File size: 5,130 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 | #include <iostream>
#include <vector>
#include <algorithm>
#include <map>
using namespace std;
const int MAXN = 1005;
int n;
int p[MAXN];
vector<pair<int,int>> adj[MAXN]; // {neighbor, edge_id}
int par[MAXN]; // parent in rooted tree
int tin[MAXN], tout[MAXN], timer_val;
pair<int,int> edges[MAXN]; // edge i -> {u, v}
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) { // is v in subtree of u?
return tin[u] <= tin[v] && tout[v] <= tout[u];
}
// Maximum weight matching on tree using DP
int dp_val[MAXN][2];
int dp_child[MAXN]; // which child v is matched to (for reconstruction)
int w_edge[MAXN]; // weight of edge i
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);
}
}
}
}
void solve() {
cin >> n;
for (int i = 1; i <= n; i++) {
cin >> p[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);
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;
// Compute edge weights
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;
}
w_edge[i] = weight;
}
// Set negative weights to 0
for (int i = 1; i < n; i++) {
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()) {
// Fallback: find unsorted element, move it one step toward target
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]);
}
}
cout << operations.size() << "\n";
for (auto& op : operations) {
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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