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1fd0050 | 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 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 | #include <vector>
#include <cmath>
#include <algorithm>
#include <cstdlib>
#include <ctime>
#include <iostream>
#include <map>
using namespace std;
// Global variables for convenience within create_map
static bool adj[45][45];
static int color_counts[45];
static int grid[245][245];
static int edge_realized_counts[45][45];
static int N_val, M_val;
// Helper to check if placing a color at (r, c) is valid according to problem conditions
// Condition: For each pair of adjacent cells with different colors, the countries must be adjacent.
bool is_valid(int r, int c, int color, int K) {
int dr[] = {-1, 1, 0, 0};
int dc[] = {0, 0, -1, 1};
for (int i = 0; i < 4; i++) {
int nr = r + dr[i];
int nc = c + dc[i];
if (nr >= 0 && nr < K && nc >= 0 && nc < K) {
int neighbor_color = grid[nr][nc];
// 0 is treated as empty, which will be filled later.
// A non-empty neighbor must be either same color or adjacent in graph.
if (neighbor_color != 0 && neighbor_color != color) {
if (!adj[color][neighbor_color]) return false;
}
}
}
return true;
}
// Recursive function to embed a spanning tree into the grid
bool embed_tree(int u, int r, int c, int K, const vector<vector<int>>& tree_adj, vector<bool>& visited) {
visited[u] = true;
grid[r][c] = u;
color_counts[u]++;
// Randomize processing order of neighbors to produce different layouts
vector<int> neighbors = tree_adj[u];
for (int i = 0; i < neighbors.size(); i++) swap(neighbors[i], neighbors[rand() % neighbors.size()]);
for (int v : neighbors) {
if (!visited[v]) {
int dr[] = {-1, 1, 0, 0};
int dc[] = {0, 0, -1, 1};
vector<int> dirs = {0, 1, 2, 3};
for (int i = 0; i < 4; i++) swap(dirs[i], dirs[rand() % 4]);
bool placed = false;
for (int i : dirs) {
int nr = r + dr[i];
int nc = c + dc[i];
if (nr >= 0 && nr < K && nc >= 0 && nc < K && grid[nr][nc] == 0) {
if (is_valid(nr, nc, v, K)) {
if (embed_tree(v, nr, nc, K, tree_adj, visited)) {
placed = true;
}
}
}
}
if (!placed) return false;
}
}
return true;
}
vector<vector<int>> create_map(int N, int M, vector<int> A, vector<int> B) {
N_val = N;
M_val = M;
// Reset adjacency matrix
for (int i = 1; i <= N; i++) {
for (int j = 1; j <= N; j++) adj[i][j] = false;
}
for (int i = 0; i < M; i++) {
adj[A[i]][B[i]] = true;
adj[B[i]][A[i]] = true;
}
// Build spanning forest to ensure initial connectivity and presence of all nodes
vector<vector<int>> tree_adj(N + 1);
{
vector<bool> vis(N + 1, false);
for(int start_node = 1; start_node <= N; ++start_node) {
if(vis[start_node]) continue;
vis[start_node] = true;
vector<int> bfs_q;
bfs_q.push_back(start_node);
int h = 0;
while(h < bfs_q.size()){
int u = bfs_q[h++];
vector<int> nb;
for(int v=1; v<=N; ++v) if(adj[u][v]) nb.push_back(v);
for(int k=0; k<nb.size(); ++k) swap(nb[k], nb[rand()%nb.size()]);
for(int v : nb){
if(!vis[v]){
vis[v] = true;
tree_adj[u].push_back(v);
tree_adj[v].push_back(u);
bfs_q.push_back(v);
}
}
}
}
}
// Iteratively try to find a solution for K, starting from a small heuristic value
int start_K = (int)ceil(sqrt(N));
if (start_K < 2 && N > 1) start_K = 2;
if (N == 1) start_K = 1;
for (int K = start_K; K <= 240; K++) {
// Number of attempts for current K.
