#include "insects.h"
#include <vector>
#include <random>
#include <algorithm>
#include <numeric>
#include <cassert>
using namespace std;
#define SZ(x) int((x).size())
mt19937 gen(123);
class DisjointSet {
int N;
int ncomp;
vector<int> par;
vector<int> sz;
public:
DisjointSet(size_t _N) : N(_N), ncomp(_N), par(_N, -1), sz(_N, 1) {}
int num_comp() const {
return ncomp;
}
int size(int u) {
return sz[ find_rep(u) ];
}
int find_rep(int u) {
return par[u] < 0 ? u : par[u] = find_rep(par[u]);
}
bool union_rep(int u, int v) {
int u_root = find_rep(u);
int v_root = find_rep(v);
if (u_root == v_root)
return false;
if (sz[u_root] < sz[v_root])
swap(u_root, v_root);
par[v_root] = u_root;
sz[u_root] += sz[v_root];
--ncomp;
return true;
}
};
int min_cardinality(int N) {
vector<int> order(N);
iota(order.begin(), order.end(), 0);
std::shuffle(order.begin(), order.end(), gen);
vector<int> distinct;
DisjointSet dset(N);
for (int i : order) {
move_inside(i);
if (!distinct.empty() and press_button() == 2) {
std::shuffle(distinct.begin(), distinct.end(), gen);
for (int k = SZ(distinct)-1; k >= 0; --k) {
int& j = distinct[k];
move_outside(j);
if (press_button() == 1) {
dset.union_rep(i, j);
j = i;
break;
}
move_inside(j);
}
}
else {
distinct.push_back(i);
}
}
int ret = N;
for (int i = 0; i < N; ++i)
ret = min(ret, dset.size(i));
return ret;
}
