File size: 2,821 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 | #include <iostream>
#include <vector>
#include <numeric>
#include <algorithm>
#include <map>
using namespace std;
long long query(int u, int v) {
cout << "? " << u << " " << v << endl;
long long dist;
cin >> dist;
return dist;
}
struct Edge {
int u, v, w;
};
void solve() {
int n;
cin >> n;
if (n == 1) {
cout << "!" << endl;
return;
}
vector<long long> d(n + 1, 0);
for (int i = 2; i <= n; ++i) {
d[i] = query(1, i);
}
vector<pair<long long, int>> sorted_vertices;
for (int i = 2; i <= n; ++i) {
sorted_vertices.push_back({d[i], i});
}
sort(sorted_vertices.begin(), sorted_vertices.end());
vector<int> p(n + 1, 0);
vector<vector<int>> children(n + 1);
vector<Edge> edges;
if (n > 1) {
int v2 = sorted_vertices[0].second;
p[v2] = 1;
children[1].push_back(v2);
edges.push_back({1, v2, (int)d[v2]});
}
for (size_t i = 1; i < sorted_vertices.size(); ++i) {
int v = sorted_vertices[i].second;
int u = sorted_vertices[i - 1].second;
long long dist_uv = query(u, v);
long long d_lca = (d[u] + d[v] - dist_uv) / 2;
int curr = u;
while (d[curr] > d_lca) {
curr = p[curr];
}
int lca = curr;
curr = lca;
while (true) {
int next_node = -1;
int child_on_path_to_u = -1;
if (curr != u) {
int temp = u;
while (p[temp] != curr) {
temp = p[temp];
}
child_on_path_to_u = temp;
}
// To make search potentially faster, process children in a random order
vector<int> current_children = children[curr];
random_shuffle(current_children.begin(), current_children.end());
for (int child : current_children) {
if (child == child_on_path_to_u) continue;
long long dist_child_v = query(child, v);
if (d[v] - d[child] == dist_child_v) {
next_node = child;
break;
}
}
if (next_node != -1) {
curr = next_node;
} else {
p[v] = curr;
children[curr].push_back(v);
edges.push_back({curr, v, (int)(d[v] - d[curr])});
break;
}
}
}
cout << "!";
for (const auto& edge : edges) {
cout << " " << edge.u << " " << edge.v << " " << edge.w;
}
cout << endl;
}
int main() {
ios_base::sync_with_stdio(false);
cin.tie(NULL);
int t;
cin >> t;
while (t--) {
solve();
}
return 0;
} |