
					dfs(j)
		(rank, initial) = (collections.defaultdict(list), set(initial))
		for node in sorted(initial):
			nodes = set()
			dfs(node)
			if nodes & initial == {node}:
				rank[len(nodes)].append(node)
		return rank[max(rank)][0] if rank else min(initial)


class Solution:

	def minMalwareSpread(self, graph: List[List[int]], initial: List[int]) -> int:
		infected_nodes = set(initial)
		max_infected = len(graph)
		node_to_remove = initial[0]
		for infected_node in initial:
			infected_nodes.remove(infected_node)
			infected = set()
			for node in infected_nodes:
				self.dfs(node, graph, infected)
			infected_nodes.add(infected_node)
			if len(infected) < max_infected or (len(infected) == max_infected and infected_node < node_to_remove):
				node_to_remove = infected_node
				max_infected = len(infected)
		return node_to_remove

	def dfs(self, node, graph, infected):
		infected.add(node)
		for (col, val) in enumerate(graph[node]):
			if val == 1 and col not in infected:
				self.dfs(col, graph, infected)


class Solution:

	def minMalwareSpread(self, graph: List[List[int]], initial: List[int]) -> int:
		init = set(initial)
		total_visited = set()
		(res, max_subgraph_len) = (min(initial), 0)
		for node in range(len(graph)):
			if node not in total_visited:
				visited = set([node])
				self.dfsConnected(graph, node, visited)
				infected = visited & init
				if len(infected) == 1:
					if len(visited) > max_subgraph_len or (len(visited) == max_subgraph_len and min(infected) < res):
						(res, max_subgraph_len) = (min(infected), len(visited))
				total_visited |= visited
		return res

	def dfsConnected(self, graph, node, visited):
		for neighbor in range(len(graph[node])):
			if graph[node][neighbor] == 1 and neighbor not in visited:
				visited.add(neighbor)
				self.dfsConnected(graph, neighbor, visited)


class Solution:

	def minMalwareSpread(self, graph: List[List[int]], initial: List[int]) -> int:
		if len(initial) == len(graph):
			m = 0
			r = initial[0]
			for i in initial:
				if m < sum((x == 0 for x in graph[i])):
					m = sum((x == 0 for x in graph[i]))
					r = i
			return r
		d = collections.defaultdict(list)
		for init in initial:
			q = collections.deque()
			q.append(init)
			visit = set()
			visit.add(init)
			while q:
				virus = q.popleft()
				for i in range(len(graph[virus])):
					if graph[virus][i] == 0 or i in visit:
						continue
					visit.add(i)
					d[i].append(init)
					q.append(i)
		res = [0] * len(graph)
		for m in d:
			if len(d[m]) == 1:
				res[d[m][0]] += 1
		print(d)
		if max(res) == 0:
			return min(initial)
		return res.index(max(res))


class Solution:

	def minMalwareSpread(self, graph: List[List[int]], initial: List[int]) -> int:
		initial.sort()
		visited = []
		result = [-1, 0]
		for i in range(len(graph)):
			if i in visited:
				continue
			else:
				temp = [-1, 0]
				stack = [i]
				visited.append(i)
				stack_num = 1
				while stack:
					index = stack.pop(0)
					if index in initial:
						if temp[0] == -1:
							temp[0] = index
						temp[1] += 1
					for j in range(len(graph[index])):
						if graph[index][j] == 1 and j not in visited:
							stack.append(j)
							stack_num += 1
							visited.append(j)
				if temp[1] == 1:
					if result[1] < stack_num:
						result[0] = temp[0]
						result[1] = stack_num
		return result[0] if result[0] != -1 else initial[0]


import math
import queue

class Solution:

	def minMalwareSpread(self, graph: List[List[int]], initial: List[int]) -> int:
		if len(initial) == 0:
			return 0
		best = None
		best_val = math.inf
		initial_set = set(initial)
		for index in initial:
			initial_set.remove(index)
			seen = set()
			Q = queue.Queue()
			for elt in initial_set:
				seen.add(elt)
				Q.put(elt)
			while not Q.empty():
				u = Q.get()
				for (i, v) in enumerate(graph[u]):
					if v == 0 or i in seen:
						continue
					seen.add(i)
					Q.put(i)
			if len(seen) < best_val:
				best_val = len(seen)
				best = index
			elif len(seen) == best_val and index < best:
				best = index
			initial_set.add(index)
		return best


class Solution:

