File size: 8,027 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 | #include <bits/stdc++.h>
using namespace std;
int main() {
ios::sync_with_stdio(false);
cin.tie(nullptr);
int T;
cin >> T;
for (int t = 0; t < T; ++t) {
int n;
cin >> n;
vector<int> current_p(n + 1);
for (int i = 1; i <= n; ++i) {
cin >> current_p[i];
}
vector<vector<int>> adj(n + 1);
vector<pair<int, int>> tree_edges(n - 1);
vector<vector<int>> edge_to(n + 1, vector<int>(n + 1, 0));
for (int i = 0; i < n - 1; ++i) {
int u, v;
cin >> u >> v;
tree_edges[i] = {u, v};
adj[u].push_back(v);
adj[v].push_back(u);
edge_to[u][v] = i + 1;
edge_to[v][u] = i + 1;
}
// Build children, root at 1
vector<vector<int>> children(n + 1);
vector<int> parent(n + 1, -1);
queue<int> q;
q.push(1);
parent[1] = 0;
while (!q.empty()) {
int u = q.front();
q.pop();
for (int v : adj[u]) {
if (v != parent[u]) {
parent[v] = u;
children[u].push_back(v);
q.push(v);
}
}
}
// Precompute next_step and dist
vector<vector<int>> next_step(n + 1, vector<int>(n + 1, 0));
vector<vector<int>> distance(n + 1, vector<int>(n + 1, 0));
for (int tt = 1; tt <= n; ++tt) {
vector<int> par(n + 1, -1);
vector<int> d(n + 1, -1);
queue<int> qq;
qq.push(tt);
par[tt] = tt;
d[tt] = 0;
while (!qq.empty()) {
int u = qq.front();
qq.pop();
for (int v : adj[u]) {
if (d[v] == -1) {
d[v] = d[u] + 1;
par[v] = u;
qq.push(v);
}
}
}
for (int s = 1; s <= n; ++s) {
distance[s][tt] = d[s];
if (s != tt) {
next_step[s][tt] = par[s];
} else {
next_step[s][tt] = 0;
}
}
}
// Now simulation
vector<vector<int>> operations;
vector<int> M0(n + 1), M1(n + 1, -1000000000), best_c(n + 1, -1);
auto dfs = [&](auto&& self, int u, int p, const vector<int>& edge_typee) -> void {
vector<int> subm;
int sum_m0 = 0;
int idx = 0;
for (int c : children[u]) {
if (c == p) continue;
self(self, c, u, edge_typee);
int mx = M0[c];
if (M1[c] > mx) mx = M1[c];
subm.push_back(mx);
sum_m0 += mx;
++idx;
}
M0[u] = sum_m0;
int nc = children[u].size();
int best_size = -1000000000;
int bestchild = -1;
for (int i = 0; i < nc; ++i) {
int c = children[u][i];
if (c == p) continue;
int eidx = edge_to[u][c];
int typp = edge_typee[eidx];
if (typp == 0) continue;
int this_sum = sum_m0 - subm[i] + M0[c];
int this_size = 1 + this_sum;
if (this_size > best_size) {
best_size = this_size;
bestchild = c;
}
}
if (bestchild != -1) {
M1[u] = best_size;
best_c[u] = bestchild;
}
};
auto collect = [&](auto&& self, int u, int p, bool useM1, vector<int>& sel, const vector<int>& edge_typee) -> void {
if (useM1) {
int c = best_c[u];
if (c == -1) return;
int eidx = edge_to[u][c];
sel.push_back(eidx);
self(self, c, u, false, sel, edge_typee);
for (int v : children[u]) {
if (v == c || v == p) continue;
bool ch_use = (M1[v] >= M0[v]);
self(self, v, u, ch_use, sel, edge_typee);
}
} else {
for (int v : children[u]) {
if (v == p) continue;
bool ch_use = (M1[v] >= M0[v]);
self(self, v, u, ch_use, sel, edge_typee);
}
}
};
int max_steps = 4 * n;
int step = 0;
bool is_sorted = true;
for (int i = 1; i <= n; ++i) {
if (current_p[i] != i) {
is_sorted = false;
break;
}
}
while (!is_sorted && step < max_steps) {
++step;
is_sorted = true;
for (int i = 1; i <= n; ++i) {
if (current_p[i] != i) {
is_sorted = false;
break;
}
}
if (is_sorted) break;
// compute edge_type
vector<int> edge_type(n);
for (int i = 1; i <= n - 1; ++i) {
int u = tree_edges[i - 1].first;
int v = tree_edges[i - 1].second;
int tu = current_p[u];
int tv = current_p[v];
bool wuv = (next_step[u][tu] == v);
bool wvu = (next_step[v][tv] == u);
edge_type[i] = (wuv ? 1 : 0) + (wvu ? 1 : 0);
}
// reset dp
fill(M0.begin(), M0.end(), 0);
fill(M1.begin(), M1.end(), -1000000000);
fill(best_c.begin(), best_c.end(), -1);
// dfs
dfs(dfs, 1, -1, edge_type);
int size0 = M0[1];
int size1 = (M1[1] > -100000000 ? M1[1] : -1000000000);
vector<int> chosen_sel;
vector<int> temp_sel;
if (size1 > size0) {
temp_sel.clear();
collect(collect, 1, -1, true, temp_sel, edge_type);
chosen_sel = temp_sel;
} else if (size0 > size1) {
temp_sel.clear();
collect(collect, 1, -1, false, temp_sel, edge_type);
chosen_sel = temp_sel;
} else {
// equal
temp_sel.clear();
collect(collect, 1, -1, false, temp_sel, edge_type);
vector<int> sel0 = temp_sel;
int ben0 = 0;
for (int e : sel0) ben0 += edge_type[e];
vector<int> sel1;
int ben1 = 0;
bool can1 = (M1[1] > -100000000);
if (can1) {
temp_sel.clear();
collect(collect, 1, -1, true, temp_sel, edge_type);
sel1 = temp_sel;
for (int e : sel1) ben1 += edge_type[e];
}
if (!can1 || ben0 > ben1) {
chosen_sel = sel0;
} else {
chosen_sel = sel1;
}
}
if (chosen_sel.empty()) {
// stuck, break
break;
}
// perform swaps
for (int eidx : chosen_sel) {
int u = tree_edges[eidx - 1].first;
int v = tree_edges[eidx - 1].second;
swap(current_p[u], current_p[v]);
}
// add to operations
operations.push_back(chosen_sel);
}
// output
cout << operations.size() << '\n';
for (auto& op : operations) {
cout << op.size();
for (int e : op) {
cout << ' ' << e;
}
cout << '\n';
}
}
return 0;
} |