File size: 8,772 Bytes
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 | #include <bits/stdc++.h>
using namespace std;
struct Layout {
int w = 0, h = 0; // total rectangle size including 1-cell border
int innerW = 0, innerH = 0; // inner size
int childrenH = 0; // packed children height inside inner area
int sep = 0; // separator rows between children and gadgets (0/1)
int gadgetW = 0, gadgetH = 0;
int gadgetStartY = 0; // relative to top of rectangle
vector<int> order; // children order
vector<pair<int,int>> pos; // child positions in inner coords (y,x), aligned with order
};
static int pack_children_height(const vector<int>& order, const vector<Layout>& lay, int innerW) {
if (order.empty()) return 0;
int x = 0, y = 0, rowH = 0;
for (int v : order) {
int wv = lay[v].w;
int hv = lay[v].h;
if (x > 0 && x + wv > innerW) {
y += rowH + 1; // 1-row gap between shelves
x = 0;
rowH = 0;
}
// place at (y, x)
x += wv;
if (x < innerW) x += 1; // 1-col gap to next
rowH = max(rowH, hv);
}
return y + rowH;
}
static int pack_children_positions(const vector<int>& order, const vector<Layout>& lay, int innerW, vector<pair<int,int>>& outPos) {
outPos.clear();
if (order.empty()) return 0;
outPos.reserve(order.size());
int x = 0, y = 0, rowH = 0;
for (int v : order) {
int wv = lay[v].w;
int hv = lay[v].h;
if (x > 0 && x + wv > innerW) {
y += rowH + 1;
x = 0;
rowH = 0;
}
outPos.push_back({y, x});
x += wv;
if (x < innerW) x += 1;
rowH = max(rowH, hv);
}
return y + rowH;
}
struct Builder {
int N = 0, M = 0;
vector<int> A, B;
vector<vector<int>> adj;
bool isEdge[41][41]{};
bool isTree[41][41]{};
vector<int> parent;
vector<vector<int>> children;
vector<vector<int>> gadgets;
vector<Layout> lay;
int slotRows = 2; // gadget slots rows count => gadgetH = 2*slotRows-1 = 3
int gadgetHConst = 3;
bool build_spanning_tree() {
parent.assign(N + 1, -1);
children.assign(N + 1, {});
queue<int> q;
parent[1] = 0;
q.push(1);
while (!q.empty()) {
int u = q.front(); q.pop();
for (int v : adj[u]) {
if (parent[v] == -1) {
parent[v] = u;
q.push(v);
}
}
}
for (int i = 2; i <= N; i++) {
if (parent[i] == -1) return false;
int p = parent[i];
isTree[min(i,p)][max(i,p)] = true;
children[p].push_back(i);
}
return true;
}
void assign_gadgets() {
gadgets.assign(N + 1, {});
vector<int> load(N + 1, 0);
for (int i = 0; i < M; i++) {
int a = A[i], b = B[i];
int x = min(a,b), y = max(a,b);
if (isTree[x][y]) continue;
int u;
if (load[a] < load[b]) u = a;
else if (load[b] < load[a]) u = b;
else u = min(a,b);
int v = (u == a ? b : a);
gadgets[u].push_back(v);
load[u]++;
}
}
void compute_gadget_dims(int u, int& gW, int& gH) {
int g = (int)gadgets[u].size();
if (g == 0) { gW = 0; gH = 0; return; }
int cols = (g + slotRows - 1) / slotRows;
gW = 2 * cols - 1;
gH = gadgetHConst;
}
bool dfs_size(int u, int Kmax) {
for (int v : children[u]) {
if (!dfs_size(v, Kmax)) return false;
}
Layout L;
int gW, gH;
compute_gadget_dims(u, gW, gH);
L.gadgetW = gW;
L.gadgetH = gH;
// child order: sort by width desc, then height desc
L.order = children[u];
sort(L.order.begin(), L.order.end(), [&](int a, int b) {
if (lay[a].w != lay[b].w) return lay[a].w > lay[b].w;
return lay[a].h > lay[b].h;
});
int maxChildW = 0;
for (int v : L.order) maxChildW = max(maxChildW, lay[v].w);
int minInnerW = max(1, max(maxChildW, gW));
