#include <cstdio>
#include <cassert>
#include <vector>
#include <map>
struct uf_t {
uf_t* parent;
int rank;
int vertex;
};
struct edge_t {
int target;
int next_edge;
};
struct vertex_t {
int first_edge;
int who_won;
uf_t wildcard_rep;
std::map<int, uf_t> party_to_rep;
};
struct party_t {
int first_member;
int connected_components;
};
static const int WILDCARD_PARTY = -1;
// This is a thing of beauty
static uf_t* uf_find(uf_t* p) {
assert(p != nullptr);
if (p->parent == nullptr) {
return p;
}
// TODO: Avoid recursion by reversing in place
p->parent = uf_find(p->parent);
return p->parent;
}
// Returns true if pa and pb weren't already in the same component
static bool uf_union(uf_t* pa, uf_t* pb) {
uf_t* pa_root = uf_find(pa);
uf_t* pb_root = uf_find(pb);
if (pa_root == pb_root) {
return false; // Fast path - nothing to do
}
if (pa_root->rank > pb_root->rank) {
pb_root->parent = pa_root;
} else if (pa_root->rank < pb_root->rank) {
pa_root->parent = pb_root;
} else {
pb_root->parent = pa_root;
pa_root->rank += 1;
}
return true;
}
// Can use it to either only merge vertices of the same color, or with wildcards
static void vertex_multi_union(std::vector<int>& candidates, std::vector<party_t>& parties, vertex_t& va, vertex_t& vb, int b) {
if (&va == &vb) {
// fprintf(stderr, " Skipping mult-union because vertices are the same\n");
return;
}
assert(va.party_to_rep.size() <= vb.party_to_rep.size());
for (auto&& [party_idx, uf] : va.party_to_rep) {
// fprintf(stderr, " Multi-unifying party %d\n", party_idx+1);
auto [it, inserted] = vb.party_to_rep.try_emplace(party_idx, uf_t{nullptr, 0, b});
if (uf_union(&uf, &it->second)) {
// fprintf(stderr, " Performed a successful union\n");
if (inserted) {
// fprintf(stderr, " Wildcard did not have the party already, not decreasing the counter\n");
} else if (--parties[party_idx].connected_components == 1) {
// fprintf(stderr, " Adding the party to candidates\n");
candidates.push_back(party_idx);
} else {
// fprintf(stderr, " The counter of the party decreased to %d\n", parties[party_idx].connected_components);
}
} else {
// fprintf(stderr, " Parties already unified\n");
}
}
}
static bool solve() {
int n, m, k;
scanf("%d %d %d", &n, &m, &k);
// assert(n <= 100 * 1000);
// assert(m <= 100 * 1000);
// assert(k <= 100 * 1000);
std::vector<vertex_t> vertices;
std::vector<edge_t> edges;
std::vector<party_t> parties;
std::vector<int> party_next_member;
vertices.reserve(n);
edges.reserve(2 * m);
parties.reserve(k);
party_next_member.reserve(n);
for (int i = 0; i < k; i++) {
parties.push_back(party_t{
.first_member = -1,
.connected_components = 0,
});
}
for (int i = 0; i < n; i++) {
int who_won;
scanf("%d", &who_won);
assert(who_won > 0);
who_won -= 1;
assert(who_won < k);
vertices.push_back(vertex_t{
.first_edge = -1,
.who_won = who_won,
.wildcard_rep = uf_t{nullptr, 0, i},
.party_to_rep = {},
});
vertices.back().party_to_rep.insert({who_won, uf_t{nullptr, 0, i}});
party_next_member.push_back(parties[who_won].first_member);
parties[who_won].first_member = i;
parties[who_won].connected_components++;
}
for (int i = 0; i < m; i++) {
int a, b;
scanf("%d %d", &a, &b);
assert(a > 0);
assert(b > 0);
a -= 1;
b -= 1;
assert(a < n);
assert(b < n);
edges.push_back(edge_t{
.target = b,
.next_edge = vertices[a].first_edge,
});
vertices[a].first_edge = 2 * i + 0;
edges.push_back(edge_t{
.target = a,
.next_edge = vertices[b].first_edge,
});
vertices[b].first_edge = 2 * i + 1;
}
std::vector<int> candidate_parties;
candidate_parties.reserve(n);
// Create the initial per-color connected components
// fprintf(stderr, "Looking for parties with zero or one city\n");
for (int i = 0; i < k; i++) {
// If there is at least one successfully processed party with non-zero
// cities, we can say that zero-city parties are legit because they
// could have just entered any city that was covered by the last
// party that had a tour.
