File size: 4,604 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 | #include <iostream>
#include <vector>
#include <algorithm>
#include <map>
using namespace std;
int n;
vector<long long> dists;
vector<int> p_node;
vector<vector<int>> adj;
vector<int> sub_sz;
map<pair<int,int>, long long> memo;
long long 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 d;
cin >> d;
return memo[{u, v}] = d;
}
int get_heavy_leaf(int u) {
while (!adj[u].empty()) {
int best = -1, max_s = -1;
for (int c : adj[u]) {
if (sub_sz[c] > max_s) {
max_s = sub_sz[c];
best = c;
}
}
u = best;
}
return u;
}
int get_ancestor_at_depth(int u, long long d) {
while (u != 0 && dists[u] > d) {
u = p_node[u];
}
return u;
}
void solve() {
if (!(cin >> n)) return;
memo.clear();
if (n == 1) {
cout << "! " << endl;
return;
}
dists.assign(n + 1, 0);
for (int i = 2; i <= n; ++i) {
dists[i] = query(1, i);
}
vector<int> nodes(n - 1);
for (int i = 0; i < n - 1; ++i) nodes[i] = i + 2;
sort(nodes.begin(), nodes.end(), [&](int a, int b) {
return dists[a] < dists[b];
});
p_node.assign(n + 1, 0);
adj.assign(n + 1, vector<int>());
sub_sz.assign(n + 1, 1);
// Incrementally insert nodes
for (int u : nodes) {
int curr = 1;
while (true) {
if (adj[curr].empty()) {
p_node[u] = curr;
adj[curr].push_back(u);
int tmp = u;
while (tmp != 0) {
sub_sz[tmp]++;
tmp = p_node[tmp];
}
break;
}
// Identify heavy child
int heavy_child = -1, max_s = -1;
for (int c : adj[curr]) {
if (sub_sz[c] > max_s) {
max_s = sub_sz[c];
heavy_child = c;
}
}
// Query against a leaf in the heavy subtree
int v = get_heavy_leaf(heavy_child);
long long d_uv = query(u, v);
long long lca_d = (dists[u] + dists[v] - d_uv) / 2;
int w = get_ancestor_at_depth(v, lca_d);
if (w != curr) {
curr = w;
// w is a descendant of curr, so we moved down the heavy path.
// We know u branches off at w, and u is NOT in the child of w that leads to v.
}
// Identify the child of curr that leads to v (to exclude it)
int child_towards_v = -1;
int tmp = v;
while (p_node[tmp] != curr) {
tmp = p_node[tmp];
}
child_towards_v = tmp;
// Check other children (candidates)
vector<int> candidates;
for (int c : adj[curr]) {
if (c != child_towards_v) candidates.push_back(c);
}
// Sort by size to check larger subtrees first (heuristic)
sort(candidates.begin(), candidates.end(), [&](int a, int b){
return sub_sz[a] > sub_sz[b];
});
bool found = false;
for (int c : candidates) {
int v_prime = get_heavy_leaf(c);
long long d_uv_p = query(u, v_prime);
long long lca_d_p = (dists[u] + dists[v_prime] - d_uv_p) / 2;
if (lca_d_p > dists[curr]) {
// LCA is inside c's subtree
curr = get_ancestor_at_depth(v_prime, lca_d_p);
found = true;
break;
}
}
if (found) continue;
// If not in any existing child's subtree, attach to curr
p_node[u] = curr;
adj[curr].push_back(u);
tmp = u;
while (tmp != 0) {
sub_sz[tmp]++;
tmp = p_node[tmp];
}
break;
}
}
cout << "!";
for (int i = 2; i <= n; ++i) {
cout << " " << p_node[i] << " " << i << " " << (dists[i] - dists[p_node[i]]);
}
cout << endl;
}
int main() {
ios_base::sync_with_stdio(false);
cin.tie(NULL);
int t;
if (cin >> t) {
while (t--) {
solve();
}
}
return 0;
} |