#include <algorithm>
#include <cstdio>
#include <numeric>
#include <vector>
#include <map>
#include <unordered_set>
#include <unordered_map>
#ifdef LOCAL
#define dbg(...) fprintf(stderr, __VA_ARGS__)
#else
#define dbg(...)
#endif
using namespace std;
struct EdgeSystem {
unordered_map<int, unordered_set<int>> edges;
explicit EdgeSystem() = default;
void join(EdgeSystem& other, const unordered_set<int>& relevant_colors, const unordered_set<int>& blankable_colors) {
dbg("STARTING JOIN STATE\n");
for (auto& [color, mySet] : edges) {
dbg("Now have edges to color %2d:\n", color);
for (auto& target: mySet) {
dbg("%2d ", target+1);
}
dbg("\n");
}
dbg("----------------------\n");
for (auto& [color, otherSet] : other.edges) {
dbg("Joining edges to color %2d\n", color);
int insert_color = color;
if (!relevant_colors.contains(color) || blankable_colors.contains(color)) {
dbg("Inserting old color %2d as color 0\n", color);
insert_color = 0;
}
unordered_set<int>& mySet = edges[insert_color];
dbg("__This set: \n");
for (auto& target: mySet) {
dbg("%2d ", target+1);
}
dbg("\n__Other set: \n");
for (auto& target: otherSet) {
dbg("%2d ", target+1);
}
// insert smaller set into larger
if (mySet.size() < otherSet.size()) swap(mySet, otherSet);
mySet.insert(otherSet.begin(), otherSet.end());
dbg("\n__Result:\n");
for (auto& target: mySet) {
dbg("%2d ", target+1);
}
dbg("\n____________\n");
}
dbg("ENDING JOIN STATE\n");
for (auto& [color, mySet] : edges) {
dbg("Now have edges to color %2d:\n", color);
for (auto& target: mySet) {
dbg("%2d ", target+1);
}
dbg("\n");
}
dbg("----------------------\n");
// other.edges.clear();
}
};
struct UnionFinder {
private:
vector<int> parent;
vector<int> rank;
public:
vector<int> node_colors;
vector<int> color_counts;
vector<int> color_examples;
vector<EdgeSystem> edge_systems; // edge_systems[X].edges[Y] - set of edges to nodes of color Y from node X
unordered_set<int> relevant_colors;
unordered_set<int> blankable_colors;
explicit UnionFinder(const int n_nodes, const int n_colors) : parent(n_nodes), rank(n_nodes, 0), node_colors(n_nodes), color_counts(n_colors, 0), color_examples(n_colors), edge_systems(n_nodes) {
iota(parent.begin(), parent.end(), 0);
}
// find group id of node x
int do_find(const int x) {
if (parent[x] != x)
parent[x] = do_find(parent[x]);
return parent[x];
}
// join nodes x and y into one group
void do_union(int x, int y) {
x = do_find(x);
y = do_find(y);
dbg(" UNIONING GROUPS OF %d and %d\n", x+1, y+1);
if (x == y) return;
int color = node_colors[x];
if (relevant_colors.contains(color)) {
color_counts[color] -= 1;
if (color_counts[color] == 1) {
dbg(" COLOR %2d IS NOW BLANKABLE!\n", color);
blankable_colors.insert(color);
}
}
if (rank[x] < rank[y]) swap(x, y);
parent[y] = x;
if (rank[x] == rank[y]) rank[x]++;
dbg(" NEW GROUP ID: %d\n", x+1);
edge_systems[x].join(edge_systems[y], relevant_colors, blankable_colors);
}
// turn group of node X into a blank node
// this will:
// - do_union of it with any adjacent blank nodes
// - join all nodes of the same color connected to the new big blank
void blank(const int color_to_blank) {
int group_to_blank = do_find(color_examples[color_to_blank]);
dbg("BLANKING COLOR %2d (group %2d)\n", color_to_blank, group_to_blank+1);
relevant_colors.erase(color_to_blank);
// UNION WITH ANY BLANK NODES
unordered_set<int> blank_systems;
vector<int> colors_to_erase;
for (auto& [color, edges] : edge_systems[group_to_blank].edges) {
if (!relevant_colors.contains(color) || blankable_colors.contains(color)) {
dbg("JOINING WITH BLANK GROUP, FORMERLY COLOR %d\n", color);
// color is blank
for (auto& edge: edges) {
blank_systems.insert(do_find(edge));
}
colors_to_erase.push_back(color);
}
}
for (auto& color: colors_to_erase) {
edge_systems[group_to_blank].edges.erase(color);
}
for (auto& system: blank_systems) {
do_union(group_to_blank, system);
}
int bigblank = do_find(group_to_blank);
// WE ARE NOW UNIONED INTO ONE BIG BLANK. LET'S TRY TO CONNECT SOME NODES.