int restarts = (K <= N + 2) ? 10 : 2;
if (K > N + 5) restarts = 1;
for (int rst = 0; rst < restarts; rst++) {
// Clear grid and counters
for(int i=0; i<K; ++i) for(int j=0; j<K; ++j) grid[i][j] = 0;
for(int i=1; i<=N; ++i) color_counts[i] = 0;
for(int i=1; i<=N; ++i) for(int j=1; j<=N; ++j) edge_realized_counts[i][j] = 0;
// Embed the spanning forest
vector<bool> visited(N + 1, false);
bool fail = false;
for(int i=1; i<=N; ++i) {
if(!visited[i]) {
int r = -1, c = -1;
// Try to place new component
if(i == 1 && grid[K/2][K/2] == 0) { r=K/2; c=K/2; }
else {
// Find a random free spot
int tries = 0;
while(tries < 50) {
int tr = rand()%K; int tc = rand()%K;
if(grid[tr][tc] == 0) { r=tr; c=tc; break; }
tries++;
}
// If random fail, linear scan
if(r == -1) {
for(int rr=0; rr<K; ++rr){
for(int cc=0; cc<K; ++cc){
if(grid[rr][cc] == 0) { r=rr; c=cc; goto found; }
}
}
found:;
}
}
if(r == -1) { fail = true; break; }
if(!embed_tree(i, r, c, K, tree_adj, visited)) {
fail = true; break;
}
}
}
if(fail) continue;
// Initialize stats based on the embedding
int current_realized = 0;
int empty_cells = 0;
for(int i=0; i<K; ++i){
for(int j=0; j<K; ++j){
if(grid[i][j] == 0) { empty_cells++; continue; }
int u = grid[i][j];
// Check neighbors to count edges
int dr[] = {0, 1};
int dc[] = {1, 0};
for(int d=0; d<2; ++d) {
int ni = i + dr[d];
int nj = j + dc[d];
if (ni < K && nj < K && grid[ni][nj] != 0) {
int v = grid[ni][nj];
if(u != v){
if(edge_realized_counts[u][v] == 0 && adj[u][v]) current_realized++;
edge_realized_counts[u][v]++;
edge_realized_counts[v][u]++;
}
}
}
}
}
// Simulated Annealing / Random Search
int max_iter = 15000;
if (K < N) max_iter = 30000;
for(int iter=0; iter<max_iter; ++iter){
if(empty_cells == 0 && current_realized == M) break;
int r = rand() % K;
int c = rand() % K;
int old_c = grid[r][c];
// Prioritize filling empty cells
if(empty_cells > 0 && old_c != 0 && rand()%100 < 70) continue;
if(empty_cells > 0 && old_c == 0) {
// Find an empty cell if we picked a filled one by luck?
// Or just rely on random picking eventually hitting an empty one.
// To speed up, try to pick empty explicitly sometimes
int tries = 0;
while(grid[r][c] != 0 && tries < 5) {
r = rand() % K; c = rand() % K;
tries++;
}
if(grid[r][c] != 0) continue;
old_c = 0;
}
int new_c = (rand() % N) + 1;
if(new_c == old_c) continue;
// Cannot remove last instance of a color
if(old_c != 0 && color_counts[old_c] == 1) continue;
if(!is_valid(r, c, new_c, K)) continue;
// Calculate gain
int realized_gain = 0;
int dr[] = {-1, 1, 0, 0};
int dc[] = {0, 0, -1, 1};
// Impact of removing old
if(old_c != 0){
for(int d=0; d<4; ++d){
int nr = r+dr[d]; int nc = c+dc[d];
if(nr>=0 && nr<K && nc>=0 && nc<K){
int nb = grid[nr][nc];
if(nb!=0 && nb!=old_c){
if(edge_realized_counts[old_c][nb] == 1 && adj[old_c][nb]) realized_gain--;
}
}
}
}
// Impact of adding new
for(int d=0; d<4; ++d){
int nr = r+dr[d]; int nc = c+dc[d];
if(nr>=0 && nr<K && nc>=0 && nc<K){
int nb = grid[nr][nc];
if(nb!=0 && nb!=new_c){
if(edge_realized_counts[new_c][nb] == 0 && adj[new_c][nb]) realized_gain++;
}
}
}
// Acceptance probability
bool accept = false;
if(old_c == 0) accept = true; // Always fill empty cells
else {
if(realized_gain > 0) accept = true;
else if(realized_gain == 0 && rand()%20==0) accept = true;
else if(realized_gain < 0 && rand()%1000==0) accept = true;
}
if(accept){
if(old_c != 0){
color_counts[old_c]--;
for(int d=0; d<4; ++d){
int nr = r+dr[d]; int nc = c+dc[d];
if(nr>=0 && nr<K && nc>=0 && nc<K){
int nb = grid[nr][nc];
if(nb!=0 && nb!=old_c){
if(edge_realized_counts[old_c][nb] == 1 && adj[old_c][nb]) current_realized--;
edge_realized_counts[old_c][nb]--;
edge_realized_counts[nb][old_c]--;
}
}
}
} else {
empty_cells--;
}
grid[r][c] = new_c;
color_counts[new_c]++;
for(int d=0; d<4; ++d){
int nr = r+dr[d]; int nc = c+dc[d];
if(nr>=0 && nr<K && nc>=0 && nc<K){
int nb = grid[nr][nc];
if(nb!=0 && nb!=new_c){
if(edge_realized_counts[new_c][nb] == 0 && adj[new_c][nb]) current_realized++;
edge_realized_counts[new_c][nb]++;
edge_realized_counts[nb][new_c]++;
}
}
}
}
}
if(empty_cells == 0 && current_realized == M){
vector<vector<int>> res(K, vector<int>(K));
for(int i=0; i<K; ++i) for(int j=0; j<K; ++j) res[i][j] = grid[i][j];
return res;
}
}
}
return {};
}
int main() {
srand(time(NULL));
int T;
if (cin >> T) {
while(T--) {
int N, M;
if (!(cin >> N >> M)) break;
vector<int> A(M), B(M);
for(int i=0; i<M; ++i) cin >> A[i] >> B[i];
vector<vector<int>> result = create_map(N, M, A, B);
cout << result.size() << endl;
for(int i=0; i<result.size(); ++i) {
cout << result[i].size();
for(int j=0; j<result[i].size(); ++j) {
cout << " " << result[i][j];
}
cout << endl;
}
}
}
return 0;
} |