// Add these parties to the list of parties to process, those will be
// no-op.
if (parties[i].connected_components <= 1) {
// fprintf(stderr, " Adding party %d to candidates\n", i+1);
candidate_parties.push_back(i);
}
}
// fprintf(stderr, "Tying initial cities together\n");
for (int i = 0; i < n; i++) {
// fprintf(stderr, " Visiting vertex %d\n", i+1);
auto& my_vert = vertices[i];
for (int e = vertices[i].first_edge; e != -1; e = edges[e].next_edge) {
// fprintf(stderr, " Visiting neighbor %d\n", edges[e].target+1);
if (edges[e].target <= i) {
// fprintf(stderr, " Skipping, the pair will be or was processed (bidirectionality)\n");
continue;
}
auto& target_vert = vertices[edges[e].target];
if (my_vert.who_won == target_vert.who_won) {
vertex_multi_union(candidate_parties, parties, my_vert, target_vert, edges[e].target);
} else {
// fprintf(stderr, " Party does not match, %d vs. %d\n", my_vert.who_won+1, target_vert.who_won+1);
}
}
}
int parties_processed = 0;
while (!candidate_parties.empty()) {
parties_processed++;
const int curr_party = candidate_parties.back();
candidate_parties.pop_back();
// fprintf(stderr, "Processing party: %d\n", curr_party + 1);
for (int v = parties[curr_party].first_member; v != -1; v = party_next_member[v]) {
// fprintf(stderr, " Visiting vertex %d\n", v+1);
auto& my_vert = vertices[v];
my_vert.who_won = WILDCARD_PARTY;
for (int e = vertices[v].first_edge; e != -1; e = edges[e].next_edge) {
// fprintf(stderr, " Visiting neighbor %d\n", edges[e].target+1);
auto& target_vert = vertices[edges[e].target];
if (target_vert.who_won == curr_party) {
// Connections are bidirectional, we will process this pair later
// when the other vertex becomes a wildcard
continue;
}
int my_wildcard_rep = uf_find(&my_vert.wildcard_rep)->vertex;
if (target_vert.who_won == WILDCARD_PARTY) {
int target_wildcard_rep = uf_find(&target_vert.wildcard_rep)->vertex;
int giving_wildcard_rep, receiving_wildcard_rep;
if (vertices[my_wildcard_rep].party_to_rep.size()
<= vertices[target_wildcard_rep].party_to_rep.size()) {
giving_wildcard_rep = my_wildcard_rep;
receiving_wildcard_rep = target_wildcard_rep;
} else {
giving_wildcard_rep = target_wildcard_rep;
receiving_wildcard_rep = my_wildcard_rep;
}
// fprintf(stderr, " Multi-union of wildcard %d with wildcard %d\n", giving_wildcard_rep+1, receiving_wildcard_rep+1);
vertex_multi_union(candidate_parties, parties, vertices[giving_wildcard_rep], vertices[receiving_wildcard_rep], receiving_wildcard_rep);
uf_union(&my_vert.wildcard_rep, &target_vert.wildcard_rep);
// fprintf(stderr, " Union find chose %d as the new rep\n", uf_find(&my_vert.wildcard_rep)->vertex+1);
if (uf_find(&my_vert.wildcard_rep)->vertex != receiving_wildcard_rep) {
// fprintf(stderr, " Swapping the sets as union find chose the other vertex\n");
std::swap(vertices[my_wildcard_rep].party_to_rep, vertices[target_wildcard_rep].party_to_rep);
} else {
// fprintf(stderr, " No need to swap, union find chose correctly\n");
}
} else {
// fprintf(stderr, " Multi-union of non-wildcard %d with wildcard %d\n", edges[e].target+1, my_wildcard_rep+1);
vertex_multi_union(candidate_parties, parties, target_vert, vertices[my_wildcard_rep], my_wildcard_rep);
}
}
}
}
// fprintf(stderr, "Processed vs. k: %d, %d\n", parties_processed, k);
return parties_processed == k;
}
int main() {
int t;
scanf("%d", &t);
while (t --> 0) {
puts(solve() ? "TAK" : "NIE");
}
