#include "supertrees.h"
#include <vector>
using namespace std;
int construct(vector<vector<int>> p) {
int n = p.size();
for (int i = 0; i < n; ++i) {
for (int j = 0; j < n; ++j) {
if (p[i][j] == 3) return 0;
}
}
// Split into components
vector<vector<int>> components;
vector<int> myCmp(n, -1);
for (int i = 0; i < n; ++i) {
if (myCmp[i] != -1) continue;
components.push_back({});
for (int j = 0; j < n; ++j) {
if (p[i][j]) {
if (myCmp[j] != -1) return 0;
components.back().push_back(j);
myCmp[j] = (int)components.size()-1;
}
}
}
// Check components are separate
for (int i = 0; i < n; ++i) {
for (int j = 0; j < n; ++j) {
if ((myCmp[i] == myCmp[j]) ^ (p[i][j] != 0)) return 0;
}
}
// Build answer here
vector<vector<int>> edge(n, vector<int>(n));
// Now solve separately for each component
for (vector<int> &c : components) {
// Split into 1-chains
vector<vector<int>> chains;
vector<int> myChain(n, -1);
for (int i : c) {
if (myChain[i] != -1) continue;
chains.push_back({});
for (int j : c) {
if (p[i][j] == 1) {
if (myChain[j] != -1) return 0;
chains.back().push_back(j);
myChain[j] = (int)chains.size()-1;
}
}
}
// Check 1-chains are separate
for (int i : c) {
for (int j : c) {
if ((myChain[i] == myChain[j]) ^ (p[i][j] == 1)) return 0;
}
}
// Assign a chain leader to each chain
int m = chains.size();
vector<int> chainLeader(m);
for (int i = 0; i < m; ++i) chainLeader[i] = chains[i][0];
// Check chains and their leaders behave in the same way
for (int i : c) {
for (int j : c) {
if (p[i][j] != p[chainLeader[myChain[i]]][j]) return 0;
}
}
// There will be two ways to travel between a pair of nodes in different chains
if (m == 2) return 0; // cannot have two chains (cannot make cycle)
// Connect within chains
for (int i : c) {
if (chainLeader[myChain[i]] != i) {
edge[i][chainLeader[myChain[i]]] = edge[chainLeader[myChain[i]]][i] = 1;
}
}
// Connect chain leaders in a cycle
if (m == 1) continue; // only one chain - no need
for (int i = 0; i < m; ++i) {
int j = (i+1)%m;
edge[chainLeader[i]][chainLeader[j]] = edge[chainLeader[j]][chainLeader[i]] = 1;
}
}
build(edge);
return 1;
}
