File size: 6,379 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 | #include <iostream>
#include <vector>
#include <numeric>
#include <algorithm>
#include <queue>
using namespace std;
struct Edge {
int u, v, id;
};
int n;
vector<int> p;
vector<vector<pair<int, int>>> adj;
vector<Edge> edges;
vector<vector<int>> dists;
// DP for matching
// dp[u][0]: max weight in subtree u, u NOT matched with children
// dp[u][1]: max weight in subtree u, u IS matched with a child
long long dp[1005][2];
long long edge_weights[1005]; // weight of edge with id i
void bfs(int start, vector<int>& d) {
fill(d.begin(), d.end(), -1);
d[start] = 0;
queue<int> q;
q.push(start);
while(!q.empty()){
int u = q.front();
q.pop();
for(auto& edge : adj[u]){
int v = edge.first;
if(d[v] == -1){
d[v] = d[u] + 1;
q.push(v);
}
}
}
}
void solve_dp(int u, int parent) {
long long sum_unmatched = 0;
for(auto& edge : adj[u]){
int v = edge.first;
if(v == parent) continue;
solve_dp(v, u);
sum_unmatched += max(dp[v][0], dp[v][1]);
}
dp[u][0] = sum_unmatched;
dp[u][1] = -2e18; // Initialize with a very small value
for(auto& edge : adj[u]){
int v = edge.first;
int id = edge.second;
if(v == parent) continue;
long long w = edge_weights[id];
// If we match u-v, we take dp[v][0] from v (since v is matched with u, v cannot match its children)
// and sum_unmatched - max(dp[v][0], dp[v][1]) from other children
long long val = sum_unmatched - max(dp[v][0], dp[v][1]) + dp[v][0] + w;
if(val > dp[u][1]){
dp[u][1] = val;
}
}
}
void get_matching(int u, int parent, int state, vector<int>& selected_edges) {
if (state == 0) { // u is not matched with any child
for(auto& edge : adj[u]){
int v = edge.first;
if(v == parent) continue;
// v can be matched with its own children or not
if(dp[v][1] > dp[v][0]) get_matching(v, u, 1, selected_edges);
else get_matching(v, u, 0, selected_edges);
}
} else { // u is matched with a child
long long sum_unmatched = dp[u][0];
long long best_val = -2e18;
int best_v = -1;
int best_id = -1;
// Re-find the best child
for(auto& edge : adj[u]){
int v = edge.first;
int id = edge.second;
if(v == parent) continue;
long long w = edge_weights[id];
long long val = sum_unmatched - max(dp[v][0], dp[v][1]) + dp[v][0] + w;
if(val > best_val){
best_val = val;
best_v = v;
best_id = id;
}
}
if(best_id != -1) selected_edges.push_back(best_id);
for(auto& edge : adj[u]){
int v = edge.first;
if(v == parent) continue;
if(v == best_v) {
// v is matched with u, so v acts as root of its subtree not matched with children
get_matching(v, u, 0, selected_edges);
} else {
if(dp[v][1] > dp[v][0]) get_matching(v, u, 1, selected_edges);
else get_matching(v, u, 0, selected_edges);
}
}
}
}
void solve() {
cin >> n;
p.assign(n + 1, 0);
for(int i = 1; i <= n; ++i) cin >> p[i];
adj.assign(n + 1, vector<pair<int, int>>());
edges.clear();
for(int i = 0; i < n - 1; ++i) {
int u, v;
cin >> u >> v;
adj[u].push_back({v, i + 1});
adj[v].push_back({u, i + 1});
edges.push_back({u, v, i + 1});
}
dists.assign(n + 1, vector<int>(n + 1));
for(int i = 1; i <= n; ++i) bfs(i, dists[i]);
struct Op {
vector<int> edge_indices;
};
vector<Op> ops;
while(true) {
bool sorted = true;
for(int i = 1; i <= n; ++i) {
if(p[i] != i) {
sorted = false;
break;
}
}
if(sorted) break;
for(const auto& e : edges) {
int u = e.u;
int v = e.v;
int pu = p[u];
int pv = p[v];
bool u_wants_cross = (dists[v][pu] < dists[u][pu]);
bool v_wants_cross = (dists[u][pv] < dists[v][pv]);
long long w = -1e15;
if(u_wants_cross && v_wants_cross) {
w = 100000;
} else if(!u_wants_cross && !v_wants_cross) {
w = -100000;
} else if(u_wants_cross && !v_wants_cross) {
int d_pu = dists[u][pu] - 1;
int d_pv = dists[v][pv];
if(d_pu > d_pv) {
w = 1000 + (d_pu - d_pv);
} else if(d_pu == d_pv) {
if(pu < pv) w = 1000;
else w = -1000;
} else {
w = -100000;
}
} else { // !u_wants_cross && v_wants_cross
int d_pu = dists[u][pu];
int d_pv = dists[v][pv] - 1;
if(d_pv > d_pu) {
w = 1000 + (d_pv - d_pu);
} else if(d_pv == d_pu) {
if(pv < pu) w = 1000;
else w = -1000;
} else {
w = -100000;
}
}
edge_weights[e.id] = w;
}
solve_dp(1, 0);
vector<int> selected;
if(dp[1][1] > dp[1][0]) get_matching(1, 0, 1, selected);
else get_matching(1, 0, 0, selected);
if(selected.empty()) break;
ops.push_back({selected});
for(int id : selected) {
int u = edges[id-1].u;
int v = edges[id-1].v;
swap(p[u], p[v]);
}
}
cout << ops.size() << "\n";
for(const auto& op : ops) {
cout << op.edge_indices.size();
for(int id : op.edge_indices) {
cout << " " << id;
}
cout << "\n";
}
}
int main() {
ios_base::sync_with_stdio(false);
cin.tie(NULL);
int t;
if (cin >> t) {
while(t--) {
solve();
}
}
return 0;
} |