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 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 | #include <cstdio> #include <cassert> #include <vector> #include <map> struct uf_t { uf_t* parent; int rank; int vertex; }; struct edge_t { int target; int next_edge; }; struct vertex_t { int first_edge; int who_won; uf_t wildcard_rep; std::map<int, uf_t> party_to_rep; }; struct party_t { int first_member; int connected_components; }; static const int WILDCARD_PARTY = -1; // This is a thing of beauty static uf_t* uf_find(uf_t* p) { assert(p != nullptr); if (p->parent == nullptr) { return p; } // TODO: Avoid recursion by reversing in place p->parent = uf_find(p->parent); return p->parent; } // Returns true if pa and pb weren't already in the same component static bool uf_union(uf_t* pa, uf_t* pb) { uf_t* pa_root = uf_find(pa); uf_t* pb_root = uf_find(pb); if (pa_root == pb_root) { return false; // Fast path - nothing to do } if (pa_root->rank > pb_root->rank) { pb_root->parent = pa_root; } else if (pa_root->rank < pb_root->rank) { pa_root->parent = pb_root; } else { pb_root->parent = pa_root; pa_root->rank += 1; } return true; } // Can use it to either only merge vertices of the same color, or with wildcards static void vertex_multi_union(std::vector<int>& candidates, std::vector<party_t>& parties, vertex_t& va, vertex_t& vb, int b) { if (&va == &vb) { // fprintf(stderr, " Skipping mult-union because vertices are the same\n"); return; } assert(va.party_to_rep.size() <= vb.party_to_rep.size()); for (auto&& [party_idx, uf] : va.party_to_rep) { // fprintf(stderr, " Multi-unifying party %d\n", party_idx+1); auto [it, inserted] = vb.party_to_rep.try_emplace(party_idx, uf_t{nullptr, 0, b}); if (uf_union(&uf, &it->second)) { // fprintf(stderr, " Performed a successful union\n"); if (inserted) { // fprintf(stderr, " Wildcard did not have the party already, not decreasing the counter\n"); } else if (--parties[party_idx].connected_components == 1) { // fprintf(stderr, " Adding the party to candidates\n"); candidates.push_back(party_idx); } else { // fprintf(stderr, " The counter of the party decreased to %d\n", parties[party_idx].connected_components); } } else { // fprintf(stderr, " Parties already unified\n"); } } } static bool solve() { int n, m, k; scanf("%d %d %d", &n, &m, &k); // assert(n <= 100 * 1000); // assert(m <= 100 * 1000); // assert(k <= 100 * 1000); std::vector<vertex_t> vertices; std::vector<edge_t> edges; std::vector<party_t> parties; std::vector<int> party_next_member; vertices.reserve(n); edges.reserve(2 * m); parties.reserve(k); party_next_member.reserve(n); for (int i = 0; i < k; i++) { parties.push_back(party_t{ .first_member = -1, .connected_components = 0, }); } for (int i = 0; i < n; i++) { int who_won; scanf("%d", &who_won); assert(who_won > 0); who_won -= 1; assert(who_won < k); vertices.push_back(vertex_t{ .first_edge = -1, .who_won = who_won, .wildcard_rep = uf_t{nullptr, 0, i}, .party_to_rep = {}, }); vertices.back().party_to_rep.insert({who_won, uf_t{nullptr, 0, i}}); party_next_member.push_back(parties[who_won].first_member); parties[who_won].first_member = i; parties[who_won].connected_components++; } for (int i = 0; i < m; i++) { int a, b; scanf("%d %d", &a, &b); assert(a > 0); assert(b > 0); a -= 1; b -= 1; assert(a < n); assert(b < n); edges.push_back(edge_t{ .target = b, .next_edge = vertices[a].first_edge, }); vertices[a].first_edge = 2 * i + 0; edges.push_back(edge_t{ .target = a, .next_edge = vertices[b].first_edge, }); vertices[b].first_edge = 2 * i + 1; } std::vector<int> candidate_parties; candidate_parties.reserve(n); // Create the initial per-color connected components // fprintf(stderr, "Looking for parties with zero or one city\n"); for (int i = 0; i < k; i++) { // If there is at least one successfully processed party with non-zero // cities, we can say that zero-city parties are legit because they // could have just entered any city that was covered by the last // party that had a tour. // Add these parties to the list of parties to process, those will be // no-op. if (parties[i].connected_components <= 1) { // fprintf(stderr, " Adding party %d to candidates\n", i+1); candidate_parties.push_back(i); } } // fprintf(stderr, "Tying initial cities together\n"); for (int i = 0; i < n; i++) { // fprintf(stderr, " Visiting vertex %d\n", i+1); auto& my_vert = vertices[i]; for (int e = vertices[i].first_edge; e != -1; e = edges[e].next_edge) { // fprintf(stderr, " Visiting neighbor %d\n", edges[e].target+1); if (edges[e].target <= i) { // fprintf(stderr, " Skipping, the pair will be or was processed (bidirectionality)\n"); continue; } auto& target_vert = vertices[edges[e].target]; if (my_vert.who_won == target_vert.who_won) { vertex_multi_union(candidate_parties, parties, my_vert, target_vert, edges[e].target); } else { // fprintf(stderr, " Party does not match, %d vs. %d\n", my_vert.who_won+1, target_vert.who_won+1); } } } int parties_processed = 0; while (!candidate_parties.empty()) { parties_processed++; const int curr_party = candidate_parties.back(); candidate_parties.pop_back(); // fprintf(stderr, "Processing party: %d\n", curr_party + 1); for (int v = parties[curr_party].first_member; v != -1; v = party_next_member[v]) { // fprintf(stderr, " Visiting vertex %d\n", v+1); auto& my_vert = vertices[v]; my_vert.who_won = WILDCARD_PARTY; for (int e = vertices[v].first_edge; e != -1; e = edges[e].next_edge) { // fprintf(stderr, " Visiting neighbor %d\n", edges[e].target+1); auto& target_vert = vertices[edges[e].target]; if (target_vert.who_won == curr_party) { // Connections are bidirectional, we will process this pair later // when the other vertex becomes a wildcard continue; } int my_wildcard_rep = uf_find(&my_vert.wildcard_rep)->vertex; if (target_vert.who_won == WILDCARD_PARTY) { int target_wildcard_rep = uf_find(&target_vert.wildcard_rep)->vertex; int giving_wildcard_rep, receiving_wildcard_rep; if (vertices[my_wildcard_rep].party_to_rep.size() <= vertices[target_wildcard_rep].party_to_rep.size()) { giving_wildcard_rep = my_wildcard_rep; receiving_wildcard_rep = target_wildcard_rep; } else { giving_wildcard_rep = target_wildcard_rep; receiving_wildcard_rep = my_wildcard_rep; } // fprintf(stderr, " Multi-union of wildcard %d with wildcard %d\n", giving_wildcard_rep+1, receiving_wildcard_rep+1); vertex_multi_union(candidate_parties, parties, vertices[giving_wildcard_rep], vertices[receiving_wildcard_rep], receiving_wildcard_rep); uf_union(&my_vert.wildcard_rep, &target_vert.wildcard_rep); // fprintf(stderr, " Union find chose %d as the new rep\n", uf_find(&my_vert.wildcard_rep)->vertex+1); if (uf_find(&my_vert.wildcard_rep)->vertex != receiving_wildcard_rep) { // fprintf(stderr, " Swapping the sets as union find chose the other vertex\n"); std::swap(vertices[my_wildcard_rep].party_to_rep, vertices[target_wildcard_rep].party_to_rep); } else { // fprintf(stderr, " No need to swap, union find chose correctly\n"); } } else { // fprintf(stderr, " Multi-union of non-wildcard %d with wildcard %d\n", edges[e].target+1, my_wildcard_rep+1); vertex_multi_union(candidate_parties, parties, target_vert, vertices[my_wildcard_rep], my_wildcard_rep); } } } } // fprintf(stderr, "Processed vs. k: %d, %d\n", parties_processed, k); return parties_processed == k; } int main() { int t; scanf("%d", &t); while (t --> 0) { puts(solve() ? "TAK" : "NIE"); } return 0; } |
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