File size: 3,669 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 | #include <bits/stdc++.h>
using namespace std;
int main() {
ios::sync_with_stdio(false);
cin.tie(0);
int T;
cin >> T;
while (T--) {
int n;
cin >> n;
vector<int> p(n + 1);
for (int i = 1; i <= n; ++i) {
cin >> p[i];
}
vector<tuple<int, int, int>> edges; // (u, v, idx)
vector<vector<int>> adj(n + 1);
for (int i = 1; i <= n - 1; ++i) {
int u, v;
cin >> u >> v;
edges.emplace_back(u, v, i);
adj[u].push_back(v);
adj[v].push_back(u);
}
// Precompute all-pairs distances
vector<vector<int>> dist(n + 1, vector<int>(n + 1, -1));
for (int s = 1; s <= n; ++s) {
queue<int> q;
dist[s][s] = 0;
q.push(s);
while (!q.empty()) {
int u = q.front();
q.pop();
for (int v : adj[u]) {
if (dist[s][v] == -1) {
dist[s][v] = dist[s][u] + 1;
q.push(v);
}
}
}
}
// Process operations
vector<vector<int>> operations;
while (true) {
bool sorted = true;
for (int i = 1; i <= n; ++i) {
if (p[i] != i) {
sorted = false;
break;
}
}
if (sorted) break;
vector<bool> used(n + 1, false);
vector<int> matching;
// First pass: direct swaps (both values are at each other's target)
for (auto &[u, v, idx] : edges) {
if (!used[u] && !used[v] && p[u] == v && p[v] == u) {
matching.push_back(idx);
used[u] = used[v] = true;
}
}
// Second pass: positive gain swaps
for (auto &[u, v, idx] : edges) {
if (!used[u] && !used[v]) {
int gain = (dist[u][p[u]] + dist[v][p[v]]) - (dist[u][p[v]] + dist[v][p[u]]);
if (gain > 0) {
matching.push_back(idx);
used[u] = used[v] = true;
}
}
}
// Third pass: fallback – any edge with at least one misplaced endpoint
if (matching.empty()) {
for (auto &[u, v, idx] : edges) {
if (!used[u] && !used[v] && (p[u] != u || p[v] != v)) {
matching.push_back(idx);
used[u] = used[v] = true;
break; // take only one
}
}
}
// Emergency: should not happen, but take any edge if still empty
if (matching.empty()) {
for (auto &[u, v, idx] : edges) {
if (!used[u] && !used[v]) {
matching.push_back(idx);
break;
}
}
}
// Apply the swaps of this operation
for (int idx : matching) {
int u = get<0>(edges[idx - 1]);
int v = get<1>(edges[idx - 1]);
swap(p[u], p[v]);
}
operations.push_back(matching);
}
// Output
cout << operations.size() << "\n";
for (auto &matching : operations) {
cout << matching.size();
for (int idx : matching) {
cout << " " << idx;
}
cout << "\n";
}
}
return 0;
} |