#include "cave.h"
#include <bits/stdc++.h>
#define sz(x) (int)x.size()
using namespace std;
int S[5010], D[5010], cur, idx, W, n;
int Try() {
int r = tryCombination(S);
return r == -1 ? n : r;
}
void FindAll(int s, int e) {
vector<int> a;
for(int i=s; i<=e; i++)
if(D[i] == -1) a.push_back(i);
int B = (int)sqrt(sz(a));
if(s == 0 && e == n - 1) B = (sz(a) + 9) / 10;
else B = (sz(a) + 1) / 2;
for(int i=0; i<sz(a); i+=B) {
int rgt = min(sz(a), i+B);
for(int j=i; j<rgt; j++) S[a[j]] ^= 1;
int r = Try();
for(int j=i; j<rgt; j++) S[a[j]] ^= 1;
if(r != idx) {
if(B == 1) {
if(idx < r) {
D[a[i]] = idx;
W = a[i];
} else if(r < idx) D[a[i]] = r;
} else FindAll(a[i], a[rgt - 1]);
}
}
}
void exploreCave(int N) {
n = N;
srand(123);
memset(D, -1, sizeof(D));
for(int i=0; i<N; i++) S[i] = rand() % 2;
cur = 0;
while(cur < N) {
idx = Try();
FindAll(0, n - 1);
if(idx < n) S[W] ^= 1;
cur = idx + 1;
}
answer(S, D);
}
