#include <bits/stdc++.h>
using namespace std;
using ll = int64_t;
using vi = vector<int>;
// https://github.com/kth-competitive-programming/kactl/blob/main/content/data-structures/UnionFind.h
struct UF {
vi e;
UF() = default;
UF(int n) : e(n, -1) {}
bool sameSet(int a, int b) { return find(a) == find(b); }
int size(int x) { return -e[find(x)]; }
int find(int x) { return e[x] < 0 ? x : e[x] = find(e[x]); }
bool join(int a, int b) {
a = find(a), b = find(b);
if (a == b) return false;
if (e[a] > e[b]) swap(a, b);
e[a] += e[b]; e[b] = a;
return true;
}
};
void solve() {
int n, m, k;
cin >> n >> m >> k;
vector<int> colors(n);
for(auto& c : colors) {
cin >> c;
c--;
}
vector<vector<int>> graph(n);
for(int i = 0; i < m; i++) {
int a, b;
cin >> a >> b;
a--;
b--;
graph[a].push_back(b);
graph[b].push_back(a);
}
vector<int> ccnt(k);
vector<int> id(n);
for(int i = 0; i < n; i++) {
id[i] = ccnt[colors[i]]++;
}
vector<UF> ufs(k);
for(int i = 0; i < k; i++) {
ufs[i] = UF(ccnt[i]);
}
UF uf(n);
vector<map<int, int>> maps(n);
vector<bool> removed(n);
vector<int> ncomp = ccnt;
for(int i = 0; i < n; i++) {
for(int to : graph[i]) {
if(colors[i] == colors[to] && !ufs[colors[i]].sameSet(id[i], id[to])) {
ufs[colors[i]].join(id[i], id[to]);
ncomp[colors[i]]--;
}
}
}
vector<vector<int>> withColor(k);
for(int i = 0; i < n; i++) {
withColor[colors[i]].push_back(i);
}
vector<int> stack;
for(int i = 0; i < k; i++) {
if(ncomp[i] == 1) {
stack.push_back(i);
}
}
auto remove = [&] (int v) {
removed[v] = true;
auto add = [&] (map<int, int>& mp, int i) {
if(mp.count(colors[i]) == 0) {
mp[colors[i]] = i;
}
else {
if(!ufs[colors[i]].sameSet(id[i], id[mp[colors[i]]])) {
ncomp[colors[i]]--;
if(ncomp[colors[i]] == 1) {
stack.push_back(colors[i]);
}
ufs[colors[i]].join(id[i], id[mp[colors[i]]]);
}
}
};
set<pair<int, int>> rs;
rs.emplace(maps[uf.find(v)].size(), uf.find(v));
for(int nei : graph[v]) {
if(removed[nei]) {
rs.emplace(maps[uf.find(nei)].size(), uf.find(nei));
}
}
int leader = rs.rbegin()->second;
for(auto it = next(rs.rbegin()); it != rs.rend(); it++) {
uf.join(leader, it->second);
for(auto [k, v] : maps[it->second]) {
add(maps[leader], v);
}
}
for(int nei : graph[v]) {
if(!removed[nei]) {
add(maps[leader], nei);
}
}
if(leader != uf.find(leader)) {
swap(maps[leader], maps[uf.find(leader)]);
}
};
while(!stack.empty()) {
int color = stack.back();
stack.pop_back();
for(auto v : withColor[color]) {
remove(v);
}
}
for(int i = 0; i < n; i++) {
if(!removed[i]) {
cout << "NIE";
return;
}
}
cout << "TAK";
}
int main() {
ios_base::sync_with_stdio(0);
cin.tie(0);
cout.tie(0);
//freopen("kam1.in", "r", stdin);
int t;
cin >> t;
int i = 1;
while(t--) {
solve();
cout << "\n";
i++;
}
}
// idea:
/*
DSU na kolor
DSU na usuniete
Robimy usun wierzcholek (czy cos takiego)
- najpierw patrzy na wszystkich sasiadow, ktorzy sa usunieci mergujemy ich w jednego usunietego
- dla kazdego sasiada patrzymy czy jest juz w zbiorze naszego zmergowanego jezeli nie to union i zmniejszami liczbe componentow
- jak robimy mergowanie:
- - mamy kilka usunietych (znamy ich id w uf) np 1, 2, 3, 10
- - robimy na nich union
- - mamy tez vector<set<int>> - zbior sasiadow dla usunietego
- - do najwiekszego setu dodajemy reszte
- - std::swap i cleary
- - no i teoria jest taka, wartosci w setach mamy sumarycznie tyle co krawedzi wiec to powinny byc mlogm czy cos, ale moze to nie prawda
*/
