#include "cave.h"
#include <bits/stdc++.h>
#include <string>
#include <iostream>
#include <cmath>
#include <numeric>
using namespace std;
typedef long long ll;
typedef unsigned long long ull;
typedef long double ld;
typedef pair<int, int> pi;
typedef pair<int, int> pl;
typedef pair<ld, ld> pd;
typedef vector<int> vi;
typedef vector<bool> vb;
typedef vector<vector<int>> vvi;
typedef vector<ld> vd;
typedef vector<long> vl;
typedef vector<pi> vpi;
typedef vector<pl> vpl;
#define FOR(i, a, b) for (int i = a; i < (b); i++)
#define F0R(i, a) for (int i = 0; i < (a); i++)
#define FORd(i, a, b) for (int i = (b)-1; i >= a; i--)
#define F0Rd(i, a) for (int i = (a)-1; i >= 0; i--)
#define trav(a, x) for (auto &a : x)
#define uid(a, b) uniform_int_distribution<int>(a, b)(rng)
#define len(x) (int)(x).size()
#define mp make_pair
#define pb push_back
#define F first
#define nl endl
#define S second
#define lb lower_bound
#define ub upper_bound
#define aint(x) x.begin(), x.end()
#define raint(x) x.rbegin(), x.rend()
#define ins insert
const int MOD = 1000000007;
vi solved;
int n;
int tryCombination2(vi arr){
int arr2[n];
FOR(i,0,n)arr2[i] = arr[i];
return tryCombination(arr2);
}
int binarySearch(int left,int right,int activeType,int length){
if(left == right){
// cout << "end - " << left << endl;
return left;
}
int mid = (left+right)/2;
vi temp = solved;
FOR(i,0,n){
if(temp[i] == -1){
if(i<=mid and i>=left)
temp[i] = activeType;
else
temp[i] = (activeType+1)%2;
}
}
// cout << left << " " << right << " " << mid << " " << activeType << " | ";
// for(auto i:temp)cout << i << " ";
// cout << " | " << tryCombination2(temp) << endl;
int val = tryCombination2(temp);
if(val > length || val == -1){
return binarySearch(left,mid,activeType,length);
}else{
return binarySearch(mid+1,right,activeType,length);
}
}
int tryActive(int length){
vi temp = solved;
FOR(i,0,n){
if(temp[i] == -1)temp[i] = 1;
}
int val = tryCombination2(temp);
return ((val > length) || (val == -1));
}
void exploreCave(int N) {
n = N;
solved = vi(N,-1);
int doornum[N],active[N];
FOR(i,0,N){
// cout << i << endl;
int activeType = tryActive(i);
int pos = binarySearch(0,n,activeType,i);
solved[pos] = activeType;
doornum[pos] = i;
active[pos] = activeType;
// cout << endl;
}
answer(active,doornum);
}
