File size: 3,573 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 | #include <bits/stdc++.h>
using namespace std;
int main() {
ios::sync_with_stdio(false);
cin.tie(nullptr);
int T;
if (!(cin >> T)) return 0;
while (T--) {
int n;
cin >> n;
vector<int> p(n + 1);
for (int i = 1; i <= n; ++i) cin >> p[i];
vector<int> U(n), V(n); // 1..n-1 used
vector<vector<pair<int,int>>> adj(n + 1);
for (int i = 1; i <= n - 1; ++i) {
int u, v;
cin >> u >> v;
U[i] = u; V[i] = v;
adj[u].push_back({v, i});
adj[v].push_back({u, i});
}
// Root the tree at 1 and compute parent, depth, and parent edge
vector<int> parent(n + 1, 0), depth(n + 1, 0), pedge(n + 1, 0);
vector<char> vis(n + 1, false);
vector<int> q;
q.push_back(1);
vis[1] = true;
parent[1] = 0; pedge[1] = 0; depth[1] = 0;
for (int i = 0; i < (int)q.size(); ++i) {
int u = q[i];
for (auto [v, ei] : adj[u]) {
if (!vis[v]) {
vis[v] = true;
parent[v] = u;
pedge[v] = ei;
depth[v] = depth[u] + 1;
q.push_back(v);
}
}
}
// Position of each label
vector<int> pos(n + 1);
for (int u = 1; u <= n; ++u) pos[p[u]] = u;
// Remaining graph degrees and membership
vector<int> deg(n + 1, 0);
for (int u = 1; u <= n; ++u) deg[u] = (int)adj[u].size();
vector<char> inR(n + 1, true);
int rem = n;
deque<int> leaves;
for (int u = 1; u <= n; ++u) if (deg[u] <= 1) leaves.push_back(u);
vector<int> ops;
auto do_swap = [&](int e) {
int a = U[e], b = V[e];
ops.push_back(e);
int va = p[a], vb = p[b];
p[a] = vb; p[b] = va;
pos[va] = b; pos[vb] = a;
};
auto move_token_along_path = [&](int start, int target) {
int x = start, y = target;
vector<int> up, down;
while (depth[x] > depth[y]) { up.push_back(pedge[x]); x = parent[x]; }
while (depth[y] > depth[x]) { down.push_back(pedge[y]); y = parent[y]; }
while (x != y) {
up.push_back(pedge[x]); x = parent[x];
down.push_back(pedge[y]); y = parent[y];
}
for (int e : up) do_swap(e);
for (int i = (int)down.size() - 1; i >= 0; --i) do_swap(down[i]);
};
while (rem > 1) {
while (!leaves.empty() && (!inR[leaves.front()] || deg[leaves.front()] != 1)) leaves.pop_front();
if (leaves.empty()) {
for (int u = 1; u <= n; ++u)
if (inR[u] && deg[u] == 1) leaves.push_back(u);
if (leaves.empty()) break;
}
int v = leaves.front(); leaves.pop_front();
if (!inR[v] || deg[v] != 1) continue;
int cur = pos[v];
if (cur != v) move_token_along_path(cur, v);
inR[v] = false;
--rem;
int neighbor = 0;
for (auto [to, ei] : adj[v]) if (inR[to]) { neighbor = to; break; }
deg[v] = 0;
if (neighbor) {
--deg[neighbor];
if (deg[neighbor] == 1) leaves.push_back(neighbor);
}
}
cout << ops.size() << "\n";
for (int e : ops) {
cout << 1 << " " << e << "\n";
}
}
return 0;
} |