File size: 4,443 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 | #include <iostream>
#include <vector>
#include <numeric>
#include <algorithm>
#include <map>
using namespace std;
long long query(int u, int v) {
if (u == v) return 0;
cout << "? " << u << " " << v << endl;
long long dist;
cin >> dist;
return dist;
}
map<pair<int, int>, long long> memo;
long long get_dist(int u, int v) {
if (u == v) return 0;
if (u > v) swap(u, v);
if (memo.count({u, v})) {
return memo[{u, v}];
}
return memo[{u, v}] = query(u, v);
}
struct Edge {
int u, v;
long long w;
};
void solve() {
int n;
cin >> n;
memo.clear();
if (n == 1) {
cout << "!" << endl;
return;
}
vector<long long> dist1(n + 1);
for (int i = 2; i <= n; ++i) {
dist1[i] = get_dist(1, i);
}
int u = 2;
if (n > 2) {
for (int i = 3; i <= n; ++i) {
if (dist1[i] > dist1[u]) {
u = i;
}
}
} else {
u = 2;
}
if (n>1 && dist1[u] == 0) u=1; // case n=2, dist(1,2)=0 not possible, but just in case
if (u == 1) { // all nodes at same distance from 1, could be a star graph
if (n>2) u=2;
}
vector<long long> dist_u(n + 1);
for (int i = 1; i <= n; ++i) {
if (i == u) continue;
dist_u[i] = get_dist(u, i);
}
int v = 1;
if (v == u) v = 2;
for (int i = 1; i <= n; ++i) {
if (i == u) continue;
if (dist_u[i] > dist_u[v]) {
v = i;
}
}
long long D = dist_u[v];
vector<long long> dist_v(n + 1);
for (int i = 1; i <= n; ++i) {
if (i == v) continue;
dist_v[i] = get_dist(v, i);
}
vector<pair<long long, int>> diameter_nodes;
vector<int> non_diameter_nodes;
for (int i = 1; i <= n; ++i) {
if (dist_u[i] + dist_v[i] == D) {
diameter_nodes.push_back({dist_u[i], i});
} else {
non_diameter_nodes.push_back(i);
}
}
sort(diameter_nodes.begin(), diameter_nodes.end());
vector<Edge> edges;
for (size_t i = 0; i < diameter_nodes.size() - 1; ++i) {
edges.push_back({diameter_nodes[i].second, diameter_nodes[i+1].second, diameter_nodes[i+1].first - diameter_nodes[i].first});
}
map<int, vector<int>> subproblems;
for (int node : non_diameter_nodes) {
long long dist_on_diam = (dist_u[node] - dist_v[node] + D) / 2;
auto it = lower_bound(diameter_nodes.begin(), diameter_nodes.end(), make_pair(dist_on_diam, 0));
int p_node = it->second;
subproblems[p_node].push_back(node);
}
for (auto const& [p_node, s_nodes] : subproblems) {
if (s_nodes.empty()) continue;
vector<pair<long long, int>> sorted_s_nodes;
for (int node : s_nodes) {
long long d_p_node = (dist_u[node] + dist_v[node] - D) / 2;
sorted_s_nodes.push_back({d_p_node, node});
}
sort(sorted_s_nodes.begin(), sorted_s_nodes.end());
vector<pair<long long, int>> component;
component.push_back({0, p_node});
for (auto const& [d_w, w] : sorted_s_nodes) {
int low = 0, high = component.size() - 1;
int parent_idx = 0;
while(low <= high) {
int mid_idx = low + (high - low) / 2;
long long d_z = component[mid_idx].first;
int z = component[mid_idx].second;
if (get_dist(w, z) == d_w - d_z) {
parent_idx = mid_idx;
low = mid_idx + 1;
} else {
high = mid_idx - 1;
}
}
int parent_node = component[parent_idx].second;
long long parent_dist = component[parent_idx].first;
edges.push_back({w, parent_node, d_w - parent_dist});
auto insert_it = lower_bound(component.begin(), component.end(), make_pair(d_w, w));
component.insert(insert_it, {d_w, w});
}
}
cout << "! ";
for (size_t i = 0; i < edges.size(); ++i) {
cout << edges[i].u << " " << edges[i].v << " " << edges[i].w << (i == edges.size() - 1 ? "" : " ");
}
cout << endl;
}
int main() {
ios_base::sync_with_stdio(false);
cin.tie(NULL);
cout.flush();
int t;
cin >> t;
while (t--) {
solve();
}
return 0;
} |