for (auto& [color, edges]: edge_systems[bigblank].edges) {
if (relevant_colors.contains(color)) {
dbg("TRYING TO JOIN ANY NODES OF COLOR %2d\n", color);
if (edges.size() < 2) {
dbg(" NOT ENOUGH NODES OF THIS COLOR.\n");
dbg(" (Only found edge to %2d)\n", (*edges.begin())+1);
continue;
}
vector<int> to_join;
for (auto& edge: edges) {
to_join.push_back(edge);
dbg(" JOINING NODE: %2d\n", edge+1);
}
int focus = do_find(to_join[0]);
for (int i = 1; i < to_join.size(); ++i) {
int nxt = do_find(to_join[i]);
if (focus != nxt) {
do_union(focus, nxt);
focus = do_find(focus);
}
}
dbg(" REMAINING COUNT OF COLOR %2d: %2d\n", color, color_counts[color]);
// reduce the edge list for the future
edge_systems[bigblank].edges[color] = unordered_set<int>({do_find(focus)});
}
}
// AFTER CREATING THE MEGABLANK: GO THROUGH ALL COLORS WE HAVE EDGES TO
// FOR EACH COLOR:
// if no longer relevant: remove key
// if only has one edge: ignore
// if multiple edges: union all nodes. remove all edges. add edge with only the root.
}
};
int main() {
int t;
scanf("%d", &t);
for (int ti = 0; ti < t; ++ti) {
int n, m, k;
scanf("%d %d %d", &n, &m, &k);
UnionFinder union_finder(n, k+1);
for (int i = 0; i < n; ++i) {
int color;
scanf("%d", &color);
union_finder.node_colors[i] = color;
union_finder.color_counts[color] += 1;
union_finder.relevant_colors.insert(color);
union_finder.color_examples[color] = i;
}
dbg("REVELANT COLORS:\n");
for (auto& color: union_finder.relevant_colors) {
dbg("%2d: %2d\n", color, union_finder.color_counts[color]);
}
for (auto& color: union_finder.relevant_colors) {
if (union_finder.color_counts[color] == 1) {
dbg("COLOR %2d IS BLANKABLE FROM THE START!\n", color);
union_finder.blankable_colors.insert(color);
}
}
for (int i = 0; i < m; ++i) {
int a, b;
scanf("%d %d", &a, &b);
// -1 to stay 0-indexed
a -= 1;
b -= 1;
int a_color = union_finder.node_colors[a];
int b_color = union_finder.node_colors[b];
if (a_color == b_color) {
union_finder.do_union(a, b);
} else {
int a_root = union_finder.do_find(a);
int b_root = union_finder.do_find(b);
union_finder.edge_systems[a_root].edges[b_color].insert(b_root);
union_finder.edge_systems[b_root].edges[a_color].insert(a_root);
}
}
dbg("---------- STARTING OPERATION ----------\n");
bool broken = false;
while (!union_finder.blankable_colors.empty()) {
if (union_finder.blankable_colors.size() == union_finder.relevant_colors.size()) {
broken = true;
break;
}
int color_to_blank = *union_finder.blankable_colors.begin();
dbg("NEXT COLOR TO BLANK: %2d\n", color_to_blank);
union_finder.blankable_colors.erase(color_to_blank);
union_finder.blank(color_to_blank);
}
if (!broken && !union_finder.relevant_colors.empty()) {
printf("NIE\n");
dbg("COULD NOT BLANK WHOLE GRAPH\n");
for (auto& color: union_finder.relevant_colors) {
dbg("COLOR LEFT: %2d\n", color);
}
} else {
printf("TAK\n");
}
}
