File size: 7,468 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 | #include <bits/stdc++.h>
using namespace std;
const int INF = 1e9 + 5;
vector<vector<int>> adj, edge_id, distt, dp0, dp1, best_match_child;
vector<pair<int, int>> edge_list;
pair<int, int> compute_dp(int u, int par, const vector<vector<pair<int, pair<int, int>>>>& adj_u, vector<bool>& vis) {
vis[u] = true;
vector<int> children;
vector<pair<int, int>> child_dps;
vector<int> child_weights; // weight to this child
int sum_max = 0;
int max_add = -INF;
int best_j = -1;
for (auto& pr : adj_u[u]) {
int v = pr.first;
int w = pr.second.second;
int eid = pr.second.first;
if (v == par) continue;
children.push_back(v);
child_weights.push_back(w);
auto res = compute_dp(v, u, adj_u, vis);
dp0[v] = res.first;
dp1[v] = res.second;
int maxv = max(res.first, res.second);
child_dps.push_back({res.first, res.second});
sum_max += maxv;
int delta = w + res.first - maxv;
if (delta > max_add) {
max_add = delta;
best_j = children.size() - 1;
}
}
int m0 = sum_max;
int m1;
if (children.empty()) {
m1 = -INF;
} else {
m1 = sum_max + max_add;
best_match_child[u] = children[best_j];
}
dp0[u] = m0;
dp1[u] = m1;
return {m0, m1};
}
void collect_sub(int u, int par, bool covered_by_parent, const vector<vector<pair<int, pair<int, int>>>>& adj_u, vector<int>& selected) {
if (covered_by_parent) {
// take M0
for (auto& prr : adj_u[u]) {
int v = prr.first;
if (v == par) continue;
collect_sub(v, u, false, adj_u, selected);
}
return;
}
// not covered, decide M0 or M1
bool use_m1_here = (dp1[u] > dp0[u]);
if (use_m1_here && dp1[u] != -INF) {
int v = best_match_child[u];
// find eid
for (auto& prr : adj_u[u]) {
if (prr.first == v) {
selected.push_back(prr.second.first);
break;
}
}
collect_sub(v, u, true, adj_u, selected);
for (auto& prr : adj_u[u]) {
int w = prr.first;
if (w != par && w != v) {
collect_sub(w, u, false, adj_u, selected);
}
}
} else {
// take M0
for (auto& prr : adj_u[u]) {
int v = prr.first;
if (v == par) continue;
collect_sub(v, u, false, adj_u, selected);
}
}
}
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> p(n + 1);
for (int i = 1; i <= n; i++) {
cin >> p[i];
}
adj.assign(n + 1, {});
edge_id.assign(n + 1, vector<int>(n + 1, 0));
edge_list.assign(n, {});
for (int i = 1; i <= n - 1; i++) {
int u, v;
cin >> u >> v;
adj[u].push_back(v);
adj[v].push_back(u);
edge_id[u][v] = i;
edge_id[v][u] = i;
edge_list[i] = {u, v};
}
// precompute dist
distt.assign(n + 1, vector<int>(n + 1, -1));
for (int s = 1; s <= n; s++) {
queue<int> q;
q.push(s);
distt[s][s] = 0;
vector<bool> vis_dist(n + 1, false);
vis_dist[s] = true;
while (!q.empty()) {
int u = q.front();
q.pop();
for (int v : adj[u]) {
if (!vis_dist[v]) {
vis_dist[v] = true;
distt[s][v] = distt[s][u] + 1;
q.push(v);
}
}
}
}
// now simulate
vector<vector<int>> ops;
int max_steps = 4 * n; // safety
for (int step = 0; step < max_steps; step++) {
bool done = true;
for (int i = 1; i <= n; i++) {
if (p[i] != i) {
done = false;
break;
}
}
if (done) break;
// compute adj_u
vector<vector<pair<int, pair<int, int>>>> adj_u(n + 1);
for (int u = 1; u <= n; u++) {
for (int v : adj[u]) {
if (u >= v) continue; // to add once
int a = p[u], b = p[v];
int old_da = distt[u][a];
int old_db = distt[v][b];
int new_da = distt[v][a];
int new_db = distt[u][b];
int ch = (new_da + new_db) - (old_da + old_db);
if (ch <= 0) {
int w = -ch;
int eid = edge_id[u][v];
adj_u[u].emplace_back(v, make_pair(eid, w));
adj_u[v].emplace_back(u, make_pair(eid, w));
}
}
}
// now process components
vector<bool> vis(n + 1, false);
dp0.assign(n + 1, 0);
dp1.assign(n + 1, 0);
best_match_child.assign(n + 1, 0);
vector<int> this_op;
for (int i = 1; i <= n; i++) {
if (!vis[i] && !adj_u[i].empty()) {
compute_dp(i, 0, adj_u, vis);
// now collect
vector<int> comp_sel;
bool use_m1_root = (dp1[i] > dp0[i]);
if (use_m1_root && dp1[i] != -INF) {
int v = best_match_child[i];
// find eid
for (auto& prr : adj_u[i]) {
if (prr.first == v) {
comp_sel.push_back(prr.second.first);
break;
}
}
collect_sub(v, i, true, adj_u, comp_sel);
for (auto& prr : adj_u[i]) {
int w = prr.first;
if (w != v && w != 0) {
collect_sub(w, i, false, adj_u, comp_sel);
}
}
} else {
for (auto& prr : adj_u[i]) {
int w = prr.first;
if (w != 0) {
collect_sub(w, i, false, adj_u, comp_sel);
}
}
}
for (int e : comp_sel) {
this_op.push_back(e);
}
}
}
// now if this_op empty, but not done, problem, but assume not
if (this_op.empty()) {
// perhaps add nothing, but to prevent infinite, break
break;
}
ops.push_back(this_op);
// perform swaps
for (int ei : this_op) {
auto [u, v] = edge_list[ei];
swap(p[u], p[v]);
}
}
// output
cout << ops.size() << '\n';
for (auto& op : ops) {
cout << op.size();
for (int e : op) {
cout << ' ' << e;
}
cout << '\n';
}
}
return 0;
} |