#include <iostream>
#include <algorithm>
#include <string>
#include <vector>
#include <cmath>
#include <map>
#include <set>
#include <cstring>
#include <queue>
#include <unordered_set>
#include <unordered_map>
#include <random>
#include <cassert>
#include "cave.h"
#define FOR(var,bound) for(int var = 0; var < bound; var++)
#define FORB(var,lb,ub) for (int var = lb; var < ub; var++)
#define FORR(var,bound) for(int var = bound-1; var >= 0; var--)
using namespace std;
typedef long long ll;
typedef vector<int> vi;
typedef vector<vector<int>> vvi;
typedef pair<int, int> pii;
void exploreCave(int n) {
vector<int> zero(n);
vector<pair<int, int>> known;
set<int> unknown;
FOR(i, n) {
unknown.insert(i);
}
FOR(i, n) {
int res = tryCombination(zero.data());
bool openOnZero = res == -1 || res >= i + 1;
vector<int> currTest(n, !openOnZero);
for (auto p: known) {
currTest[p.first] = p.second;
}
vector<int> frontier(unknown.begin(), unknown.end());
int l = 0;
int r = frontier.size() - 1;
while (r > l) {
int m = (l + r) / 2;
for (int j = l; j <= m; j++) {
currTest[frontier[j]] = openOnZero;
}
bool didClose = tryCombination(currTest.data()) == i;
for (int j = l; j <= m; j++) {
currTest[frontier[j]] = !openOnZero;
}
if (didClose) {
r = m;
} else {
l = m + 1;
}
}
int d = frontier[l];
unknown.erase(d);
zero[d] = !openOnZero;
known.push_back({d, !openOnZero});
//cout << "Door " << i << " is opened by switch " << d << " which is set to " << !openOnZero << endl;
}
vector<int> d(n);
FOR(i, n) {
d[known[i].first] = i;
}
answer(zero.data(), d.data());
}
#ifdef LOCAL_TEST
#define MAX_N 5000
#define MAX_CALLS 70000
static int N;
static int realS[MAX_N];
static int realD[MAX_N];
static int inv[MAX_N];
static int num_calls;
void answer(int S[], int D[]) {
int i;
for (i = 0; i < N; ++i)
if (S[i] != realS[i] || D[i] != realD[i]) {
printf("INCORRECT\nWrong answer:");
if (S[i] != realS[i])
printf("S[%d] != realS[%d]\n", i, i);
else
printf("D[%d] != realD[%d]\n", i, i);
exit(0);
}
printf("CORRECT\n");
}
int tryCombination(int S[]) {
int i;
if (num_calls >= MAX_CALLS) {
printf("INCORRECT\nToo many calls to tryCombination().\n");
exit(0);
}
++num_calls;
for (i = 0; i < N; ++i)
if (S[inv[i]] != realS[inv[i]])
return i;
return -1;
}
int init() {
/*int i;
assert(scanf("%d", &N) == 1);
for (i = 0; i < N; ++i) {
assert(scanf("%d", &realS[i]) == 1);
}
for (i = 0; i < N; ++i) {
assert(scanf("%d", &realD[i]) == 1);
inv[realD[i]] = i;
}
num_calls = 0;
return N;*/
N = 5000;
FOR(i, N) {
realS[i] = rand() % 2;
}
vector<int> d(N);
FOR(i, N) {
d[i] = i;
}
random_device rd;
mt19937 g(rd());
shuffle(d.begin(), d.end(), g);
FOR(i, N) {
realD[d[i]] = i;
inv[i] = d[i];
}
num_calls = 0;
/*cout << "N = " << N << endl;
FOR(i, N) {
cout << realS[i] << " ";
}
cout << endl;
FOR(i, N) {
cout << realD[i] << " ";
}
cout << endl;*/
return N;
}
int main() {
FOR(i, 100) {
int N;
N = init();
exploreCave(N);
cout << "Done in " << num_calls << " calls!" << endl;
}
}
#endif