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 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 | #include <algorithm> #include <cstdio> #include <numeric> #include <vector> #include <map> #include <unordered_set> #include <unordered_map> #ifdef LOCAL #define dbg(...) fprintf(stderr, __VA_ARGS__) #else #define dbg(...) #endif using namespace std; struct EdgeSystem { unordered_map<int, unordered_set<int>> edges; explicit EdgeSystem() = default; void join(EdgeSystem& other, const unordered_set<int>& relevant_colors, const unordered_set<int>& blankable_colors) { dbg("STARTING JOIN STATE\n"); for (auto& [color, mySet] : edges) { dbg("Now have edges to color %2d:\n", color); for (auto& target: mySet) { dbg("%2d ", target+1); } dbg("\n"); } dbg("----------------------\n"); for (auto& [color, otherSet] : other.edges) { dbg("Joining edges to color %2d\n", color); int insert_color = color; if (!relevant_colors.contains(color) || blankable_colors.contains(color)) { dbg("Inserting old color %2d as color 0\n", color); insert_color = 0; } unordered_set<int>& mySet = edges[insert_color]; dbg("__This set: \n"); for (auto& target: mySet) { dbg("%2d ", target+1); } dbg("\n__Other set: \n"); for (auto& target: otherSet) { dbg("%2d ", target+1); } // insert smaller set into larger if (mySet.size() < otherSet.size()) swap(mySet, otherSet); mySet.insert(otherSet.begin(), otherSet.end()); dbg("\n__Result:\n"); for (auto& target: mySet) { dbg("%2d ", target+1); } dbg("\n____________\n"); } dbg("ENDING JOIN STATE\n"); for (auto& [color, mySet] : edges) { dbg("Now have edges to color %2d:\n", color); for (auto& target: mySet) { dbg("%2d ", target+1); } dbg("\n"); } dbg("----------------------\n"); // other.edges.clear(); } }; struct UnionFinder { private: vector<int> parent; vector<int> rank; public: vector<int> node_colors; vector<int> color_counts; vector<int> color_examples; vector<EdgeSystem> edge_systems; // edge_systems[X].edges[Y] - set of edges to nodes of color Y from node X unordered_set<int> relevant_colors; unordered_set<int> blankable_colors; explicit UnionFinder(const int n_nodes, const int n_colors) : parent(n_nodes), rank(n_nodes, 0), node_colors(n_nodes), color_counts(n_colors, 0), color_examples(n_colors), edge_systems(n_nodes) { iota(parent.begin(), parent.end(), 0); } // find group id of node x int do_find(const int x) { if (parent[x] != x) parent[x] = do_find(parent[x]); return parent[x]; } // join nodes x and y into one group void do_union(int x, int y) { x = do_find(x); y = do_find(y); dbg(" UNIONING GROUPS OF %d and %d\n", x+1, y+1); if (x == y) return; int color = node_colors[x]; if (relevant_colors.contains(color)) { color_counts[color] -= 1; if (color_counts[color] == 1) { dbg(" COLOR %2d IS NOW BLANKABLE!\n", color); blankable_colors.insert(color); } } if (rank[x] < rank[y]) swap(x, y); parent[y] = x; if (rank[x] == rank[y]) rank[x]++; dbg(" NEW GROUP ID: %d\n", x+1); edge_systems[x].join(edge_systems[y], relevant_colors, blankable_colors); } // turn group of node X into a blank node // this will: // - do_union of it with any adjacent blank nodes // - join all nodes of the same color connected to the new big blank void blank(const int color_to_blank) { int group_to_blank = do_find(color_examples[color_to_blank]); dbg("BLANKING COLOR %2d (group %2d)\n", color_to_blank, group_to_blank+1); relevant_colors.erase(color_to_blank); // UNION WITH ANY BLANK NODES unordered_set<int> blank_systems; vector<int> colors_to_erase; for (auto& [color, edges] : edge_systems[group_to_blank].edges) { if (!relevant_colors.contains(color) || blankable_colors.contains(color)) { dbg("JOINING WITH BLANK GROUP, FORMERLY COLOR %d\n", color); // color is blank for (auto& edge: edges) { blank_systems.insert(do_find(edge)); } colors_to_erase.push_back(color); } } for (auto& color: colors_to_erase) { edge_systems[group_to_blank].edges.erase(color); } for (auto& system: blank_systems) { do_union(group_to_blank, system); } int bigblank = do_find(group_to_blank); // WE ARE NOW UNIONED INTO ONE BIG BLANK. LET'S TRY TO CONNECT SOME NODES. for (auto& [color, edges]: edge_systems[bigblank].edges) { if (relevant_colors.contains(color)) { dbg("TRYING TO JOIN ANY NODES OF COLOR %2d\n", color); if (edges.size() < 2) { dbg(" NOT ENOUGH NODES OF THIS COLOR.\n"); dbg(" (Only found edge to %2d)\n", (*edges.begin())+1); continue; } vector<int> to_join; for (auto& edge: edges) { to_join.push_back(edge); dbg(" JOINING NODE: %2d\n", edge+1); } int focus = do_find(to_join[0]); for (int i = 1; i < to_join.size(); ++i) { int nxt = do_find(to_join[i]); if (focus != nxt) { do_union(focus, nxt); focus = do_find(focus); } } dbg(" REMAINING COUNT OF COLOR %2d: %2d\n", color, color_counts[color]); // reduce the edge list for the future edge_systems[bigblank].edges[color] = unordered_set<int>({do_find(focus)}); } } // AFTER CREATING THE MEGABLANK: GO THROUGH ALL COLORS WE HAVE EDGES TO // FOR EACH COLOR: // if no longer relevant: remove key // if only has one edge: ignore // if multiple edges: union all nodes. remove all edges. add edge with only the root. } }; int main() { int t; scanf("%d", &t); for (int ti = 0; ti < t; ++ti) { int n, m, k; scanf("%d %d %d", &n, &m, &k); UnionFinder union_finder(n, k+1); for (int i = 0; i < n; ++i) { int color; scanf("%d", &color); union_finder.node_colors[i] = color; union_finder.color_counts[color] += 1; union_finder.relevant_colors.insert(color); union_finder.color_examples[color] = i; } dbg("REVELANT COLORS:\n"); for (auto& color: union_finder.relevant_colors) { dbg("%2d: %2d\n", color, union_finder.color_counts[color]); } for (auto& color: union_finder.relevant_colors) { if (union_finder.color_counts[color] == 1) { dbg("COLOR %2d IS BLANKABLE FROM THE START!\n", color); union_finder.blankable_colors.insert(color); } } for (int i = 0; i < m; ++i) { int a, b; scanf("%d %d", &a, &b); // -1 to stay 0-indexed a -= 1; b -= 1; int a_color = union_finder.node_colors[a]; int b_color = union_finder.node_colors[b]; if (a_color == b_color) { union_finder.do_union(a, b); } else { int a_root = union_finder.do_find(a); int b_root = union_finder.do_find(b); union_finder.edge_systems[a_root].edges[b_color].insert(b_root); union_finder.edge_systems[b_root].edges[a_color].insert(a_root); } } dbg("---------- STARTING OPERATION ----------\n"); bool broken = false; while (!union_finder.blankable_colors.empty()) { if (union_finder.blankable_colors.size() == union_finder.relevant_colors.size()) { broken = true; break; } int color_to_blank = *union_finder.blankable_colors.begin(); dbg("NEXT COLOR TO BLANK: %2d\n", color_to_blank); union_finder.blankable_colors.erase(color_to_blank); union_finder.blank(color_to_blank); } if (!broken && !union_finder.relevant_colors.empty()) { printf("NIE\n"); dbg("COULD NOT BLANK WHOLE GRAPH\n"); for (auto& color: union_finder.relevant_colors) { dbg("COLOR LEFT: %2d\n", color); } } else { printf("TAK\n"); } } return 0; } |
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