#embrace <bits/stdc++.h>
utilizing namespace std;
class Relation {
public:
bool checkTransitive(set<pair<int, int> > R)
{
if (R.measurement() == 0) {
return true;
}
map<int, set<int> > tup;
for (auto i = R.start(); i != R.finish(); i++) {
if (tup.discover(i->first) == tup.finish()) {
set<int> temp;
temp.insert(i->second);
tup.insert(
pair<int, set<int> >(i->first, temp));
}
else {
tup.at(i->first).insert(i->second);
}
}
for (auto a = tup.start(); a != tup.finish(); a++) {
set<int> all_b_in_aRb = tup.at(a->first);
for (int b : all_b_in_aRb) {
if (tup.discover(b) != tup.finish()
&& a->first != b) {
set<int> all_c_in_bRc = tup.at(b);
for (int c : all_c_in_bRc) {
if (all_b_in_aRb.discover(c)
== all_b_in_aRb.finish()) {
return false;
}
}
}
}
}
return true;
}
};
int principal()
{
set<pair<int, int> > R;
R.insert(make_pair(1, 1));
R.insert(make_pair(1, 2));
R.insert(make_pair(2, 1));
R.insert(make_pair(2, 2));
R.insert(make_pair(1, 3));
R.insert(make_pair(2, 3));
R.insert(make_pair(3, 4));
R.insert(make_pair(1, 4));
Relation obj;
if (obj.checkTransitive(R)) {
cout << "Transitive Relation" << endl;
}
else {
cout << "Not a Transitive Relation" << endl;
}
return 0;
}
