#include <iostream>
#include <vector>
#include <unordered_map>
#include <fstream>
#include "supertrees.h"
using namespace std;
typedef vector<int> vi;
typedef vector<vi> vvi;
int root(int a, vector<int> & parent) {
if (a == parent[a])
return a;
return parent[a] = root(parent[a], parent);
}
void merge(int i, int j, vector<int> & parent, vector<int> & rnk, int & numCCs) {
int root_i = root(i, parent), root_j = root(j, parent);
if (root_i == root_j) return;
numCCs--;
if (rnk[i] != rnk[j]) {
if (rnk[i] > rnk[j]) parent[root_j] = parent[root_i];
else parent[root_i] = parent[root_j];
} else {
parent[root_i] = parent[root_j];
rnk[j]++;
}
}
int construct(vvi p) {
int N = (int) p.size(), numCCs = N;
vector<int> parent(N), rnk(N, 0);
for (int i = 0; i < N; i++)
parent[i] = i;
for (int i = 0; i < N; i++) {
for (int j = i+1; j < N; j++) {
if (p[i][j]) {
if (p[i][j] == 3) {
return 0;
}
merge(i, j, parent, rnk, numCCs);
} else if (root(i, parent) == root(j, parent))
return 0;
}
}
unordered_map<int, int> roots;
int c = 0;
for (int i = 0; i < N; i++) {
if (parent[i] == i)
roots[i] = c++;
}
vvi CCs(numCCs, vi());
for (int i = 0; i < N; i++)
CCs[roots[root(i, parent)]].push_back(i);
int CCsize, u, v, n, root_u, root_v;
vvi result(N, vi(N, 0)), oneTails;
for (int i = 0; i < numCCs; i++) {
CCsize = (int) CCs[i].size();
if (CCsize == 1) continue;
n = CCsize;
for (auto node: CCs[i]) {
parent[node] = node;
rnk[node] = 0;
}
for (int j = 0; j < CCsize; j++) {
u = CCs[i][j];
root_u = root(u, parent);
for (int k = j+1; k < CCsize; k++) {
v = CCs[i][k];
if (p[u][v] == 1)
merge(u, v, parent, rnk, n);
else if (root_u == root(v, parent))
return 0;
}
}
if (n == 2) return 0;
roots.clear();
c = 0;
for (int j = 0; j < CCsize; j++) {
u = CCs[i][j];
root_u = root(u, parent);
if (root_u == u)
roots[u] = c++;
for (int k = j+1; k < CCsize; k++) {
v = CCs[i][k];
root_v = root(v, parent);
if (root_u != root_v) {
if (p[u][v] != 2) {
return 0;
}
} else if (p[u][v] != 1) {
return 0;
}
}
}
// connect each tail amongst itself
oneTails = vvi(n, vi());
for (int j = 0; j < CCsize; j++)
oneTails[roots[root(CCs[i][j], parent)]].push_back(CCs[i][j]);
for (int j = 0; j < n; j++) {
for (int k = 0; k < (int) oneTails[j].size() - 1; k++)
result[oneTails[j][k]][oneTails[j][k+1]] = result[oneTails[j][k+1]][oneTails[j][k]] = 1;
}
// connect cycle of tail roots
for (int j = 0; j < n-1; j++)
result[oneTails[j][0]][oneTails[j+1][0]] = result[oneTails[j+1][0]][oneTails[j][0]] = 1;
if (n > 1)
result[oneTails[0][0]][oneTails[n-1][0]] = result[oneTails[n-1][0]][oneTails[0][0]] = 1;
}
build(result);
return 1;
}
