File size: 4,885 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 | #include <iostream>
#include <vector>
#include <queue>
#include <algorithm>
#include <cstdlib>
using namespace std;
struct Edge {
int to;
int id;
};
int n;
vector<int> p;
vector<vector<Edge>> adj;
vector<vector<int>> dists;
vector<pair<int, int>> edges_list;
// BFS to compute all-pairs distances
void bfs_all() {
dists.assign(n + 1, vector<int>(n + 1, 0));
for (int i = 1; i <= n; ++i) {
queue<int> q;
q.push(i);
vector<int> d(n + 1, -1);
d[i] = 0;
while (!q.empty()) {
int u = q.front();
q.pop();
dists[i][u] = d[u];
for (auto& e : adj[u]) {
if (d[e.to] == -1) {
d[e.to] = d[u] + 1;
q.push(e.to);
}
}
}
}
}
struct Step {
int k;
vector<int> ids;
};
long long dp[1005][2];
int choice[1005];
long long edge_weight[1005];
void dfs_dp(int u, int parent) {
long long sum_max = 0;
for (auto& e : adj[u]) {
if (e.to == parent) continue;
dfs_dp(e.to, u);
sum_max += max(dp[e.to][0], dp[e.to][1]);
}
dp[u][0] = sum_max;
dp[u][1] = -1e18;
choice[u] = -1;
for (auto& e : adj[u]) {
if (e.to == parent) continue;
long long val = sum_max - max(dp[e.to][0], dp[e.to][1]) + dp[e.to][0] + edge_weight[e.id];
if (val > dp[u][1]) {
dp[u][1] = val;
choice[u] = e.to;
}
}
}
vector<int> selected_edges;
void reconstruct(int u, int parent, int state) {
if (state == 0) {
for (auto& e : adj[u]) {
if (e.to == parent) continue;
if (dp[e.to][1] > dp[e.to][0]) {
reconstruct(e.to, u, 1);
} else {
reconstruct(e.to, u, 0);
}
}
} else {
int v_matched = choice[u];
for (auto& e : adj[u]) {
if (e.to == parent) continue;
if (e.to == v_matched) {
selected_edges.push_back(e.id);
reconstruct(e.to, u, 0);
} else {
if (dp[e.to][1] > dp[e.to][0]) {
reconstruct(e.to, u, 1);
} else {
reconstruct(e.to, u, 0);
}
}
}
}
}
void solve() {
if (!(cin >> n)) return;
p.assign(n + 1, 0);
for (int i = 1; i <= n; ++i) cin >> p[i];
adj.assign(n + 1, vector<Edge>());
edges_list.assign(n, {0, 0});
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_list[i] = {u, v};
}
bfs_all();
vector<Step> ans;
// Limit operations to avoid infinite loops, though it should converge
int max_ops = 4 * n;
for (int iter = 0; iter < max_ops; ++iter) {
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_list[i].first;
int v = edges_list[i].second;
int val_u = p[u];
int val_v = p[v];
int d_before = dists[u][val_u] + dists[v][val_v];
int d_after = dists[v][val_u] + dists[u][val_v];
int gain = d_before - d_after;
if (gain == 2) {
edge_weight[i] = 100000;
} else if (gain == 0) {
// Add randomness to break cycles and potential stagnation
edge_weight[i] = 200 + (rand() % 50);
// Prefer swaps that help items far from destination
edge_weight[i] += (dists[u][val_u] + dists[v][val_v]);
} else {
edge_weight[i] = -1000000;
}
}
dfs_dp(1, 0);
selected_edges.clear();
if (dp[1][1] > dp[1][0]) {
reconstruct(1, 0, 1);
} else {
reconstruct(1, 0, 0);
}
if (selected_edges.empty()) break;
Step s;
s.k = selected_edges.size();
s.ids = selected_edges;
ans.push_back(s);
for (int id : selected_edges) {
int u = edges_list[id].first;
int v = edges_list[id].second;
swap(p[u], p[v]);
}
}
cout << ans.size() << "\n";
for (auto& s : ans) {
cout << s.k;
for (int id : s.ids) cout << " " << id;
cout << "\n";
}
}
int main() {
ios_base::sync_with_stdio(false);
cin.tie(NULL);
srand(5489);
int t;
if (cin >> t) {
while (t--) {
solve();
}
}
return 0;
} |