#include "insects.h"
#include <bits/stdc++.h>
using namespace std;
set<int> calcInter(set<int> &a, set<int> &b) {
set<int> ret;
for (int x : a)
if (b.count(x))
ret.insert(x);
return ret;
}
int min_cardinality(int N) {
vector<int> roots;
int nbCC = 0;
for (int i = 0; i < N; ++i) {
move_inside(i);
if (i and press_button() == 2)
move_outside(i);
else
roots.push_back(i), nbCC++;
}
vector<bool> isRoot(N);
for (int r : roots)
isRoot[r] = true;
vector<int> toProcess;
for (int i = 0; i < N; ++i)
if (!isRoot[i])
toProcess.push_back(i);
if (nbCC == 1)
return N;
for (int r : roots) {
move_outside(r);
toProcess.push_back(r);
}
int lo = 1, up = N / nbCC;
// invariant : everything outside of toProcess has majority element <= lo
// We never need to reconsider insects !!
int toAdd = 0;
while (lo < up) {
int mid = (lo + up + 1) / 2;
vector<int> popped;
vector<int> insideMachine;
for (int u : toProcess) {
move_inside(u);
if (press_button() > mid)
popped.push_back(u), move_outside(u);
else
insideMachine.push_back(u);
}
if ((int)popped.size() == N - mid * nbCC) {
for (int u : insideMachine)
move_outside(u);
toProcess = popped;
N = popped.size();
toAdd += mid;
lo = 0, up = min(N / nbCC, up - mid);
} else {
for (int u : insideMachine)
move_outside(u);
toProcess = insideMachine;
N = toProcess.size();
up = mid - 1;
}
}
return lo + toAdd;
}
