#include "insects.h"
#include <vector>
#include <numeric>
#include <map>
#include <set>
#include <random>
#include <algorithm>
using namespace std;
vector<int> p;
vector<int> sz;
int ufind(int i) {
if (p[i] == i) return i;
return p[i] = ufind(p[i]);
}
int usz(int i) {
return sz[ufind(i)];
}
void umerge(int a, int b) {
if (ufind(a) == ufind(b))
return;
p[a] = b;
sz[b] += sz[a];
}
int min_cardinality(int N) {
p.resize(N);
sz.resize(N);
iota(p.begin(), p.end(), 0);
fill(sz.begin(), sz.end(), 1);
int minsz = N;
random_device dev;
mt19937 rng(dev());
uniform_int_distribution dist(0,N-1);
set<pair<int,int>> precheck;
vector<int> lookup(N);
iota(lookup.begin(), lookup.end(), 0);
shuffle(lookup.begin(), lookup.end(), rng);
/*while (N >= 10 && precheck.size() < min(10000, 2*N)) {
int a = dist(rng);
int b = dist(rng);
if (a == b)
continue;
int x = min(a,b);
int y = max(a,b);
if (precheck.count({x,y}) || ufind(x) == ufind(y))
continue;
move_inside(lookup[x]);
move_inside(lookup[y]);
if (press_button() == 2) {
umerge(x,y);
}
move_outside(lookup[x]);
move_outside(lookup[y]);
precheck.insert({x,y});
}*/
for (int i = 0; i < N; i++) {
if (ufind(i) != i)
continue;
move_inside(lookup[i]);
vector<int> checked;
for (int j = i+1; j < N; j++) {
if (ufind(i) == ufind(j))
continue;
//if (usz(i) >= minsz)
// continue;
bool halt = false;
for (auto x : checked) {
if (ufind(x) == ufind(j)) {
halt = true;
break;
}
}
if (halt) continue;
/*
for (auto x : precheck) {
if (
(ufind(x.first) == ufind(i) && ufind(x.second) == ufind(j)) ||
(ufind(x.first) == ufind(j) && ufind(x.second) == ufind(i))
) {
// they must be different
halt = true;
break;
}
}
if (halt) continue;*/
move_inside(lookup[j]);
if (press_button() == 2)
umerge(j, i);
move_outside(lookup[j]);
checked.push_back(j);
}
move_outside(lookup[i]);
minsz = min(minsz, usz(i));
}
return minsz;
}
