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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 | #include <bits/stdc++.h>
using namespace std;
struct Solver {
int N, M;
vector<int> A, B;
bool need[41][41];
mt19937_64 rng;
Solver(int n, int m, const vector<int>& a, const vector<int>& b)
: N(n), M(m), A(a), B(b) {
memset(need, 0, sizeof(need));
for (int i = 0; i < M; ++i) {
int u = A[i];
int v = B[i];
if (u > v) swap(u, v);
need[u][v] = true;
}
rng.seed((uint64_t)chrono::high_resolution_clock::now().time_since_epoch().count());
}
pair<int, vector<vector<int>>> attempt(int K) {
const int PEN_MISS = 10;
const int PEN_FORBID = 100;
const int PEN_UNUSED = 50;
vector<vector<int>> grid(K, vector<int>(K));
vector<int> colorCount(N + 1, 0);
int curAdj[41][41];
memset(curAdj, 0, sizeof(curAdj));
uniform_int_distribution<int> colorDist(1, N);
// Initial random grid
for (int r = 0; r < K; ++r) {
for (int c = 0; c < K; ++c) {
int col = colorDist(rng);
grid[r][c] = col;
}
}
// Ensure each color appears at least once in first N cells
for (int i = 0; i < N; ++i) {
int r = i / K;
int c = i % K;
grid[r][c] = i + 1;
}
// Recompute colorCount and adjacency
auto recompute_all = [&]() -> int {
fill(colorCount.begin(), colorCount.end(), 0);
memset(curAdj, 0, sizeof(curAdj));
for (int r = 0; r < K; ++r) {
for (int c = 0; c < K; ++c) {
int col = grid[r][c];
colorCount[col]++;
}
}
for (int r = 0; r < K; ++r) {
for (int c = 0; c < K; ++c) {
int col = grid[r][c];
if (c + 1 < K) {
int col2 = grid[r][c + 1];
if (col != col2) {
int i = min(col, col2);
int j = max(col, col2);
curAdj[i][j]++;
}
}
if (r + 1 < K) {
int col2 = grid[r + 1][c];
if (col != col2) {
int i = min(col, col2);
int j = max(col, col2);
curAdj[i][j]++;
}
}
}
}
int pen = 0;
for (int col = 1; col <= N; ++col) {
if (colorCount[col] == 0) pen += PEN_UNUSED;
}
for (int i = 1; i <= N; ++i) {
for (int j = i + 1; j <= N; ++j) {
int cnt = curAdj[i][j];
if (need[i][j]) {
if (cnt == 0) pen += PEN_MISS;
} else {
if (cnt > 0) pen += PEN_FORBID;
}
}
}
return pen;
};
int totalPenalty = recompute_all();
vector<vector<int>> bestGrid = grid;
int bestPenalty = totalPenalty;
if (bestPenalty == 0) return {0, bestGrid};
long long TOT_ITERS = 400LL * K * K;
if (TOT_ITERS < 20000) TOT_ITERS = 20000;
const double Tstart = 2.0;
const double Tend = 0.01;
double alpha = pow(Tend / Tstart, 1.0 / (double)TOT_ITERS);
double T = Tstart;
uniform_real_distribution<double> realDist(0.0, 1.0);
struct PairDelta {
int u, v;
int delta;
};
for (long long it = 0; it < TOT_ITERS && bestPenalty > 0; ++it) {
int r = (int)(rng() % K);
int c = (int)(rng() % K);
int oldColor = grid[r][c];
if (N == 1) break; // should not happen here because N>1 in this attempt
int newColor = (int)(rng() % (N - 1)) + 1;
if (newColor >= oldColor) ++newColor;
if (newColor == oldColor) continue;
int deltaColor = 0;
int oldCountA = colorCount[oldColor];
int oldCountB = colorCount[newColor];
if (oldCountA == 1) deltaColor += PEN_UNUSED;
if (oldCountB == 0) deltaColor -= PEN_UNUSED;
