File size: 4,381 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 | #include <bits/stdc++.h>
using namespace std;
typedef pair<int, int> pii;
int main() {
ios::sync_with_stdio(false);
cin.tie(nullptr);
int T;
cin >> T;
while (T--) {
int n;
cin >> n;
if (n == 1) {
cout << "!\n";
cout.flush();
continue;
}
vector<int> depth(n + 1);
depth[1] = 0;
// query distances from root 1 to all other nodes
for (int i = 2; i <= n; i++) {
cout << "? 1 " << i << endl;
cout.flush();
int d;
cin >> d;
depth[i] = d;
}
// nodes except root sorted by depth
vector<int> order(n - 1);
iota(order.begin(), order.end(), 2);
sort(order.begin(), order.end(),
[&](int a, int b) { return depth[a] < depth[b]; });
// processed nodes in increasing depth order (root first, then others)
vector<int> processed;
processed.push_back(1);
vector<int> parent(n + 1, 0);
map<pii, int> cache;
// store known distances from root
for (int i = 2; i <= n; i++) {
cache[{1, i}] = depth[i];
cache[{i, 1}] = depth[i];
}
for (int u : order) {
int sz = processed.size();
int sample_cnt = min(30, sz);
// take the deepest 'sample_cnt' nodes from processed
vector<int> samples;
for (int i = 0; i < sample_cnt; i++) {
samples.push_back(processed[sz - 1 - i]);
}
int Lmax = -1;
for (int v : samples) {
int d_uv;
auto it = cache.find({u, v});
if (it != cache.end()) {
d_uv = it->second;
} else {
cout << "? " << u << " " << v << endl;
cout.flush();
cin >> d_uv;
cache[{u, v}] = d_uv;
cache[{v, u}] = d_uv;
}
int L = (depth[u] + depth[v] - d_uv) / 2;
if (L > Lmax) Lmax = L;
}
bool found = false;
// check nodes with depth == Lmax (from deepest to shallowest)
for (int idx = sz - 1; idx >= 0; idx--) {
int v = processed[idx];
if (depth[v] < Lmax) break;
if (depth[v] == Lmax) {
int d_uv;
auto it = cache.find({u, v});
if (it != cache.end()) {
d_uv = it->second;
} else {
cout << "? " << u << " " << v << endl;
cout.flush();
cin >> d_uv;
cache[{u, v}] = d_uv;
cache[{v, u}] = d_uv;
}
if (d_uv == depth[u] - depth[v]) {
parent[u] = v;
found = true;
break;
}
}
}
if (!found) {
// fallback: check all processed nodes from deepest to shallowest
for (int idx = sz - 1; idx >= 0; idx--) {
int v = processed[idx];
int d_uv;
auto it = cache.find({u, v});
if (it != cache.end()) {
d_uv = it->second;
} else {
cout << "? " << u << " " << v << endl;
cout.flush();
cin >> d_uv;
cache[{u, v}] = d_uv;
cache[{v, u}] = d_uv;
}
if (d_uv == depth[u] - depth[v]) {
parent[u] = v;
found = true;
break;
}
}
}
// add u to processed list (maintain sorted by depth)
processed.push_back(u);
}
// output answer
cout << "!";
for (int u = 2; u <= n; u++) {
int p = parent[u];
int w = depth[u] - depth[p];
cout << " " << p << " " << u << " " << w;
}
cout << endl;
cout.flush();
}
return 0;
} |