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minimize-malware-spread-ii.cpp
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minimize-malware-spread-ii.cpp
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// Time: O(n^2)
// Space: O(n)
class Solution {
public:
int minMalwareSpread(vector<vector<int>>& graph, vector<int>& initial) {
unordered_set<int> initial_set(initial.cbegin(), initial.cend());
vector<int> clean;
for (int i = 0; i < graph.size(); ++i) {
if (!initial_set.count(i)) {
clean.emplace_back(i);
}
}
UnionFind union_find(graph.size());
for (int i = 0; i < clean.size(); ++i) {
for (int j = i + 1; j < clean.size(); ++j) {
if (graph[clean[i]][clean[j]] == 1) {
union_find.union_set(clean[i], clean[j]);
}
}
}
unordered_map<int, int> union_size;
for (int i = 0; i < graph.size(); ++i) {
++union_size[union_find.find_set(i)];
}
unordered_map<int, unordered_set<int>> shared_union;
for (const auto& i: initial) {
for (const auto& j : clean) {
if (graph[i][j] == 1) {
auto x = union_find.find_set(j);
shared_union[x].emplace(i);
}
}
}
int result = numeric_limits<int>::max();
int total = numeric_limits<int>::min();
for (const auto& i : initial) {
unordered_set<int> lookup;
int curr = 0;
for (const auto& j : clean) {
if (graph[i][j] == 1) {
auto x = union_find.find_set(j);
if (shared_union[x].size() == 1 &&
!lookup.count(x)) {
curr += union_size[x];
lookup.emplace(x);
}
}
}
if (curr > total ||
(curr == total && i < result)) {
total = curr;
result = i;
}
}
return result;
}
private:
class UnionFind {
public:
UnionFind(const int n) : set_(n) {
iota(set_.begin(), set_.end(), 0);
}
int find_set(const int x) {
if (set_[x] != x) {
set_[x] = find_set(set_[x]); // Path compression.
}
return set_[x];
}
bool union_set(const int x, const int y) {
int x_root = find_set(x), y_root = find_set(y);
if (x_root == y_root) {
return false;
}
set_[min(x_root, y_root)] = max(x_root, y_root);
return true;
}
private:
vector<int> set_;
};
};