PairDelta pd[8];
int pdSize = 0;
auto addDelta = [&](int u, int v, int d) {
if (u == v) return;
if (u > v) swap(u, v);
for (int k = 0; k < pdSize; ++k) {
if (pd[k].u == u && pd[k].v == v) {
pd[k].delta += d;
return;
}
}
pd[pdSize].u = u;
pd[pdSize].v = v;
pd[pdSize].delta = d;
++pdSize;
};
auto process_neighbor = [&](int nr, int nc) {
int x = grid[nr][nc];
if (x == oldColor) {
if (newColor != x) {
addDelta(min(newColor, x), max(newColor, x), +1);
}
} else if (x == newColor) {
addDelta(min(oldColor, x), max(oldColor, x), -1);
} else {
addDelta(min(oldColor, x), max(oldColor, x), -1);
addDelta(min(newColor, x), max(newColor, x), +1);
}
};
if (r > 0) process_neighbor(r - 1, c);
if (r + 1 < K) process_neighbor(r + 1, c);
if (c > 0) process_neighbor(r, c - 1);
if (c + 1 < K) process_neighbor(r, c + 1);
int deltaEdges = 0;
for (int k = 0; k < pdSize; ++k) {
int u = pd[k].u;
int v = pd[k].v;
int d = pd[k].delta;
if (d == 0) continue;
int oldCnt = curAdj[u][v];
int newCnt = oldCnt + d;
int oldP, newP;
if (need[u][v]) {
oldP = (oldCnt == 0 ? PEN_MISS : 0);
newP = (newCnt == 0 ? PEN_MISS : 0);
} else {
oldP = (oldCnt > 0 ? PEN_FORBID : 0);
newP = (newCnt > 0 ? PEN_FORBID : 0);
}
deltaEdges += newP - oldP;
}
int delta = deltaColor + deltaEdges;
int newPenalty = totalPenalty + delta;
bool accept = false;
if (delta <= 0) {
accept = true;
} else {
double prob = exp(- (double)delta / T);
if (realDist(rng) < prob) accept = true;
}
if (accept) {
grid[r][c] = newColor;
colorCount[oldColor]--;
colorCount[newColor]++;
for (int k = 0; k < pdSize; ++k) {
int u = pd[k].u;
int v = pd[k].v;
int d = pd[k].delta;
if (d != 0) curAdj[u][v] += d;
}
totalPenalty = newPenalty;
if (totalPenalty < bestPenalty) {
bestPenalty = totalPenalty;
bestGrid = grid;
if (bestPenalty == 0) break;
}
}
T *= alpha;
if (T < Tend) T = Tend;
}
return {bestPenalty, bestGrid};
}
vector<vector<int>> solve() {
if (N == 1) {
return vector<vector<int>>(1, vector<int>(1, 1));
}
int K = min(240, max(3 * N, 5));
int bestPenalty = INT_MAX;
vector<vector<int>> bestGrid;
int TRIES = 3;
for (int t = 0; t < TRIES; ++t) {
auto res = attempt(K);
if (res.first < bestPenalty) {
bestPenalty = res.first;
bestGrid = res.second;
}
if (bestPenalty == 0) break;
}
// As a fallback, if somehow not perfect, just return bestGrid (may be invalid in worst case).
return bestGrid;
}
};
vector<vector<int>> create_map(int N, int M, vector<int> A, vector<int> B) {
Solver solver(N, M, A, B);
return solver.solve();
}
int main() {
ios::sync_with_stdio(false);
cin.tie(nullptr);
int T;
if (!(cin >> T)) return 0;
while (T--) {
int N, M;
cin >> N >> M;
vector<int> A(M), B(M);
for (int i = 0; i < M; ++i) cin >> A[i] >> B[i];
vector<vector<int>> C = create_map(N, M, A, B);
int P = (int)C.size();
cout << P << "\n";
for (int i = 0; i < P; ++i) {
cout << (int)C[i].size() << (i + 1 == P ? '\n' : ' ');
}
for (int i = 0; i < P; ++i) {
for (int j = 0; j < (int)C[i].size(); ++j) {
if (j) cout << ' ';
cout << C[i][j];
}
cout << "\n";
}
}
return 0;
} |