	def minMalwareSpread(self, graph: List[List[int]], initial: List[int]) -> int:
		heap = []
		sizes = {}
		component = 0
		for i in initial:
			if graph[i][i] < 0:
				heappush(heap, (-sizes[component], i, graph[i][i]))
				continue
			queue = deque([i])
			size = 0
			component = component - 1
			while len(queue) > 0:
				current = queue.popleft()
				if graph[current][current] == 1:
					size = size + 1
					graph[current][current] = component
					queue.extend((i for (i, x) in enumerate(graph[current]) if x == 1))
			heappush(heap, (-size, i, component))
			sizes[component] = size
		return self.select(heap)

	def select(self, heap):
		if len(heap) == 1:
			return heap[0][1]
		res = heappop(heap)
		others = []
		while len(heap) > 0 and res[0] == heap[0][0] and (res[2] == heap[0][2]):
			others.append(heappop(heap))
		if len(others) == 1 and len(heap) == 0 or len(others) == 0:
			return res[1]
		if len(heap) == 0:
			return res[1]
		return self.select(heap)


import heapq

class Solution:

	def minMalwareSpread(self, graph: List[List[int]], initial: List[int]) -> int:
		nodes = set(initial)
		useless = set()
		best = 0
		initial.sort()
		index = initial[0]

		def dfs(start):
			count = 0
			stack = [start]
			visited = set()
			while stack:
				curr = stack.pop()
				if curr in visited:
					continue
				if curr != start and curr in nodes:
					useless.add(curr)
					useless.add(start)
				visited.add(curr)
				count += 1
				for i in range(len(graph[curr])):
					if graph[curr][i]:
						stack.append(i)
			return count
		for i in initial:
			g = dfs(i)
			if i not in useless:
				if g > best:
					best = g
					index = i
		return index


class Solution:

	def minMalwareSpread(self, graph: List[List[int]], initial: List[int]) -> int:
		numNodes = len(graph)
		minSpread = float('inf')
		minNode = None
		initial.sort()
		for i in initial:
			visited = set()
			for j in initial:
				if j != i:
					self.helper(graph, j, visited)
			if len(visited) < minSpread:
				minSpread = len(visited)
				minNode = i
		return minNode

	def helper(self, graph, curr, visited):
		if curr in visited:
			return
		edges = graph[curr]
		visited.add(curr)
		for i in range(len(edges)):
			if graph[curr][i] == 1:
				self.helper(graph, i, visited)


class Solution:

	def minMalwareSpread(self, graph: List[List[int]], initial: List[int]) -> int:
		visited = [False] * len(graph)
		sizes = [0] * len(graph)
		for node in range(len(graph)):
			if visited[node]:
				continue
			vertices = []
			numOfInitials = self.dfs(graph, node, visited, vertices, initial)
			size = len(vertices)
			for i in vertices:
				sizes[i] = size if numOfInitials < 2 else 0
		maxSpread = -1
		maxNode = -1
		for i in initial:
			print(i)
			if sizes[i] > maxSpread:
				maxSpread = sizes[i]
				maxNode = i
			elif sizes[i] == maxSpread:
				maxNode = min(maxNode, i)
		return maxNode

	def dfs(self, graph, node, visited, vertices, initial):
		initials = 0
		if visited[node]:
			return initials
		vertices.append(node)
		visited[node] = True
		if node in initial:
			initials += 1
		for i in range(len(graph[node])):
			if graph[node][i] == 1:
				initials += self.dfs(graph, i, visited, vertices, initial)
		return initials


class Solution:

	def calcConnectedNodes(self, graph, node):
		visited = set()
		toVisit = []
		toVisit.append(node)
		while len(toVisit) != 0:
			curNode = toVisit.pop()
			if curNode in visited:
				continue
			visited.add(curNode)
			for i in range(len(graph[curNode])):
				if graph[curNode][i] == 1:
					toVisit.append(i)
		return visited

	def minMalwareSpread(self, graph: List[List[int]], initial: List[int]) -> int:
		initialSet = set(initial)
		maxNodesConnected = -1
		nodeToRemove = -1
		for node in initial:
			connectedNodes = self.calcConnectedNodes(graph, node)
			intersected = connectedNodes.intersection(initialSet)
			if len(intersected) >= 2:
				continue
			if maxNodesConnected == -1 or len(connectedNodes) > maxNodesConnected or (len(connectedNodes) == maxNodesConnected and node < nodeToRemove):
				nodeToRemove = node
				maxNodesConnected = len(connectedNodes)
		if nodeToRemove == -1:
			return min(initial)
		return nodeToRemove


