File size: 4,273 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 | #include <iostream>
#include <vector>
#include <numeric>
#include <algorithm>
#include <tuple>
using namespace std;
const int LOGN = 18;
// Use global vectors and resize them for each test case
// because sum of N is limited.
vector<vector<pair<int, int>>> adj;
vector<int> parent;
vector<long long> dist_from_root;
vector<int> depth;
vector<vector<int>> up;
long long query(int u, int v) {
cout << "? " << u << " " << v << endl;
long long d;
cin >> d;
return d;
}
void solve() {
int n;
cin >> n;
if (n <= 1) {
cout << "! " << endl;
return;
}
adj.assign(n + 1, vector<pair<int, int>>());
parent.assign(n + 1, 0);
dist_from_root.assign(n + 1, 0);
depth.assign(n + 1, 0);
up.assign(n + 1, vector<int>(LOGN, 0));
if (n == 2) {
long long w = query(1, 2);
cout << "! 1 2 " << w << endl;
return;
}
long long w12 = query(1, 2);
// Root at 1. Parent of root is 0.
parent[1] = 0;
depth[1] = 0;
dist_from_root[1] = 0;
parent[2] = 1;
depth[2] = 1;
dist_from_root[2] = w12;
adj[1].push_back({2, (int)w12});
adj[2].push_back({1, (int)w12});
up[2][0] = 1;
for (int j = 1; j < LOGN; ++j) {
up[2][j] = up[up[2][j - 1]][j - 1];
}
int a = 1, b = 2;
long long diam_len = w12;
for (int i = 3; i <= n; ++i) {
long long dia = query(i, a);
long long dib = query(i, b);
long long dist_a_m = (diam_len + dia - dib) / 2;
int u_lca = a, v_lca = b;
if (depth[u_lca] < depth[v_lca]) swap(u_lca, v_lca);
for (int j = LOGN - 1; j >= 0; --j) {
if (depth[u_lca] - (1 << j) >= depth[v_lca]) {
u_lca = up[u_lca][j];
}
}
if (u_lca != v_lca) {
for (int j = LOGN - 1; j >= 0; --j) {
if (up[u_lca][j] != 0 && up[u_lca][j] != up[v_lca][j]) {
u_lca = up[u_lca][j];
v_lca = up[v_lca][j];
}
}
u_lca = parent[u_lca];
}
int lca = u_lca;
long long dist_a_lca = dist_from_root[a] - dist_from_root[lca];
int m;
if (dist_a_m <= dist_a_lca) {
int curr = a;
long long target_dist_from_root = dist_from_root[a] - dist_a_m;
for (int j = LOGN - 1; j >= 0; --j) {
if (up[curr][j] != 0 && dist_from_root[up[curr][j]] >= target_dist_from_root) {
curr = up[curr][j];
}
}
m = curr;
} else {
long long dist_b_m = diam_len - dist_a_m;
int curr = b;
long long target_dist_from_root = dist_from_root[b] - dist_b_m;
for (int j = LOGN - 1; j >= 0; --j) {
if (up[curr][j] != 0 && dist_from_root[up[curr][j]] >= target_dist_from_root) {
curr = up[curr][j];
}
}
m = curr;
}
long long w_im = dia - dist_a_m;
adj[i].push_back({m, (int)w_im});
adj[m].push_back({i, (int)w_im});
parent[i] = m;
depth[i] = depth[m] + 1;
dist_from_root[i] = dist_from_root[m] + w_im;
up[i][0] = m;
for (int j = 1; j < LOGN; ++j) {
up[i][j] = up[up[i][j - 1]][j - 1];
if(up[i][j] == 0) break;
}
if (dia > diam_len) {
diam_len = dia;
b = i;
}
if (dib > diam_len) {
diam_len = dib;
a = i;
}
}
cout << "! ";
vector<tuple<int, int, int>> edges;
for (int u = 1; u <= n; ++u) {
for (auto& edge : adj[u]) {
int v = edge.first;
int w = edge.second;
if (u < v) {
edges.emplace_back(u, v, w);
}
}
}
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--) {
solve();
}
return 0;
} |