#include "cave.h"
#include <bits/stdc++.h>
using namespace std;
#define MAX_N 5000
int currentDoor = 0;
static int S[MAX_N];
static int F[MAX_N];
static int D[MAX_N];
int nbSwitch;
void makeCombination (int left, int right, int t0, int t1) {
int c = 0;
for (int i = 0; i < nbSwitch; i ++) {
if (F[i] != -1) {
S[i] = F[i];
} else {
S[i] = left <= c && c <= right ? t1 : t0;
c ++;
}
}
}
int nbTry = 0;
int tryComb (int left, int right, int t0, int t1) {
makeCombination(left, right, t0, t1);
int v = tryCombination(S);
nbTry ++;
if (v == -1) return nbSwitch + 1;
return v;
}
int getValid (int door) {
return tryComb(0, nbSwitch - 1 - door, 0, 1) > door ? 1 : 0;
}
int getDoor (int door, int target) {
int n_target = 1 - target;
int a = 0;
int b = nbSwitch - 1 - door;
while (a + 1 < b) {
int c = (a + b) >> 1;
if (tryComb(a, c, n_target, target) > door) {
b = c;
} else {
a = c;
}
}
int na = 0;
int nb = 0;
for (int i = a; i >= 0; na ++)
i -= F[na] == -1 ? 1 : 0;
for (int i = b; i >= 0; nb ++)
i -= F[nb] == -1 ? 1 : 0;
na --; nb --;
return tryComb(a, a, n_target, target) > door ? na : nb;
}
#define di pair<int, int>
di getDoor (int door) {
int target = getValid(door);
return { getDoor(door, target), target };
}
void solve (int door) {
di data = getDoor(door);
int idSwitch = data.first;
F[idSwitch] = data.second;
D[idSwitch] = door;
}
void exploreCave(int N) {
nbSwitch = N;
for (int i = 0; i < N; i ++)
F[i] = -1; // Signifies that it is not fixed
for (int i = 0; i < N; i ++)
solve(i);
answer(F, D);
}