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 | #include <bits/stdc++.h> using namespace std; using ll = int64_t; using vi = vector<int>; // https://github.com/kth-competitive-programming/kactl/blob/main/content/data-structures/UnionFind.h struct UF { vi e; UF() = default; UF(int n) : e(n, -1) {} bool sameSet(int a, int b) { return find(a) == find(b); } int size(int x) { return -e[find(x)]; } int find(int x) { return e[x] < 0 ? x : e[x] = find(e[x]); } bool join(int a, int b) { a = find(a), b = find(b); if (a == b) return false; if (e[a] > e[b]) swap(a, b); e[a] += e[b]; e[b] = a; return true; } }; void solve() { int n, m, k; cin >> n >> m >> k; vector<int> colors(n); for(auto& c : colors) { cin >> c; c--; } vector<vector<int>> graph(n); for(int i = 0; i < m; i++) { int a, b; cin >> a >> b; a--; b--; graph[a].push_back(b); graph[b].push_back(a); } vector<int> ccnt(k); vector<int> id(n); for(int i = 0; i < n; i++) { id[i] = ccnt[colors[i]]++; } vector<UF> ufs(k); for(int i = 0; i < k; i++) { ufs[i] = UF(ccnt[i]); } UF uf(n); vector<map<int, int>> maps(n); vector<bool> removed(n); vector<int> ncomp = ccnt; for(int i = 0; i < n; i++) { for(int to : graph[i]) { if(colors[i] == colors[to] && !ufs[colors[i]].sameSet(id[i], id[to])) { ufs[colors[i]].join(id[i], id[to]); ncomp[colors[i]]--; } } } vector<vector<int>> withColor(k); for(int i = 0; i < n; i++) { withColor[colors[i]].push_back(i); } vector<int> stack; for(int i = 0; i < k; i++) { if(ncomp[i] == 1) { stack.push_back(i); } } auto remove = [&] (int v) { removed[v] = true; auto add = [&] (map<int, int>& mp, int i) { if(mp.count(colors[i]) == 0) { mp[colors[i]] = i; } else { if(!ufs[colors[i]].sameSet(id[i], id[mp[colors[i]]])) { ncomp[colors[i]]--; if(ncomp[colors[i]] == 1) { stack.push_back(colors[i]); } ufs[colors[i]].join(id[i], id[mp[colors[i]]]); } } }; set<pair<int, int>> rs; rs.emplace(maps[uf.find(v)].size(), uf.find(v)); for(int nei : graph[v]) { if(removed[nei]) { rs.emplace(maps[uf.find(nei)].size(), uf.find(nei)); } } int leader = rs.rbegin()->second; for(auto it = next(rs.rbegin()); it != rs.rend(); it++) { uf.join(leader, it->second); for(auto [k, v] : maps[it->second]) { add(maps[leader], v); } } for(int nei : graph[v]) { if(!removed[nei]) { add(maps[leader], nei); } } if(leader != uf.find(leader)) { swap(maps[leader], maps[uf.find(leader)]); } }; while(!stack.empty()) { int color = stack.back(); stack.pop_back(); for(auto v : withColor[color]) { remove(v); } } for(int i = 0; i < n; i++) { if(!removed[i]) { cout << "NIE"; return; } } cout << "TAK"; } int main() { ios_base::sync_with_stdio(0); cin.tie(0); cout.tie(0); //freopen("kam1.in", "r", stdin); int t; cin >> t; int i = 1; while(t--) { solve(); cout << "\n"; i++; } } // idea: /* DSU na kolor DSU na usuniete Robimy usun wierzcholek (czy cos takiego) - najpierw patrzy na wszystkich sasiadow, ktorzy sa usunieci mergujemy ich w jednego usunietego - dla kazdego sasiada patrzymy czy jest juz w zbiorze naszego zmergowanego jezeli nie to union i zmniejszami liczbe componentow - jak robimy mergowanie: - - mamy kilka usunietych (znamy ich id w uf) np 1, 2, 3, 10 - - robimy na nich union - - mamy tez vector<set<int>> - zbior sasiadow dla usunietego - - do najwiekszego setu dodajemy reszte - - std::swap i cleary - - no i teoria jest taka, wartosci w setach mamy sumarycznie tyle co krawedzi wiec to powinny byc mlogm czy cos, ale moze to nie prawda */ |
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