File size: 4,767 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 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 | #include <iostream>
#include <vector>
#include <numeric>
#include <algorithm>
#include <map>
#include <tuple>
#include <set>
using namespace std;
int n;
vector<tuple<int, int, int>> edges;
map<pair<int, int>, long long> memo;
long long do_query(int u, int v) {
if (u == v) return 0;
if (u > v) swap(u, v);
if (memo.count({u, v})) {
return memo[{u, v}];
}
cout << "? " << u << " " << v << endl;
long long dist;
cin >> dist;
return memo[{u, v}] = dist;
}
void solve(const vector<int>& V) {
if (V.size() <= 1) {
return;
}
if (V.size() == 2) {
long long w = do_query(V[0], V[1]);
edges.emplace_back(V[0], V[1], w);
return;
}
int start_node = V[0];
int end1 = -1;
long long max_dist = -1;
for (int v : V) {
if (v == start_node) continue;
long long d = do_query(start_node, v);
if (d > max_dist) {
max_dist = d;
end1 = v;
}
}
if (end1 == -1) {
end1 = V[0];
for(int v : V) {
if (v != end1) {
end1 = v;
break;
}
}
}
map<int, long long> dists_e1;
int end2 = -1;
max_dist = -1;
for (int v : V) {
dists_e1[v] = do_query(end1, v);
if (dists_e1[v] > max_dist) {
max_dist = dists_e1[v];
end2 = v;
}
}
long long diameter_dist = dists_e1[end2];
map<int, long long> dists_e2;
for (int v : V) {
dists_e2[v] = do_query(end2, v);
}
vector<int> path_nodes_vec;
set<int> path_nodes_set;
map<long long, int> dist_to_node;
for (int v : V) {
if (dists_e1[v] + dists_e2[v] == diameter_dist) {
path_nodes_vec.push_back(v);
path_nodes_set.insert(v);
dist_to_node[dists_e1[v]] = v;
}
}
sort(path_nodes_vec.begin(), path_nodes_vec.end(), [&](int a, int b) {
return dists_e1[a] < dists_e1[b];
});
for (size_t i = 0; i < path_nodes_vec.size() - 1; ++i) {
int u = path_nodes_vec[i];
int v = path_nodes_vec[i + 1];
long long w = dists_e1[v] - dists_e1[u];
edges.emplace_back(u, v, w);
}
map<int, vector<int>> child_groups;
for (int v : V) {
if (path_nodes_set.find(v) == path_nodes_set.end()) {
long long dist_on_path = (diameter_dist + dists_e1[v] - dists_e2[v]) / 2;
int p_node = dist_to_node[dist_on_path];
child_groups[p_node].push_back(v);
}
}
for (auto const& [p_node, children] : child_groups) {
if (children.empty()) continue;
vector<vector<int>> components;
vector<int> remaining_children = children;
while (!remaining_children.empty()) {
int rep = remaining_children.back();
remaining_children.pop_back();
vector<int> current_comp = {rep};
vector<int> next_remaining;
long long d_p_rep = (dists_e1[rep] + dists_e2[rep] - diameter_dist) / 2;
for (int other : remaining_children) {
long long d_p_other = (dists_e1[other] + dists_e2[other] - diameter_dist) / 2;
if (do_query(rep, other) < d_p_rep + d_p_other) {
current_comp.push_back(other);
} else {
next_remaining.push_back(other);
}
}
components.push_back(current_comp);
remaining_children = next_remaining;
}
for (const auto& comp : components) {
int attach_node = -1;
long long min_dist_to_p = -1;
for (int node : comp) {
long long d_p_node = (dists_e1[node] + dists_e2[node] - diameter_dist) / 2;
if (attach_node == -1 || d_p_node < min_dist_to_p) {
min_dist_to_p = d_p_node;
attach_node = node;
}
}
edges.emplace_back(p_node, attach_node, min_dist_to_p);
solve(comp);
}
}
}
void do_test_case() {
cin >> n;
edges.clear();
memo.clear();
if (n == 1) {
cout << "!" << endl;
return;
}
vector<int> initial_V(n);
iota(initial_V.begin(), initial_V.end(), 1);
solve(initial_V);
cout << "! ";
for (size_t i = 0; i < edges.size(); ++i) {
cout << get<0>(edges[i]) << " " << get<1>(edges[i]) << " " << get<2>(edges[i]) << (i == edges.size() - 1 ? "" : " ");
}
cout << endl;
}
int main() {
ios_base::sync_with_stdio(false);
cin.tie(NULL);
int t;
cin >> t;
while (t--) {
do_test_case();
}
return 0;
} |