from collections import defaultdict

class Solution:

	def minMalwareSpread(self, graph: List[List[int]], initial: List[int]) -> int:
		edges = defaultdict(list)
		for i in range(len(graph)):
			for j in range(len(graph[i])):
				if graph[i][j] == 1:
					edges[i].append(j)
		colors = defaultdict(int)
		nodes_in_colors = defaultdict(int)
		color = 1
		for node in initial:
			if colors[node] == 0:
				colors[node] = color
			else:
				continue
			stack = [node]
			visited = set()
			curr_infected = 0
			while stack:
				curr = stack.pop()
				curr_infected += 1
				for neigh in edges[curr]:
					if neigh not in visited:
						stack.append(neigh)
						visited.add(neigh)
						colors[neigh] = color
			nodes_in_colors[color] = curr_infected
			color += 1
		initial_color = defaultdict(list)
		for node in initial:
			initial_color[colors[node]].append(node)
		print(initial_color)
		unique_color = defaultdict(int)
		for node in initial:
			unique_color[colors[node]] += 1
		unique = []
		for color in unique_color:
			if unique_color[color] == 1:
				unique.append(initial_color[color][0])
		if len(unique) == 0:
			return min(initial)
		max_infected = 0
		min_node = float('inf')
		print(unique)
		for node in unique:
			if nodes_in_colors[colors[node]] >= max_infected:
				max_infected = nodes_in_colors[colors[node]]
				min_node = min(node, min_node)
		return min_node


class Solution:

	def minMalwareSpread(self, graph: List[List[int]], initial: List[int]) -> int:
		d = collections.defaultdict(list)
		initial.sort()
		for i in range(len(graph)):
			for j in range(len(graph[i])):
				if i != j and graph[i][j] == 1:
					d[i].append(j)
				else:
					d[i].append(100)
					d[i].pop()
		print(d)
		infected = set(initial)
		maxinfected = float('inf')
		res = 0
		for i in range(len(initial)):
			self.curr_infected = 0
			infected.remove(initial[i])
			visited = set()
			for item in infected:
				self.dfs(item, d, visited, infected, True)
			print(self.curr_infected)
			if self.curr_infected < maxinfected:
				maxinfected = self.curr_infected
				res = initial[i]
			infected.add(initial[i])
		return res

	def dfs(self, curr, d, visited, infected, original_node):
		if curr in visited:
			return
		if curr in infected and (not original_node):
			return
		original_node = False
		visited.add(curr)
		self.curr_infected += 1
		neighbors = d[curr]
		for next in neighbors:
			self.dfs(next, d, visited, infected, original_node)


class Solution:

	def minMalwareSpread(self, graph, initial):

		def dfs(node, visited):
			if node in initial:
				return 0
			visited.add(node)
			res = 1
			for (nxt_node, v) in enumerate(graph[node]):
				if v == 0 or nxt_node == node:
					continue
				if nxt_node not in visited:
					sub = dfs(nxt_node, visited)
					if sub == 0:
						return 0
					res += sub
			return res
		initial = set(initial)
		res = [-1, 0]
		for n in list(initial):
			initial.discard(n)
			res = max([dfs(n, set()), -n], res)
			initial.add(n)
		return -res[1]

	def minMalwareSpread_I(self, graph, initial):

		def find(x):
			if x != parents[x]:
				parents[x] = find(parents[x])
			return parents[x]

		def union(x, y):
			parents[find(x)] = find(y)
		n = len(graph)
		parents = list(range(n))
		for i in range(n):
			for j in range(i + 1, n):
				if graph[i][j] == 1:
					union(i, j)
		area = collections.Counter((find(i) for i in range(n)))
		malware = collections.Counter((find(i) for i in initial))
		return min(initial, key=lambda i: [(malware[find(i)] == 1) * -area[find(i)], i])

	def minMalwareSpread_II(self, graph: List[List[int]], initial: List[int]) -> int:
		union_mem = {i: i for i in range(len(graph))}
		count = collections.Counter(range(len(graph)))

		def find(vertex):
			if union_mem[vertex] != vertex:
				union_mem[vertex] = find(union_mem[vertex])
			return union_mem[vertex]