int bestInnerW = -1;
int bestInnerH = -1;
int bestChildrenH = -1;
int bestSep = 0;
long long bestMetric = (1LL << 60);
for (int innerW = minInnerW; innerW <= Kmax - 2; innerW++) {
int cH = pack_children_height(L.order, lay, innerW);
int sep = (cH > 0 && gH > 0) ? 1 : 0;
int innerH = cH + sep + gH;
if (innerH < 1) innerH = 1;
int W = innerW + 2;
int H = innerH + 2;
if (W > Kmax || H > Kmax) continue;
long long metric = (long long)max(W, H) * 1000000LL + (long long)(W + H);
if (metric < bestMetric) {
bestMetric = metric;
bestInnerW = innerW;
bestInnerH = innerH;
bestChildrenH = cH;
bestSep = sep;
}
}
if (bestInnerW == -1) return false;
L.innerW = bestInnerW;
L.innerH = bestInnerH;
L.w = bestInnerW + 2;
L.h = bestInnerH + 2;
L.childrenH = bestChildrenH;
L.sep = bestSep;
L.gadgetStartY = 1 + bestChildrenH + bestSep;
// store positions
pack_children_positions(L.order, lay, bestInnerW, L.pos);
lay[u] = std::move(L);
return true;
}
void paint(int u, int top, int left, vector<vector<int>>& C) {
const Layout& L = lay[u];
for (int i = 0; i < L.h; i++) {
for (int j = 0; j < L.w; j++) {
C[top + i][left + j] = u;
}
}
// children
for (size_t i = 0; i < L.order.size(); i++) {
int v = L.order[i];
int y = L.pos[i].first;
int x = L.pos[i].second;
paint(v, top + 1 + y, left + 1 + x, C);
}
// gadgets (only overwrite in gadget area)
int g = (int)gadgets[u].size();
if (g > 0) {
int baseY = top + L.gadgetStartY;
int baseX = left + 1;
for (int idx = 0; idx < g; idx++) {
int rr = (idx % slotRows) * 2;
int cc = (idx / slotRows) * 2;
C[baseY + rr][baseX + cc] = gadgets[u][idx];
}
}
}
vector<vector<int>> create_map() {
if (N == 1) return vector<vector<int>>(1, vector<int>(1, 1));
adj.assign(N + 1, {});
memset(isEdge, 0, sizeof(isEdge));
memset(isTree, 0, sizeof(isTree));
for (int i = 0; i < M; i++) {
int a = A[i], b = B[i];
isEdge[a][b] = isEdge[b][a] = true;
adj[a].push_back(b);
adj[b].push_back(a);
}
if (!build_spanning_tree()) {
// Shouldn't happen due to guarantee; fallback to trivial (may be invalid)
return vector<vector<int>>(1, vector<int>(1, 1));
}
assign_gadgets();
int Kfound = -1;
int Kfinal = -1;
int Kstart = max(3, N);
lay.assign(N + 1, Layout());
for (int K = Kstart; K <= 240; K++) {
lay.assign(N + 1, Layout());
if (!dfs_size(1, K)) continue;
int rw = lay[1].w, rh = lay[1].h;
if (rw <= K && rh <= K) {
Kfound = K;
Kfinal = max(rw, rh);
break;
}
}
if (Kfound == -1) {
// Guaranteed to exist; last resort
Kfinal = 240;
lay.assign(N + 1, Layout());
dfs_size(1, 240);
}
vector<vector<int>> C(Kfinal, vector<int>(Kfinal, 1));
paint(1, 0, 0, C);
return C;
}
};
static vector<vector<int>> create_map(int N, int M, vector<int> A, vector<int> B) {
Builder b;
b.N = N;
b.M = M;
b.A = std::move(A);
b.B = std::move(B);
return b.create_map();
}
int main() {
ios::sync_with_stdio(false);
cin.tie(nullptr);
int T;
if (!(cin >> T)) return 0;
for (int tc = 0; tc < T; tc++) {
int N, M;
cin >> N >> M;
vector<int> A(M), B(M);
for (int i = 0; i < M; i++) cin >> A[i] >> B[i];
auto C = create_map(N, M, A, B);
int K = (int)C.size();
cout << K << "\n";
for (int i = 0; i < K; i++) {
if (i) cout << ' ';
cout << K;
}
cout << "\n\n";
for (int i = 0; i < K; i++) {
for (int j = 0; j < K; j++) {
if (j) cout << ' ';
cout << C[i][j];
}
cout << "\n";
}
}
return 0;
} |