# 928. Minimize Malware Spread II

## Description

You are given a network of n nodes represented as an n x n adjacency matrix graph, where the ith node is directly connected to the jth node 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 exactly one node from initial, completely removing it and any connections from this node to any other node.

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.

Example 1:

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


Example 2:

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


Example 3:

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


Constraints:

• n == graph.length
• n == graph[i].length
• 2 <= n <= 300
• graph[i][j] is 0 or 1.
• graph[i][j] == graph[j][i]
• graph[i][i] == 1
• 1 <= initial.length < n
• 0 <= initial[i] <= n - 1
• All the integers in initial are unique.

## Solutions

• class Solution {
private int[] p;
private int[] size;

public int minMalwareSpread(int[][] graph, int[] initial) {
int n = graph.length;
p = new int[n];
size = new int[n];
for (int i = 0; i < n; ++i) {
p[i] = i;
size[i] = 1;
}
boolean[] clean = new boolean[n];
Arrays.fill(clean, true);
for (int i : initial) {
clean[i] = false;
}
for (int i = 0; i < n; ++i) {
if (!clean[i]) {
continue;
}
for (int j = i + 1; j < n; ++j) {
if (clean[j] && graph[i][j] == 1) {
union(i, j);
}
}
}
int[] cnt = new int[n];
Map<Integer, Set<Integer>> mp = new HashMap<>();
for (int i : initial) {
Set<Integer> s = new HashSet<>();
for (int j = 0; j < n; ++j) {
if (clean[j] && graph[i][j] == 1) {
}
}
for (int root : s) {
cnt[root] += 1;
}
mp.put(i, s);
}
int mx = -1;
int ans = 0;
for (Map.Entry<Integer, Set<Integer>> entry : mp.entrySet()) {
int i = entry.getKey();
int t = 0;
for (int root : entry.getValue()) {
if (cnt[root] == 1) {
t += size[root];
}
}
if (mx < t || (mx == t && i < ans)) {
mx = t;
ans = i;
}
}
return ans;
}

private int find(int x) {
if (p[x] != x) {
p[x] = find(p[x]);
}
return p[x];
}

private void union(int a, int b) {
int pa = find(a);
int pb = find(b);
if (pa != pb) {
size[pb] += size[pa];
p[pa] = pb;
}
}
}

• class Solution {
public:
vector<int> p;
vector<int> size;

int minMalwareSpread(vector<vector<int>>& graph, vector<int>& initial) {
int n = graph.size();
p.resize(n);
size.resize(n);
for (int i = 0; i < n; ++i) p[i] = i;
fill(size.begin(), size.end(), 1);
vector<bool> clean(n, true);
for (int i : initial) clean[i] = false;
for (int i = 0; i < n; ++i) {
if (!clean[i]) continue;
for (int j = i + 1; j < n; ++j)
if (clean[j] && graph[i][j] == 1) merge(i, j);
}
vector<int> cnt(n, 0);
unordered_map<int, unordered_set<int>> mp;
for (int i : initial) {
unordered_set<int> s;
for (int j = 0; j < n; ++j)
if (clean[j] && graph[i][j] == 1) s.insert(find(j));
for (int e : s) ++cnt[e];
mp[i] = s;
}
int mx = -1, ans = 0;
for (auto& [i, s] : mp) {
int t = 0;
for (int root : s)
if (cnt[root] == 1)
t += size[root];
if (mx < t || (mx == t && i < ans)) {
mx = t;
ans = i;
}
}
return ans;
}

int find(int x) {
if (p[x] != x) p[x] = find(p[x]);
return p[x];
}

void merge(int a, int b) {
int pa = find(a), pb = find(b);
if (pa != pb) {
size[pb] += size[pa];
p[pa] = pb;
}
}
};

