File size: 5,392 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 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 | #include <bits/stdc++.h>
using namespace std;
int main() {
ios::sync_with_stdio(false);
cin.tie(nullptr);
int T;
cin >> T;
for (int t = 0; t < T; ++t) {
int n;
cin >> n;
if (n == 1) {
cout << "!" << endl;
cout.flush();
continue;
}
auto query = [&](int u, int v) -> long long {
if (u == v) return 0;
cout << "? " << u << " " << v << endl;
cout.flush();
long long d;
cin >> d;
return d;
};
auto get_dist = [&](int root, int nn) -> vector<long long> {
vector<long long> d(nn + 1, 0);
for (int v = 1; v <= nn; ++v) {
if (v != root) {
d[v] = query(root, v);
}
}
return d;
};
auto d1 = get_dist(1, n);
int a = 1;
for (int v = 1; v <= n; ++v) {
if (d1[v] > d1[a]) a = v;
}
vector<long long> da = get_dist(a, n);
int b = 1;
for (int v = 1; v <= n; ++v) {
if (da[v] > da[b]) b = v;
}
vector<long long> db = get_dist(b, n);
long long dist_ab = da[b];
vector<pair<long long, int>> onpath_init;
for (int v = 1; v <= n; ++v) {
if (da[v] + db[v] == dist_ab) {
onpath_init.emplace_back(da[v], v);
}
}
sort(onpath_init.begin(), onpath_init.end());
vector<int> path;
for (auto& p : onpath_init) path.push_back(p.second);
vector<tuple<int, int, long long>> edges;
for (size_t i = 0; i + 1 < onpath_init.size(); ++i) {
int u = onpath_init[i].second;
int v = onpath_init[i + 1].second;
long long w = onpath_init[i + 1].first - onpath_init[i].first;
edges.emplace_back(u, v, w);
}
map<long long, int> da_to_idx;
for (size_t i = 0; i < onpath_init.size(); ++i) {
da_to_idx[onpath_init[i].first] = i;
}
vector<bool> is_on_path(n + 1, false);
for (int p : path) is_on_path[p] = true;
vector<vector<int>> hangs(path.size());
for (int v = 1; v <= n; ++v) {
if (is_on_path[v]) continue;
long long cand = (da[v] + dist_ab - db[v]) / 2;
auto it = da_to_idx.find(cand);
if (it != da_to_idx.end()) {
int id = it->second;
hangs[id].push_back(v);
}
}
auto reconstruct = [&](auto&& self, int rt, vector<int> S, function<long long(int)> get_dist_rt) -> void {
if (S.empty()) return;
int l = S[0];
long long maxd = get_dist_rt(l);
for (int s : S) {
long long dd = get_dist_rt(s);
if (dd > maxd) {
maxd = dd;
l = s;
}
}
vector<long long> dl(n + 1, -1);
dl[l] = 0;
dl[rt] = query(l, rt);
for (int s : S) {
if (s != l) {
dl[s] = query(l, s);
}
}
vector<pair<long long, int>> onpath;
onpath.emplace_back(0LL, rt);
for (int s : S) {
if (get_dist_rt(s) + dl[s] == maxd) {
onpath.emplace_back(get_dist_rt(s), s);
}
}
sort(onpath.begin(), onpath.end());
for (size_t j = 0; j + 1 < onpath.size(); ++j) {
int u = onpath[j].second;
int v = onpath[j + 1].second;
long long w = onpath[j + 1].first - onpath[j].first;
edges.emplace_back(u, v, w);
}
vector<vector<int>> subhangs(onpath.size());
set<int> onpath_set;
for (auto& p : onpath) onpath_set.insert(p.second);
for (int s : S) {
if (onpath_set.count(s)) continue;
long long cand = (get_dist_rt(s) + maxd - dl[s]) / 2;
auto it = lower_bound(onpath.begin(), onpath.end(), make_pair(cand, 0));
if (it != onpath.end() && it->first == cand) {
size_t j = it - onpath.begin();
subhangs[j].push_back(s);
}
}
for (size_t j = 0; j < onpath.size(); ++j) {
int q = onpath[j].second;
vector<int> subS = subhangs[j];
if (subS.empty()) continue;
auto sub_get_dist = [get_dist_rt, q](int ss) -> long long {
return get_dist_rt(ss) - get_dist_rt(q);
};
self(self, q, subS, sub_get_dist);
}
};
for (size_t i = 0; i < path.size(); ++i) {
int pi = path[i];
vector<int> Si = hangs[i];
if (!Si.empty()) {
auto get_d = [&](int v) -> long long {
return da[v] - da[pi];
};
reconstruct(reconstruct, pi, Si, get_d);
}
}
cout << "!";
for (size_t i = 0; i < edges.size(); ++i) {
auto [u, v, w] = edges[i];
cout << " " << u << " " << v << " " << w;
}
cout << endl;
cout.flush();
}
return 0;
} |