File size: 8,239 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 | #include <bits/stdc++.h>
using namespace std;
struct Edge {
int u, v;
};
static vector<vector<int>> create_map(int N, int M, vector<int> A, vector<int> B) {
if (N == 1) {
return vector<vector<int>>(1, vector<int>(1, 1));
}
// Build base graph (0-indexed)
vector<vector<pair<int,int>>> adj(N); // (neighbor, edge id)
vector<Edge> edges;
edges.reserve(M);
vector<int> deg(N,0);
for (int i = 0; i < M; ++i) {
int u = A[i]-1, v = B[i]-1;
edges.push_back({u,v});
int id = (int)edges.size()-1;
adj[u].push_back({v,id});
adj[v].push_back({u,id});
deg[u]++; deg[v]++;
}
// Handle trivial or disconnected cases naively
// If no edges (should only be valid for N==1), fallback small
if (M == 0) {
// Put each color on diagonal in K=N grid but to avoid invalid adjacency
// we return a 1x1 with color 1 if N==1, else try to place a simple 2x2 valid if possible
// As a fallback, return N x N all color 1 to avoid invalid adjacencies except coverage (may not satisfy all cases)
vector<vector<int>> C(1, vector<int>(1, 1));
return C;
}
// Ensure we operate on the largest connected component (simple BFS/DFS)
vector<int> vis(N, 0);
vector<int> comp_id(N, -1);
int cid = 0;
for (int i = 0; i < N; ++i) if (!vis[i]) {
queue<int> q; q.push(i); vis[i]=1; comp_id[i]=cid;
while(!q.empty()){
int u=q.front();q.pop();
for(auto [v, id]: adj[u]){
if(!vis[v]){vis[v]=1; comp_id[v]=cid; q.push(v);}
}
}
cid++;
}
// find component with most edges participation
vector<int> comp_deg(cid,0);
for (auto &e: edges) {
comp_deg[comp_id[e.u]]++;
}
int best_comp = 0;
for (int i=1;i<cid;i++) if (comp_deg[i] > comp_deg[best_comp]) best_comp = i;
// Build subgraph of best component
vector<int> mapOldToNew(N, -1), mapNewToOld;
for (int i=0;i<N;i++) if (comp_id[i]==best_comp) {
mapOldToNew[i] = (int)mapNewToOld.size();
mapNewToOld.push_back(i);
}
int nC = (int)mapNewToOld.size();
vector<vector<pair<int,int>>> adjC(nC);
vector<Edge> edgesC;
edgesC.reserve(M);
vector<int> degC(nC,0);
for (auto &e: edges) {
if (comp_id[e.u]==best_comp) {
int u = mapOldToNew[e.u], v = mapOldToNew[e.v];
int id = (int)edgesC.size();
edgesC.push_back({u,v});
adjC[u].push_back({v,id});
adjC[v].push_back({u,id});
degC[u]++; degC[v]++;
}
}
// Pair odd degree vertices by adding duplicate edges along BFS paths (greedy)
vector<int> odd;
for (int i=0;i<nC;i++) if (degC[i]%2) odd.push_back(i);
auto bfs_path = [&](int s, int t)->vector<int>{
vector<int> par(nC, -1), pareid(nC, -1);
queue<int> q; q.push(s); par[s] = s;
while(!q.empty()){
int u=q.front();q.pop();
if(u==t) break;
for(auto [v,id]: adjC[u]){
if(par[v]==-1){
par[v]=u; pareid[v]=id; q.push(v);
}
}
}
vector<int> path_eids;
if(par[t]==-1) return path_eids;
int cur=t;
while(cur!=s){
path_eids.push_back(pareid[cur]);
cur=par[cur];
}
reverse(path_eids.begin(), path_eids.end());
return path_eids;
};
vector<int> unmatched = odd;
vector<int> usedOdd(nC,0);
vector<char> paired(nC,0);
while (!unmatched.empty()) {
int s = unmatched.back(); unmatched.pop_back();
if (paired[s]) continue;
// find nearest unmatched t
