#include "supertrees.h"
#include <bits/stdc++.h>
using namespace std;
struct DSU {
vector<int> parent;
vector<int> size;
DSU(int n) {
parent.resize(n);
iota(parent.begin(), parent.end(), 0);
size.assign(n, 1);
}
int find(int v) {
if (parent[v] == v) {
return v;
} else {
return parent[v] = find(parent[v]);
}
}
void unite(int u, int v) {
if (u == v) return;
u = find(u);
v = find(v);
if (size[u] > size[v]) swap(u, v);
parent[u] = v;
size[v] += size[u];
}
};
int construct(vector<vector<int>> p) {
int n = p.size();
vector<vector<int>> g(n, vector<int>(n));
// 1) must be transitive:
// p[u][w] * p[w][v] = p[v][w] * p[w][u] = p[u][v] = p[v][u], for any u, v, w
bool ok = true;
DSU dsu(n);
for (int u = 0; u < n; ++u) {
for (int v = u + 1; v < n; ++v) {
if (p[u][v] > 0) {
dsu.unite(u, v);
}
}
}
map<int, vector<int>> comps;
for (int v = 0; v < n; ++v) {
comps[dsu.find(v)].push_back(v);
}
for (const auto& [c, comp] : comps) {
bool has_two = false;
for (auto u : comp) {
for (auto v : comp) {
if (p[u][v] == 0) {
ok = false;
break;
}
if (p[u][v] == 2) {
has_two = true;
}
}
}
for (int i = 0; i < (int)comp.size() - 1; ++i) {
g[comp[i]][comp[i + 1]] = g[comp[i + 1]][comp[i]] = 1;
}
if (has_two) {
g[comp[0]][comp.back()] = g[comp.back()][comp[0]] = 1;
}
}
if (ok) {
build(g);
return 1;
}
return 0;
}
