#include <iostream>
#include <queue>
#include <unordered_map>
#include <unordered_set>
#include <vector>
// #define DEBUG
#ifdef DEBUG
const int TT = 4;
#endif
const int MAX = 100005;
int P[MAX];
struct Node {
int parent;
std::unordered_set<int> children;
int party;
std::vector<int> E;
bool processed;
std::unordered_map<int, int> partiesToConnect;
// std::queue<int> to_join;
void clean() {
processed = false;
E.clear();
children.clear();
partiesToConnect.clear();
// to_join = std::queue<int>();
}
};
class Set {
public:
void clean(int n, int k) {
for (int i = 1; i <= n; ++i) N[i].clean();
for (int i = 1; i <= k; ++i) PartyClusters[i].clear();
for (int i = 1; i <= k; ++i)
enqueued[i] = true; // avoid enqueuing before init
remaining_parties.clear();
Q = std::queue<int>();
}
int join(int u, int v) { return unionn(find(u), find(v)); }
int unionn(int u, int v) {
if (u == v) return v;
if (N[u].partiesToConnect.size() > N[v].partiesToConnect.size()) return unionn(v, u);
// if (N[u].party != N[v].party)
// std::clog << "Warning: different parties: " << u << "(" << N[u].party
// << ") vs " << v << "(" << N[v].party << ")" << std::endl;
for (const auto& [party, w]: N[u].partiesToConnect) {
int &vv = N[v].partiesToConnect[party];
if (vv == 0) vv = w;
else vv = join(vv, w);
}
N[u].partiesToConnect.clear();
PartyClusters[N[u].party].erase(u);
N[u].parent = v;
N[v].children.insert(u);
if (!enqueued[N[u].party] && PartyClusters[N[u].party].size() == 1 &&
remaining_parties.count(N[u].party) > 0) {
Q.push(v);
enqueued[N[u].party] = true;
}
return v;
}
int find(int v) {
int current_parrent = N[v].parent;
if (current_parrent == v) return v;
int new_parent = find(N[v].parent);
N[current_parrent].children.erase(v);
N[v].parent = new_parent;
N[new_parent].children.insert(v);
return new_parent;
}
int find_static(int v) {
int current_parrent = N[v].parent;
if (current_parrent == v) return v;
return find_static(N[v].parent);
}
void reg(int v, int k) {
N[v].party = k;
N[v].parent = v;
PartyClusters[k].insert(v);
remaining_parties.insert(k);
}
void reg_edge(int u, int v) {
N[u].E.push_back(v);
N[v].E.push_back(u);
}
std::unordered_set<int> fetch_neighbours(int v,
std::unordered_set<int> E = {}) {
if (!N[v].processed)
for (int w : N[v].children) E = fetch_neighbours(w, std::move(E));
N[v].processed = true;
// std::clog << "fetch_neighbours " << v << " :: ";
// for (int w : N[v].E) std::clog << " " << find(w);
// std::clog << std::endl;
// for (int w : N[v].E)
// if (find_static(w) != v) E.insert(find_static(w));
for (int w : N[v].E) E.insert(w);
N[v].E.clear();
// for (const auto& [party, w] : N[v].partiesToConnect)
// if (w != 0) E.insert(find(w));
return std::move(E);
}
std::unordered_set<int> fetch_neighbours_filter(int v) {
std::unordered_set<int> output;
for (int w : fetch_neighbours(v))
if (find(w) != v) output.insert(find(w));
return output;
}
void init(int n, int k) {
this->n = n;
this->k = k;
for (int i = 1; i <= k; ++i) enqueued[i] = false;
for (int i = 1; i <= k; ++i) {
if (!enqueued[i] && PartyClusters[i].size() == 1) {
Q.push(*PartyClusters[i].begin());
enqueued[i] = true;
}
}
}
void debug_print() {
std::clog << "Clusters " << std::endl;
for (int i = 1; i <= k; ++i) {
std::clog << i << " :: ";
for (int v : PartyClusters[i]) std::clog << " " << v;
std::clog << std::endl;
}
std::clog << "Nodes " << std::endl;
for (int i = 1; i <= n; ++i) {
std::clog << i << " :: -> " << find(i) << std::endl;
}
std::clog << "Remaining:";
for (int v : remaining_parties) std::clog << " " << v;
std::clog << std::endl;
std::clog << " ########### " << std::endl << std::endl;
}
Node N[MAX];
std::unordered_set<int> PartyClusters[MAX];
std::queue<int> Q;
int n;
int k;
std::unordered_set<int> remaining_parties;
