File size: 4,118 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 | #include <bits/stdc++.h>
using namespace std;
int n;
vector<int> p;
vector<pair<int,int>> edges;
map<pair<int,int>, int> edgeIdx;
vector<int> parent, depth, in, out;
vector<vector<int>> children;
int timer;
bool in_subtree(int v, int x) {
return in[v] <= in[x] && in[x] < out[v];
}
void dfs(int u, int par) {
parent[u] = par;
in[u] = timer++;
for (int v : children[u]) {
if (v == par) continue;
depth[v] = depth[u] + 1;
dfs(v, u);
}
out[u] = timer;
}
vector<int> get_upward_matching() {
vector<pair<int,int>> cand;
for (int v = 2; v <= n; ++v) {
int u = parent[v];
if (u == 0) continue;
if (!in_subtree(v, p[v])) {
cand.emplace_back(u, v);
}
}
sort(cand.begin(), cand.end(), [](const pair<int,int>& a, const pair<int,int>& b) {
return depth[a.second] > depth[b.second];
});
vector<bool> used(n+1, false);
vector<int> matching;
for (auto& e : cand) {
int u = e.first, v = e.second;
if (!used[u] && !used[v]) {
used[u] = used[v] = true;
matching.push_back(edgeIdx[{u, v}]);
}
}
return matching;
}
vector<int> get_downward_matching() {
vector<pair<int,int>> cand;
for (int v = 2; v <= n; ++v) {
int u = parent[v];
if (u == 0) continue;
if (in_subtree(v, p[u])) {
cand.emplace_back(u, v);
}
}
sort(cand.begin(), cand.end(), [](const pair<int,int>& a, const pair<int,int>& b) {
return depth[a.second] > depth[b.second];
});
vector<bool> used(n+1, false);
vector<int> matching;
for (auto& e : cand) {
int u = e.first, v = e.second;
if (!used[u] && !used[v]) {
used[u] = used[v] = true;
matching.push_back(edgeIdx[{u, v}]);
}
}
return matching;
}
int main() {
ios::sync_with_stdio(false);
cin.tie(nullptr);
int T;
cin >> T;
while (T--) {
cin >> n;
p.resize(n+1);
for (int i = 1; i <= n; ++i) cin >> p[i];
edges.resize(n);
edgeIdx.clear();
vector<vector<int>> adj(n+1);
for (int i = 1; i < n; ++i) {
int u, v;
cin >> u >> v;
edges[i] = {u, v};
edgeIdx[{u, v}] = i;
edgeIdx[{v, u}] = i;
adj[u].push_back(v);
adj[v].push_back(u);
}
// prepare rooted tree
parent.assign(n+1, 0);
depth.assign(n+1, 0);
in.assign(n+1, 0);
out.assign(n+1, 0);
children = adj; // temporary, will be refined
// rebuild children lists (excluding parent)
for (int i = 1; i <= n; ++i) children[i].clear();
timer = 0;
function<void(int,int)> dfs2 = [&](int u, int par) {
parent[u] = par;
in[u] = timer++;
for (int v : adj[u]) {
if (v == par) continue;
depth[v] = depth[u] + 1;
children[u].push_back(v);
dfs2(v, u);
}
out[u] = timer;
};
dfs2(1, 0);
vector<vector<int>> operations;
bool up_next = true;
while (true) {
bool sorted = true;
for (int i = 1; i <= n; ++i)
if (p[i] != i) { sorted = false; break; }
if (sorted) break;
vector<int> matching;
if (up_next) matching = get_upward_matching();
else matching = get_downward_matching();
if (matching.empty()) {
up_next = !up_next; // try the other phase
continue;
}
for (int idx : matching) {
auto [u, v] = edges[idx];
swap(p[u], p[v]);
}
operations.push_back(matching);
up_next = !up_next;
}
cout << operations.size() << "\n";
for (auto& op : operations) {
cout << op.size();
for (int idx : op) cout << " " << idx;
cout << "\n";
}
}
return 0;
} |