		def union(v1, v2):
			(v1f, v2f) = (find(v1), find(v2))
			if v1f != v2f:
				count[v1f] += count[v2f]
				union_mem[v2f] = v1f
		N = len(graph)
		for r in range(N):
			for c in range(N):
				if r != c and graph[r][c] == 1:
					union(r, c)
		groups = collections.defaultdict(list)
		for v1 in initial:
			v1f = find(v1)
			groups[v1f].append(v1)
		return -max(([count[find(v1)], -v1] for v1 in initial if len(groups[find(v1)]) == 1), default=[0, -min(initial)])[1]


from collections import defaultdict

class Solution:

	def minMalwareSpread(self, graph: List[List[int]], initial: List[int]) -> int:
		size = Counter()
		color = defaultdict(int)

		def dfs(node, c):
			color[node] = c
			size[c] += 1
			for (nextNode, val) in enumerate(graph[node]):
				if val and nextNode not in color:
					dfs(nextNode, c)
		c = 0
		for node in range(len(graph)):
			if node not in color:
				dfs(node, c)
				c += 1
		color_count = Counter()
		for node in initial:
			color_count[color[node]] += 1
		ans = -1
		for node in initial:
			c = color[node]
			if color_count[c] == 1:
				if ans == -1:
					ans = node
				elif size[c] > size[color[ans]]:
					ans = node
				elif size[c] == size[color[ans]] and node < ans:
					ans = node
		if ans == -1:
			return min(initial)
		return ans


class Solution:

	def minMalwareSpread(self, graph: List[List[int]], initial: List[int]) -> int:
		minNode = -1
		maxSpread = 0
		for node in initial:
			testInit = initial.copy()
			testInit.remove(node)
			(touch, testSpread) = touchAnyNodes([node], graph, testInit)
			if not touch:
				if testSpread > maxSpread or (testSpread == maxSpread and node < minNode):
					maxSpread = testSpread
					minNode = node
		if maxSpread == 0:
			initial.sort()
			return initial[0]
		return minNode

def touchAnyNodes(visited, graph, infected) -> (bool, int):
	newVisited = visited.copy()
	for node in visited:
		for idx in range(len(graph[node])):
			if graph[node][idx] == 1 and (not idx in visited) and (not idx in newVisited):
				if idx in infected:
					return (True, 0)
				newVisited.append(idx)
	if len(newVisited) == len(visited):
		return (False, len(visited))
	return touchAnyNodes(newVisited, graph, infected)


class Solution(object):

	def minMalwareSpread(self, graph, initial):

		def dfs(node, visited):
			for neighbor in range(len(graph[node])):
				if graph[node][neighbor] == 1 and neighbor not in visited:
					visited.add(neighbor)
					dfs(neighbor, visited)
		(res, max_size) = (min(initial), 0)
		i_set = set(initial)
		total_visited = set()
		for node in range(len(graph)):
			if node not in total_visited:
				visited = {node}
				dfs(node, visited)
				infected = visited & i_set
				if len(infected) == 1:
					if len(visited) > max_size or (len(visited) == max_size and list(infected)[0] < res):
						res = list(infected)[0]
						max_size = len(visited)
				total_visited |= visited
		return res


class Solution:

	def minMalwareSpread(self, graph: List[List[int]], initial: List[int]) -> int:
		parents = {}

		def find(parents, i):
			c = i
			while parents[c] != c:
				c = parents[c]
			parents[i] = c
			return c

		def union(parents, i, j):
			parents[find(parents, i)] = find(parents, j)
		for u in range(len(graph)):
			if u not in parents:
				parents[u] = u
			for v in range(len(graph[u])):
				if v not in parents:
					parents[v] = v
				if graph[u][v] == 1:
					union(parents, u, v)
		malware_count = collections.defaultdict(int)
		for i in initial:
			malware_count[find(parents, i)] += 1
		comp_size = collections.defaultdict(int)
		for k in parents.keys():
			comp_size[find(parents, k)] += 1
		largest_comp = None
		largest_size = 0
		for i in initial:
			k = find(parents, i)
			v = malware_count[k]
			if v == 1:
				if comp_size[k] > largest_size:
					largest_size = comp_size[k]
					largest_comp = [i]
				elif comp_size[k] == largest_size:
					largest_comp.append(i)
		if largest_comp:
			return min(largest_comp)
		return min(initial)


class Solution:

	def minMalwareSpread(self, graph: List[List[int]], initial: List[int]) -> int:
		colors = {}
		c = 0