bool enqueued[MAX];
} S;
bool solve(int t) {
int n, m, k;
std::cin >> n >> m >> k;
S.clean(n, k);
for (int i = 1; i <= n; ++i) {
std::cin >> P[i];
S.reg(i, P[i]);
#ifdef DEBUG
if (t == TT) std::clog << " " << P[i];
#endif
}
#ifdef DEBUG
if (t == TT) std::clog << std::endl;
#endif
for (int i = 0; i < m; ++i) {
int u, v;
std::cin >> u >> v;
if (P[u] == P[v]) {
S.join(u, v);
} else {
S.reg_edge(u, v);
}
}
S.init(n, k);
#ifdef DEBUG
if (t == TT) S.debug_print();
#endif
while (!S.Q.empty()) {
// process cluster to remove
int kk = S.Q.front();
int kp = P[kk];
S.Q.pop();
#ifdef DEBUG
if (t == TT)
std::clog << "process cluster " << kk << " to remove" << std::endl;
#endif
auto neighbours = S.fetch_neighbours_filter(kk);
std::unordered_set<int> joined_neighbours;
for (int u : neighbours) {
if (S.remaining_parties.count(P[u]) == 0) {
P[u] = kp;
kk = S.join(u, kk);
// for (int w : S.fetch_neighbours_filter(u))
// joined_neighbours.insert(S.find(w));
}
}
std::unordered_map<int, int>& PartiesToConnect = S.N[kk].partiesToConnect;
for (int u : neighbours) {
#ifdef DEBUG
if (t == TT) std::clog << " :: fetchd neighbours: " << u << std::endl;
#endif
int& v = PartiesToConnect[P[u]];
if (v == 0)
v = u;
else
v = S.join(v, u);
}
#ifdef DEBUG
if (t == TT)
for (auto [party, w] : PartiesToConnect) {
std::clog << "PartiesToConnect " << w << std::endl;
}
#endif
// S.N[kk].partiesToConnect = std::move(PartiesToConnect);
// for (const auto& [party, w] : PartiesToConnect) {
// S.reg_edge(S.find(kk), S.find(w));
// }
S.remaining_parties.erase(kp);
#ifdef DEBUG
if (t == TT) S.debug_print();
#endif
}
return S.remaining_parties.empty();
}
int main() {
std::ios_base::sync_with_stdio(0);
int T;
std::cin >> T;
for (int t = 1; t <= T; ++t)
std::cout << (solve(t) ? "TAK" : "NIE") << std::endl;
return 0;
}
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 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 | #include <iostream> #include <queue> #include <unordered_map> #include <unordered_set> #include <vector> // #define DEBUG #ifdef DEBUG const int TT = 4; #endif const int MAX = 100005; int P[MAX]; struct Node { int parent; std::unordered_set<int> children; int party; std::vector<int> E; bool processed; std::unordered_map<int, int> partiesToConnect; // std::queue<int> to_join; void clean() { processed = false; E.clear(); children.clear(); partiesToConnect.clear(); // to_join = std::queue<int>(); } }; class Set { public: void clean(int n, int k) { for (int i = 1; i <= n; ++i) N[i].clean(); for (int i = 1; i <= k; ++i) PartyClusters[i].clear(); for (int i = 1; i <= k; ++i) enqueued[i] = true; // avoid enqueuing before init remaining_parties.clear(); Q = std::queue<int>(); } int join(int u, int v) { return unionn(find(u), find(v)); } int unionn(int u, int v) { if (u == v) return v; if (N[u].partiesToConnect.size() > N[v].partiesToConnect.size()) return unionn(v, u); // if (N[u].party != N[v].party) // std::clog << "Warning: different parties: " << u << "(" << N[u].party // << ") vs " << v << "(" << N[v].party << ")" << std::endl; for (const auto& [party, w]: N[u].partiesToConnect) { int &vv = N[v].partiesToConnect[party]; if (vv == 0) vv = w; else vv = join(vv, w); } N[u].partiesToConnect.clear(); PartyClusters[N[u].party].erase(u); N[u].parent = v; N[v].children.insert(u); if (!enqueued[N[u].party] && PartyClusters[N[u].party].size() == 1 && remaining_parties.count(N[u].party) > 0) { Q.push(v); enqueued[N[u].party] = true; } return v; } int find(int v) { int current_parrent = N[v].parent; if (current_parrent == v) return v; int new_parent = find(N[v].parent); N[current_parrent].children.erase(v); N[v].parent = new_parent; N[new_parent].children.insert(v); return new_parent; } int find_static(int v) { int current_parrent = N[v].parent; if (current_parrent == v) return v; return find_static(N[v].parent); } void reg(int v, int k) { N[v].party = k; N[v].parent = v; PartyClusters[k].insert(v); remaining_parties.insert(k); } void reg_edge(int u, int v) { N[u].E.push_back(v); N[v].E.push_back(u); } std::unordered_set<int> fetch_neighbours(int v, std::unordered_set<int> E = {}) { if (!N[v].processed) for (int w : N[v].children) E = fetch_neighbours(w, std::move(E)); N[v].processed = true; // std::clog << "fetch_neighbours " << v << " :: "; // for (int w : N[v].E) std::clog << " " << find(w); // std::clog << std::endl; // for (int w : N[v].E) // if (find_static(w) != v) E.insert(find_static(w)); for (int w : N[v].E) E.insert(w); N[v].E.clear(); // for (const auto& [party, w] : N[v].partiesToConnect) // if (w != 0) E.insert(find(w)); return std::move(E); } std::unordered_set<int> fetch_neighbours_filter(int v) { std::unordered_set<int> output; for (int w : fetch_neighbours(v)) if (find(w) != v) output.insert(find(w)); return output; } void init(int n, int k) { this->n = n; this->k = k; for (int i = 1; i <= k; ++i) enqueued[i] = false; for (int i = 1; i <= k; ++i) { if (!enqueued[i] && PartyClusters[i].size() == 1) { Q.push(*PartyClusters[i].begin()); enqueued[i] = true; } } } void debug_print() { std::clog << "Clusters " << std::endl; for (int i = 1; i <= k; ++i) { std::clog << i << " :: "; for (int v : PartyClusters[i]) std::clog << " " << v; std::clog << std::endl; } std::clog << "Nodes " << std::endl; for (int i = 1; i <= n; ++i) { std::clog << i << " :: -> " << find(i) << std::endl; } std::clog << "Remaining:"; for (int v : remaining_parties) std::clog << " " << v; std::clog << std::endl; std::clog << " ########### " << std::endl << std::endl; } Node N[MAX]; std::unordered_set<int> PartyClusters[MAX]; std::queue<int> Q; int n; int k; std::unordered_set<int> remaining_parties; bool enqueued[MAX]; } S; bool solve(int t) { int n, m, k; std::cin >> n >> m >> k; S.clean(n, k); for (int i = 1; i <= n; ++i) { std::cin >> P[i]; S.reg(i, P[i]); #ifdef DEBUG if (t == TT) std::clog << " " << P[i]; #endif } #ifdef DEBUG if (t == TT) std::clog << std::endl; #endif for (int i = 0; i < m; ++i) { int u, v; std::cin >> u >> v; if (P[u] == P[v]) { S.join(u, v); } else { S.reg_edge(u, v); } } S.init(n, k); #ifdef DEBUG if (t == TT) S.debug_print(); #endif while (!S.Q.empty()) { // process cluster to remove int kk = S.Q.front(); int kp = P[kk]; S.Q.pop(); #ifdef DEBUG if (t == TT) std::clog << "process cluster " << kk << " to remove" << std::endl; #endif auto neighbours = S.fetch_neighbours_filter(kk); std::unordered_set<int> joined_neighbours; for (int u : neighbours) { if (S.remaining_parties.count(P[u]) == 0) { P[u] = kp; kk = S.join(u, kk); // for (int w : S.fetch_neighbours_filter(u)) // joined_neighbours.insert(S.find(w)); } } std::unordered_map<int, int>& PartiesToConnect = S.N[kk].partiesToConnect; for (int u : neighbours) { #ifdef DEBUG if (t == TT) std::clog << " :: fetchd neighbours: " << u << std::endl; #endif int& v = PartiesToConnect[P[u]]; if (v == 0) v = u; else v = S.join(v, u); } #ifdef DEBUG if (t == TT) for (auto [party, w] : PartiesToConnect) { std::clog << "PartiesToConnect " << w << std::endl; } #endif // S.N[kk].partiesToConnect = std::move(PartiesToConnect); // for (const auto& [party, w] : PartiesToConnect) { // S.reg_edge(S.find(kk), S.find(w)); // } S.remaining_parties.erase(kp); #ifdef DEBUG if (t == TT) S.debug_print(); #endif } return S.remaining_parties.empty(); } int main() { std::ios_base::sync_with_stdio(0); int T; std::cin >> T; for (int t = 1; t <= T; ++t) std::cout << (solve(t) ? "TAK" : "NIE") << std::endl; return 0; } |
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