File size: 5,401 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 | #include <iostream>
#include <vector>
#include <algorithm>
#include <random>
using namespace std;
const int MAXN = 1005;
int n;
int p_orig[MAXN], p[MAXN];
vector<pair<int,int>> adj[MAXN];
int par[MAXN];
int tin[MAXN], tout[MAXN], timer_val;
pair<int,int> edges[MAXN];
void dfs_pre(int v, int pa) {
par[v] = pa;
tin[v] = ++timer_val;
for (auto& e : adj[v]) {
if (e.first != pa) dfs_pre(e.first, v);
}
tout[v] = ++timer_val;
}
bool in_subtree(int u, int v) {
return tin[u] <= tin[v] && tout[v] <= tout[u];
}
int dp_val[MAXN][2];
int dp_child[MAXN];
int w_edge[MAXN];
void dp_dfs(int u, int pa) {
int sum = 0;
for (auto& e : adj[u]) {
int v = e.first;
if (v == pa) continue;
dp_dfs(v, u);
sum += max(dp_val[v][0], dp_val[v][1]);
}
dp_val[u][0] = sum;
dp_val[u][1] = -1000000;
dp_child[u] = -1;
for (auto& e : adj[u]) {
int v = e.first;
int eid = e.second;
if (v == pa) continue;
if (w_edge[eid] <= 0) continue;
int val = sum - max(dp_val[v][0], dp_val[v][1]) + dp_val[v][0] + w_edge[eid];
if (val > dp_val[u][1]) {
dp_val[u][1] = val;
dp_child[u] = v;
}
}
}
void dp_reconstruct(int u, int pa, bool matched, vector<int>& result) {
if (matched) {
for (auto& e : adj[u]) {
if (e.first != pa) dp_reconstruct(e.first, u, false, result);
}
} else {
if (dp_val[u][1] > dp_val[u][0] && dp_child[u] != -1) {
int v = dp_child[u];
int eid = -1;
for (auto& e : adj[u]) {
if (e.first == v) { eid = e.second; break; }
}
result.push_back(eid);
dp_reconstruct(v, u, true, result);
for (auto& e : adj[u]) {
if (e.first != pa && e.first != v) dp_reconstruct(e.first, u, false, result);
}
} else {
for (auto& e : adj[u]) {
if (e.first != pa) dp_reconstruct(e.first, u, false, result);
}
}
}
}
vector<vector<int>> run_greedy(mt19937& rng, int noise_level) {
for (int i = 1; i <= n; i++) p[i] = p_orig[i];
vector<vector<int>> operations;
int max_iter = 3 * n;
while (max_iter-- > 0) {
bool sorted = true;
for (int i = 1; i <= n; i++) {
if (p[i] != i) { sorted = false; break; }
}
if (sorted) break;
for (int i = 1; i < n; i++) {
int u = edges[i].first;
int v = edges[i].second;
int u_p, v_c;
if (par[v] == u) { u_p = u; v_c = v; }
else { u_p = v; v_c = u; }
int weight = 0;
if (p[u_p] != u_p) {
weight += in_subtree(v_c, p[u_p]) ? 1 : -1;
}
if (p[v_c] != v_c) {
weight += !in_subtree(v_c, p[v_c]) ? 1 : -1;
}
// Scale up and add noise for tie-breaking
w_edge[i] = weight * 100;
if (weight > 0 && noise_level > 0) {
w_edge[i] += rng() % noise_level;
}
if (w_edge[i] < 0) w_edge[i] = 0;
}
dp_dfs(1, 0);
vector<int> matching;
dp_reconstruct(1, 0, false, matching);
if (matching.empty()) {
for (int i = 1; i <= n; i++) {
if (p[i] != i) {
int target = p[i];
if (in_subtree(i, target)) {
for (auto& e : adj[i]) {
if (e.first == par[i]) continue;
if (in_subtree(e.first, target)) {
matching.push_back(e.second);
break;
}
}
} else {
for (auto& e : adj[i]) {
if (e.first == par[i]) {
matching.push_back(e.second);
break;
}
}
}
break;
}
}
if (matching.empty()) break;
}
operations.push_back(matching);
for (int eid : matching) {
swap(p[edges[eid].first], p[edges[eid].second]);
}
}
return operations;
}
void solve() {
cin >> n;
for (int i = 1; i <= n; i++) {
cin >> p_orig[i];
adj[i].clear();
}
for (int i = 1; i < n; i++) {
int u, v;
cin >> u >> v;
adj[u].push_back({v, i});
adj[v].push_back({u, i});
edges[i] = {u, v};
}
timer_val = 0;
dfs_pre(1, 0);
mt19937 rng(42);
// Run without noise first
auto best_ops = run_greedy(rng, 0);
// Try a few random perturbations
int trials = min(50, max(5, 500 / n));
for (int t = 0; t < trials; t++) {
auto ops = run_greedy(rng, 50);
if (ops.size() < best_ops.size()) {
best_ops = ops;
}
}
cout << best_ops.size() << "\n";
for (auto& op : best_ops) {
cout << op.size();
for (int eid : op) cout << " " << eid;
cout << "\n";
}
}
int main() {
ios_base::sync_with_stdio(false);
cin.tie(NULL);
int t;
cin >> t;
while (t--) solve();
return 0;
}
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