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| 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<vector<pair<int,int>>> adj(n + 1); | |
| vector<pair<int,int>> edges(n); | |
| for (int i = 1; i <= n - 1; ++i) { | |
| int u, v; | |
| cin >> u >> v; | |
| edges[i] = {u, v}; | |
| adj[u].push_back({v, i}); | |
| adj[v].push_back({u, i}); | |
| } | |
| // Permutation psi: vertex v maps to p[v] | |
| vector<int> psi(n + 1); | |
| for (int v = 1; v <= n; ++v) psi[v] = p[v]; | |
| // Decompose psi into cycles and convert each cycle into transpositions | |
| vector<char> vis(n + 1, 0); | |
| vector<pair<int,int>> macros; | |
| macros.reserve(n); | |
| for (int v = 1; v <= n; ++v) { | |
| if (vis[v]) continue; | |
| int u = v; | |
| vector<int> cyc; | |
| while (!vis[u]) { | |
| vis[u] = 1; | |
| cyc.push_back(u); | |
| u = psi[u]; | |
| } | |
| if (cyc.size() <= 1) continue; | |
| int c0 = cyc[0]; | |
| for (size_t j = 1; j < cyc.size(); ++j) { | |
| macros.push_back({c0, cyc[j]}); | |
| } | |
| } | |
| // For each transposition (a,b), realize it by swaps along the unique path between a and b | |
| vector<int> ops; | |
| ops.reserve(2 * n * n); | |
| vector<int> parentV(n + 1), parentE(n + 1); | |
| vector<int> pathEdges; | |
| pathEdges.reserve(n); | |
| for (auto &tr : macros) { | |
| int a = tr.first; | |
| int b = tr.second; | |
| // BFS to find path from a to b | |
| fill(parentV.begin(), parentV.end(), -1); | |
| queue<int> q; | |
| q.push(a); | |
| parentV[a] = a; | |
| parentE[a] = 0; | |
| while (!q.empty()) { | |
| int x = q.front(); | |
| q.pop(); | |
| if (x == b) break; | |
| for (auto &pr : adj[x]) { | |
| int to = pr.first, eid = pr.second; | |
| if (parentV[to] == -1) { | |
| parentV[to] = x; | |
| parentE[to] = eid; | |
| q.push(to); | |
| } | |
| } | |
| } | |
| // Reconstruct path edges from a to b | |
| pathEdges.clear(); | |
| int cur = b; | |
| while (cur != a) { | |
| int e = parentE[cur]; | |
| pathEdges.push_back(e); | |
| cur = parentV[cur]; | |
| } | |
| reverse(pathEdges.begin(), pathEdges.end()); | |
| int L = (int)pathEdges.size(); | |
| // Forward along path | |
| for (int i = 0; i < L; ++i) { | |
| int eid = pathEdges[i]; | |
| ops.push_back(eid); | |
| } | |
| // Backward along path excluding the last edge | |
| for (int i = L - 2; i >= 0; --i) { | |
| int eid = pathEdges[i]; | |
| ops.push_back(eid); | |
| } | |
| } | |
| cout << ops.size() << '\n'; | |
| for (int eid : ops) { | |
| cout << 1 << ' ' << eid << '\n'; | |
| } | |
| } | |
| return 0; | |
| } |