File size: 3,261 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(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;
} |