		def dfs(node, graph, c):
			colors[node] = c
			for (nei, adj) in enumerate(graph[node]):
				if adj and nei not in colors:
					dfs(nei, graph, c)
		for i in range(len(graph)):
			if i not in colors:
				dfs(i, graph, c)
				c += 1
		size = collections.Counter(list(colors.values()))
		init_count = collections.defaultdict(int)
		for node in initial:
			init_count[colors[node]] += 1
		ans = float('inf')
		for x in initial:
			if init_count[colors[x]] == 1:
				if ans == float('inf'):
					ans = x
				elif size[colors[x]] > size[colors[ans]]:
					ans = x
				elif size[colors[x]] == size[colors[ans]] and x < ans:
					ans = x
		return ans if ans != float('inf') else min(initial)


class Solution:

	def minMalwareSpread(self, graph: List[List[int]], initial: List[int]) -> int:
		s = set(initial)
		go_visit = set()
		(del_node, length) = (min(initial), 0)

		def helper(node, visit):
			for i in range(len(graph[node])):
				if graph[node][i] == 1 and i not in visit:
					visit.add(i)
					helper(i, visit)
		for node in range(len(graph)):
			if node not in go_visit:
				visit = set()
				visit.add(node)
				helper(node, visit)
				temp = visit & s
				if len(temp) == 1:
					if length < len(visit) or (length == len(visit) and list(temp)[0] < del_node):
						del_node = list(temp)[0]
						length = len(visit)
				go_visit |= visit
		return del_node


class Solution:

	def minMalwareSpread(self, graph: List[List[int]], initial: List[int]) -> int:

		def method1():
			N = len(graph)
			colors = {}
			c = 0

			def dfs(node, color):
				colors[node] = color
				for (nei, adj) in enumerate(graph[node]):
					if adj == 1 and nei not in colors:
						dfs(nei, color)
			for node in range(N):
				if node not in colors:
					dfs(node, c)
					c += 1
			size = collections.Counter(colors.values())
			color_count = collections.Counter()
			for node in initial:
				color_count[colors[node]] += 1
			ans = float('inf')
			for initial_node in initial:
				c = colors[initial_node]
				if color_count[c] == 1:
					if ans == float('inf'):
						ans = initial_node
					elif size[c] > size[colors[ans]]:
						ans = initial_node
					elif size[c] == size[colors[ans]] and initial_node < ans:
						ans = initial_node
			return ans if ans < float('inf') else min(initial)

		def method2():

			def dfs(node, vis):
				for v in range(len(graph[node])):
					if graph[node][v] == 1 and v not in vis:
						vis.add(v)
						dfs(v, vis)
			s = set(initial)
			seen = set()
			(del_node, subgraph_len) = (min(initial), 0)
			for node in range(len(graph)):
				if node not in seen:
					vis = set([node])
					dfs(node, vis)
					infect = vis & s
					if len(infect) == 1:
						if len(vis) > subgraph_len or (len(vis) == subgraph_len and list(infect)[0] < del_node):
							(del_node, subgraph_len) = (list(infect)[0], len(vis))
					seen |= vis
			return del_node
		return method2()


class DSU:

	def __init__(self):
		self.parent = {}
		self.size = {}

	def find(self, x):
		if x != self.parent[x]:
			self.parent[x] = self.find(self.parent[x])
		return self.parent[x]

	def union(self, x, y):
		(xp, yp) = (self.find(x), self.find(y))
		if xp == yp:
			return False
		if self.size[xp] < self.size[yp]:
			(xp, yp) = (yp, xp)
		self.size[xp] += self.size[yp]
		self.parent[yp] = xp
		return True

	def add_node(self, x):
		self.parent[x] = x
		self.size[x] = 1

class Solution:

	def minMalwareSpread(self, graph: List[List[int]], initial: List[int]) -> int:
		initial.sort()
		edges = []
		for i in range(len(graph)):
			for j in range(i + 1, len(graph[0])):
				if graph[i][j]:
					edges.append([i, j])
		dsu = DSU()
		for i in range(len(graph)):
			dsu.add_node(i)
		for (e1, e2) in edges:
			if e1 != e2:
				dsu.union(e1, e2)
		ans = initial[0]
		m = len(graph) + 1
		for i in initial:
			mt = self.get_max_size(initial, dsu, i)
			if mt < m:
				m = mt
				ans = i
		return ans

	def get_max_size(self, initial, dsu, di):
		x = 0
		parents = set([])
		for i in initial:
			if i != di:
				parents.add(dsu.find(i))
		for n in dsu.parent:
			if dsu.find(n) in parents:
				x += 1
		return x


class Solution:

