#include "jumps.h"
#include<bits/stdc++.h>
using namespace std;
#define INF 1000000000
#define MAXN 200000
#define MAXH 200000
#define MAXLG 17
int n, prevHigher[MAXN + 3], nextHigher[MAXN + 3], highest[MAXH + 3][MAXLG + 3], secondHighest[MAXH + 3][MAXLG + 3];
vector<int> h;
void initPrevHigher() {
stack<int> stHeight;
for (int i = 0; i < n; i++) {
while (!stHeight.empty() && h[i] > stHeight.top()) {
stHeight.pop();
}
prevHigher[i] = (stHeight.empty() ? INF : stHeight.top());
stHeight.push(h[i]);
}
}
void initNextHigher() {
stack<int> stHeight;
for (int i = n - 1; i >= 0; i--) {
while (!stHeight.empty() && h[i] > stHeight.top()) {
stHeight.pop();
}
nextHigher[i] = (stHeight.empty() ? INF : stHeight.top());
stHeight.push(h[i]);
}
}
void initHighestAndSecondHighest() {
for (int h = 1; h <= n; h++) {
highest[h][0] = secondHighest[h][0] = INF;
}
for (int i = 0; i < n; i++) {
highest[h[i]][0] = max(prevHigher[i], nextHigher[i]);
secondHighest[h[i]][0] = min(prevHigher[i], nextHigher[i]);
}
for (int lg = 1; lg <= MAXLG; lg++) {
for (int h = 1; h <= n; h++) {
if (highest[h][lg - 1] < INF) {
highest[h][lg] = highest[highest[h][lg - 1]][lg - 1];
} else {
highest[h][lg] = INF;
}
if (secondHighest[h][lg - 1] < INF) {
secondHighest[h][lg] = secondHighest[secondHighest[h][lg - 1]][lg - 1];
} else {
secondHighest[h][lg] = INF;
}
}
}
}
int getLastHeightFollowingHighest(int startingHeight, int numJumps) {
int currentHeight = startingHeight;
for (int lg = 0; lg <= MAXLG && currentHeight < INF; lg++) {
if (numJumps & (1 << lg)) {
currentHeight = highest[currentHeight][lg];
}
}
return currentHeight;
}
int getLastHeightFollowingSecondHighest(int startingHeight, int numJumps) {
int currentHeight = startingHeight;
for (int lg = 0; lg <= MAXLG && currentHeight < INF; lg++) {
if (numJumps & (1 << lg)) {
currentHeight = secondHighest[currentHeight][lg];
}
}
return currentHeight;
}
void init(int N, std::vector<int> H) {
n = N;
h = H;
initPrevHigher();
initNextHigher();
initHighestAndSecondHighest();
// cout << "\nprevHigher\n";
// for (int i = 0; i < n; i++) {
// cout << prevHigher[i] << endl;
// }
// cout << "\nnextHigher\n";
// for (int i = 0; i < n; i++) {
// cout << nextHigher[i] << endl;
// }
// cout << endl;
// for (int i = 1; i <= 3; i++) {
// cout << "highest[" << i << "]: " << highest[i][0] << endl;
// cout << "secondHighest[" << i << "]: " << secondHighest[i][0] << endl;
// }
}
int minimum_jumps(int A, int B, int C, int D) {
int startingHeight = h[A];
// cout << "\nstartingHeight: " << startingHeight << endl;
// Calculate max number of jumps if we follow the highest pointer
int numHighestJumps;
if (true) {
int lo = 0, hi = MAXN, mid;
while (hi >= lo) {
mid = (lo + hi)/2;
if (getLastHeightFollowingHighest(startingHeight, mid) <= h[C]) {
lo = mid + 1;
} else {
hi = mid - 1;
}
}
numHighestJumps = hi;
}
// cout << "\nnumHighestJumps: " << numHighestJumps << endl;
int heightAfterFollowingHighest = getLastHeightFollowingHighest(startingHeight, numHighestJumps);
// cout << "\nheight after following highest:" << heightAfterFollowingHighest << endl;
// Calculate max number of jumps if we follow the second highest pointer
int numSecondHighestJumps;
if (true) {
int lo = 0, hi = MAXN, mid;
while (hi >= lo) {
mid = (lo + hi)/2;
if (getLastHeightFollowingSecondHighest(heightAfterFollowingHighest, mid) <= h[C]) {
lo = mid + 1;
} else {
hi = mid - 1;
}
}
numSecondHighestJumps = hi;
}
int finalHeight = getLastHeightFollowingSecondHighest(heightAfterFollowingHighest, numSecondHighestJumps);
// cout << "numSecondHighestJumps: " << numSecondHighestJumps << endl;
// cout << "finalHeight: " << finalHeight << endl;
if (finalHeight == h[C]) {
return numHighestJumps + numSecondHighestJumps;
} else {
return -1;
}
}