int best_t = -1;
vector<int> best_path;
for (int t : unmatched) if (!paired[t]) {
auto p = bfs_path(s, t);
if (p.empty()) continue;
if (best_t==-1 || p.size() < best_path.size()) {
best_t = t;
best_path = p;
}
}
if (best_t==-1) {
// fallback: pair with any other odd (if any) even without path (shouldn't happen in connected comp)
if (!unmatched.empty()) {
best_t = unmatched.back(); unmatched.pop_back();
// if still no path, break
auto p = bfs_path(s, best_t);
if (p.empty()) {
// cannot fix, break
break;
} else best_path = p;
} else break;
} else {
// remove best_t from unmatched
for (auto it = unmatched.begin(); it != unmatched.end(); ++it) {
if (*it == best_t) { unmatched.erase(it); break; }
}
}
// add duplicate edges along path
int cur = s;
for (int eid : best_path) {
int u = edgesC[eid].u, v = edgesC[eid].v;
// Add a duplicate edge instance (new edge id)
int id = (int)edgesC.size();
edgesC.push_back({u,v});
adjC[u].push_back({v,id});
adjC[v].push_back({u,id});
degC[u]++; degC[v]++;
}
paired[s]=paired[best_t]=1;
}
// Now run Hierholzer on multigraph edgesC
int start = -1;
for (int i=0;i<nC;i++) if (!adjC[i].empty()) { start=i; break; }
if (start == -1) {
// No edges in best component (shouldn't happen as M>0), fallback
vector<vector<int>> C(1, vector<int>(1, mapNewToOld.empty()?1:mapNewToOld[0]+1));
return C;
}
int E2 = (int)edgesC.size();
vector<char> used(E2, 0);
vector<int> itptr(nC, 0);
vector<vector<pair<int,int>>> adjIter = adjC;
vector<int> st;
vector<int> path;
st.push_back(start);
while(!st.empty()){
int u = st.back();
while(itptr[u] < (int)adjIter[u].size() && used[adjIter[u][itptr[u]].second]) itptr[u]++;
if (itptr[u] == (int)adjIter[u].size()) {
path.push_back(u);
st.pop_back();
} else {
auto [v, id] = adjIter[u][itptr[u]];
used[id] = 1;
st.push_back(v);
}
}
if ((int)path.size() < 2) {
// fallback
vector<vector<int>> C(1, vector<int>(1, mapNewToOld[start]+1));
return C;
}
reverse(path.begin(), path.end());
// Build sequence of original vertex labels (1-indexed)
vector<int> seq;
seq.reserve(path.size());
for (int x : path) seq.push_back(mapNewToOld[x] + 1);
// Remove last if equal to first to make a cyclic sequence edges = L
if (!seq.empty() && seq.front() == seq.back()) seq.pop_back();
int L = (int)seq.size();
if (L <= 0) {
vector<vector<int>> C(1, vector<int>(1, mapNewToOld[start]+1));
return C;
}
int K = min(L, 240);
// Build grid with rows rotated by row index, but to ensure coverage attempt to use mod spacing if L > 240 (best effort)
vector<vector<int>> C(K, vector<int>(K, 1));
if (L <= 240) {
for (int r=0;r<K;r++){
for (int c=0;c<K;c++){
C[r][c] = seq[(r + c) % L];
}
}
} else {
// When L > 240, we still fill with wrapping; correctness may not cover all edges but maintains constraints
for (int r=0;r<K;r++){
for (int c=0;c<K;c++){
C[r][c] = seq[(r + c) % L];
}
}
}
return C;
}
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');
}
cout << "\n";
for (int i = 0; i < P; ++i) {
for (int j = 0; j < (int)C[i].size(); ++j) {
cout << C[i][j] << (j+1==(int)C[i].size()?'\n':' ');
}
}
cout.flush();
}
return 0;
} |