	def minMalwareSpread(self, graph: List[List[int]], initial: List[int]) -> int:
		sizeComponents = defaultdict(int)
		nodesToComponents = defaultdict(int)
		c = 0

		def dfs(node, c):
			sizeComponents[c] += 1
			nodesToComponents[node] = c
			for neighbor in range(len(graph[node])):
				if graph[node][neighbor] == 1 and node != neighbor:
					if neighbor not in nodesToComponents:
						dfs(neighbor, c)
		for node in range(len(graph)):
			if node not in nodesToComponents:
				dfs(node, c)
				c += 1
		initialComponents = defaultdict(int)
		for node in initial:
			component = nodesToComponents[node]
			initialComponents[component] += 1
		res = float('inf')
		for node in initial:
			component = nodesToComponents[node]
			size = sizeComponents[component]
			if initialComponents[component] == 1:
				if res == float('inf'):
					res = node
				elif size > sizeComponents[nodesToComponents[res]]:
					res = node
				elif size == sizeComponents[nodesToComponents[res]] and node < res:
					res = node
		return res if res < float('inf') else min(initial)


class DisjointSetUnion:

	def __init__(self):
		self._parent = {}
		self._size = {}

	def union(self, a: int, b: int) -> None:
		(a, b) = (self.find(a), self.find(b))
		if a == b:
			return
		if self._size[a] < self._size[b]:
			(a, b) = (b, a)
		self._parent[b] = a
		self._size[a] += self._size[b]

	def find(self, x: int) -> int:
		if x not in self._parent:
			self._parent[x] = x
			self._size[x] = 1
			return x
		while self._parent[x] != x:
			self._parent[x] = self._parent[self._parent[x]]
			x = self._parent[x]
		return self._parent[x]

	def size(self, x: int) -> int:
		return self._size[self.find(x)]

class Solution:

	def minMalwareSpread(self, graph: List[List[int]], initial: List[int]) -> int:
		dsu = DisjointSetUnion()
		for (u, neighborhood) in enumerate(graph):
			for (v, is_connected) in enumerate(neighborhood):
				if is_connected:
					dsu.union(u, v)
		parent_count = collections.Counter((dsu.find(u) for u in initial))
		best_index = best_count = -1
		for index in initial:
			count = dsu.size(index) if parent_count[dsu.find(index)] == 1 else 0
			if count > best_count or (count == best_count and index < best_index):
				(best_index, best_count) = (index, count)
		return best_index


from collections import deque

class Solution:

	def minMalwareSpread(self, graph: List[List[int]], initial: List[int]) -> int:
		if graph is None or len(graph) == 0 or len(graph[0]) == 0 or (len(initial) == 0):
			return None
		n = len(graph)
		m = len(graph[0])
		k = len(initial)
		initial.sort()
		result = sys.maxsize
		idx = None
		for i in range(k):
			temp_q = initial[:]
			temp_q.pop(i)
			temp_q = deque(temp_q)
			temp_visited = set(temp_q)
			self.helper(graph, temp_q, temp_visited)
			if result > len(temp_visited):
				result = len(temp_visited)
				idx = initial[i]
		return idx

	def helper(self, graph, temp_q, temp_visited):
		(n, m) = (len(graph), len(graph[0]))
		while temp_q:
			curr = temp_q.popleft()
			for col in range(m):
				if col in temp_visited or graph[curr][col] == 0:
					continue
				temp_visited.add(col)
				temp_q.append(col)


class Solution:

	def minMalwareSpread(self, graph: List[List[int]], initial: List[int]) -> int:

		class UF:

			def __init__(self, keys):
				self.uf = {}
				for key in keys:
					self.uf[key] = key

			def find(self, x):
				if self.uf[x] == x:
					return x
				ret = self.find(self.uf[x])
				self.uf[x] = ret
				return ret

			def union(self, x, y):
				xx = self.find(x)
				yy = self.find(y)
				self.uf[xx] = yy
		uf = UF(range(len(graph)))
		for i in range(len(graph)):
			for j in range(len(graph[i])):
				if graph[i][j] == 1:
					uf.union(i, j)
		ct = collections.Counter([uf.find(x) for x in range(len(graph))])
		ct2 = collections.Counter([uf.find(x) for x in initial])
		initial.sort()
		ret = initial[0]
		score = 0
		for idx in initial:
			parent = uf.find(idx)
			if ct2[parent] > 1:
				continue
			if ct[parent] > score:
				score = ct[parent]
				ret = idx
		return ret