File size: 5,992 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 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 | #include <bits/stdc++.h>
using namespace std;
struct FastScanner {
static inline int gc() {
return getchar();
}
bool readLongLong(long long &out) {
int c = gc();
while (c != EOF && (c != '-' && (c < '0' || c > '9'))) c = gc();
if (c == EOF) return false;
int sign = 1;
if (c == '-') { sign = -1; c = gc(); }
long long x = 0;
while (c >= '0' && c <= '9') {
x = x * 10 + (c - '0');
c = gc();
}
out = x * sign;
return true;
}
bool readInt(int &out) {
long long tmp;
if (!readLongLong(tmp)) return false;
out = (int)tmp;
return true;
}
};
struct DistMatrix {
int n;
vector<long long> tri; // upper triangular (i<j) stored row-wise
vector<long long> offset; // offset for i: starting index in tri for pairs (i, j>i)
DistMatrix() : n(0) {}
DistMatrix(int _n) { init(_n); }
void init(int _n) {
n = _n;
long long m = 1LL * n * (n - 1) / 2;
tri.assign((size_t)m, 0);
offset.assign(n + 2, 0);
// offset[i] = sum_{k=1}^{i-1} (n - k) = (i-1)*n - (i-1)*i/2
for (int i = 1; i <= n; ++i) {
offset[i] = 1LL * (i - 1) * n - 1LL * (i - 1) * i / 2;
}
}
inline long long &atPairIdx(int i, int j) { // i<j
return tri[(size_t)(offset[i] + (j - i - 1))];
}
inline long long get(int i, int j) const {
if (i == j) return 0;
if (i < j) {
return tri[(size_t)(offset[i] + (j - i - 1))];
} else {
return tri[(size_t)(offset[j] + (i - j - 1))];
}
}
};
int N;
DistMatrix D;
vector<tuple<int,int,long long>> edges;
void reconstruct(const vector<int> &S) {
if (S.size() <= 1) return;
// find diameter endpoints within S using two-sweep
int s0 = S[0];
int t = s0;
long long best = -1;
for (int x : S) {
long long dv = D.get(s0, x);
if (dv > best) { best = dv; t = x; }
}
int u = t;
best = -1;
for (int x : S) {
long long dv = D.get(t, x);
if (dv > best) { best = dv; u = x; }
}
int a = u, b = t;
long long Sab = D.get(a, b);
// collect nodes on path from a to b
vector<int> pathNodes;
pathNodes.reserve(S.size());
for (int x : S) {
if (D.get(a, x) + D.get(x, b) == Sab) pathNodes.push_back(x);
}
sort(pathNodes.begin(), pathNodes.end(), [&](int x, int y){
return D.get(a, x) < D.get(a, y);
});
// add edges along the path
for (size_t i = 0; i + 1 < pathNodes.size(); ++i) {
int u1 = pathNodes[i], v1 = pathNodes[i+1];
long long w = D.get(a, v1) - D.get(a, u1);
edges.emplace_back(u1, v1, w);
}
// prepare mapping: node -> index in path, and distances from a along path
vector<int> idxInPath(N + 1, -1);
vector<long long> distAPath(pathNodes.size());
for (size_t i = 0; i < pathNodes.size(); ++i) {
idxInPath[pathNodes[i]] = (int)i;
distAPath[i] = D.get(a, pathNodes[i]);
}
// groups for recursion: for each path index, collect nodes not on path that project to that node
vector<vector<int>> groups(pathNodes.size());
vector<char> inPath(N + 1, 0);
for (int p : pathNodes) inPath[p] = 1;
for (int v : S) if (!inPath[v]) {
long long da = D.get(a, v), db = D.get(b, v);
long long delta2 = da + db - Sab; // 2*delta
long long delta = delta2 / 2;
long long xdist = da - delta; // distance from a to projection on path
// binary search xdist in distAPath
auto it = lower_bound(distAPath.begin(), distAPath.end(), xdist);
if (it == distAPath.end() || *it != xdist) {
// theoretically should not happen in a valid tree metric
// but if it does, we skip to avoid crash
continue;
}
int pos = (int)(it - distAPath.begin());
groups[pos].push_back(v);
}
// recurse on each group
for (size_t i = 0; i < groups.size(); ++i) {
if (!groups[i].empty()) {
vector<int> subS;
subS.reserve(groups[i].size() + 1);
subS.push_back(pathNodes[i]);
for (int v : groups[i]) subS.push_back(v);
reconstruct(subS);
}
}
}
int main() {
ios::sync_with_stdio(false);
cin.tie(nullptr);
FastScanner fs;
int T;
{
int tmp;
if (!fs.readInt(tmp)) return 0;
T = tmp;
}
for (int tc = 0; tc < T; ++tc) {
int n;
{
int tmp;
fs.readInt(tmp);
n = tmp;
}
N = n;
D.init(n);
long long m = 1LL * n * (n - 1) / 2;
for (int i = 1; i <= n - 1; ++i) {
for (int j = i + 1; j <= n; ++j) {
long long val;
fs.readLongLong(val);
D.atPairIdx(i, j) = val;
}
}
edges.clear();
edges.reserve((size_t)max(0, n - 1));
vector<int> all(n);
for (int i = 0; i < n; ++i) all[i] = i + 1;
reconstruct(all);
cout << "!";
// If by some chance we have more than n-1 due to duplicates, we can trim by using a map
if ((int)edges.size() != n - 1) {
// Deduplicate just in case
map<pair<int,int>, long long> mp;
for (auto &e : edges) {
int u, v; long long w;
tie(u, v, w) = e;
if (u > v) swap(u, v);
mp[{u, v}] = w;
}
edges.clear();
edges.reserve(mp.size());
for (auto &kv : mp) {
edges.emplace_back(kv.first.first, kv.first.second, kv.second);
}
}
for (auto &e : edges) {
int u, v; long long w;
tie(u, v, w) = e;
cout << " " << u << " " << v << " " << w;
}
cout << "\n";
}
return 0;
} |