• class Solution:
def minMalwareSpread(self, graph: List[List[int]], initial: List[int]) -> int:
def find(x):
if p[x] != x:
p[x] = find(p[x])
return p[x]

def union(a, b):
pa, pb = find(a), find(b)
if pa != pb:
size[pb] += size[pa]
p[pa] = pb

n = len(graph)
p = list(range(n))
size = [1] * n
clean = [True] * n
for i in initial:
clean[i] = False
for i in range(n):
if not clean[i]:
continue
for j in range(i + 1, n):
if clean[j] and graph[i][j] == 1:
union(i, j)
cnt = Counter()
mp = {}
for i in initial:
s = {find(j) for j in range(n) if clean[j] and graph[i][j] == 1}
for root in s:
cnt[root] += 1
mp[i] = s

mx, ans = -1, 0
for i, s in mp.items():
t = sum(size[root] for root in s if cnt[root] == 1)
if mx < t or mx == t and i < ans:
mx, ans = t, i
return ans


• func minMalwareSpread(graph [][]int, initial []int) int {
n := len(graph)
p := make([]int, n)
size := make([]int, n)
clean := make([]bool, n)
for i := 0; i < n; i++ {
p[i], size[i], clean[i] = i, 1, true
}
for _, i := range initial {
clean[i] = false
}

var find func(x int) int
find = func(x int) int {
if p[x] != x {
p[x] = find(p[x])
}
return p[x]
}
union := func(a, b int) {
pa, pb := find(a), find(b)
if pa != pb {
size[pb] += size[pa]
p[pa] = pb
}
}

for i := 0; i < n; i++ {
if !clean[i] {
continue
}
for j := i + 1; j < n; j++ {
if clean[j] && graph[i][j] == 1 {
union(i, j)
}
}
}
cnt := make([]int, n)
mp := make(map[int]map[int]bool)
for _, i := range initial {
s := make(map[int]bool)
for j := 0; j < n; j++ {
if clean[j] && graph[i][j] == 1 {
s[find(j)] = true
}
}
for root, _ := range s {
cnt[root]++
}
mp[i] = s
}
mx, ans := -1, 0
for i, s := range mp {
t := 0
for root, _ := range s {
if cnt[root] == 1 {
t += size[root]
}
}
if mx < t || (mx == t && i < ans) {
mx, ans = t, i
}
}
return ans
}

• class UnionFind {
p: number[];
size: number[];
constructor(n: number) {
this.p = Array(n)
.fill(0)
.map((_, i) => i);
this.size = Array(n).fill(1);
}

find(x: number): number {
if (this.p[x] !== x) {
this.p[x] = this.find(this.p[x]);
}
return this.p[x];
}

union(a: number, b: number): boolean {
const [pa, pb] = [this.find(a), this.find(b)];
if (pa === pb) {
return false;
}
if (this.size[pa] > this.size[pb]) {
this.p[pb] = pa;
this.size[pa] += this.size[pb];
} else {
this.p[pa] = pb;
this.size[pb] += this.size[pa];
}
return true;
}

getSize(root: number): number {
return this.size[root];
}
}

function minMalwareSpread(graph: number[][], initial: number[]): number {
const n = graph.length;
const s = new Set(initial);
const uf = new UnionFind(n);
for (let i = 0; i < n; ++i) {
if (!s.has(i)) {
for (let j = i + 1; j < n; ++j) {
if (graph[i][j] && !s.has(j)) {
uf.union(i, j);
}
}
}
}
const g: Set<number>[] = Array.from({ length: n }, () => new Set());
const cnt: number[] = Array(n).fill(0);
for (const i of initial) {
for (let j = 0; j < n; ++j) {
if (graph[i][j] && !s.has(j)) {
}
}
for (const root of g[i]) {
++cnt[root];
}
}
let ans = 0;
let mx = -1;
for (const i of initial) {
let t = 0;
for (const root of g[i]) {
if (cnt[root] === 1) {
t += uf.getSize(root);
}
}
if (t > mx || (t === mx && i < ans)) {
[ans, mx] = [i, t];
}
}
return ans;
}