#include "jumps.h"
#include <bits/stdc++.h>
#include <vector>
using namespace std;
const int MAXN = 2e5 + 5;
int dp_min[19][MAXN], dp_max[19][MAXN];
int seg[MAXN * 4]; // at position i stores the value H[i]
vector<int> H, REV;
int N;
void Build(int left, int right, int pos)
{
if(left == right)
{
seg[pos] = H[left];
return;
}
int mid = (left + right) / 2;
Build(left, mid, pos * 2);
Build(mid + 1, right, pos * 2 + 1);
seg[pos] = max(seg[pos * 2], seg[pos * 2 + 1]);
}
int Query(int l, int r, int pos, int ql, int qr)
{
if(ql <= l && r <= qr)
{
return seg[pos];
}
if(ql > r || l > qr)
{
return -1;
}
int mid = (l + r) >> 1;
return max(Query(l, mid, pos * 2, ql, qr), Query(mid + 1, r, pos * 2 + 1, ql, qr));
}
pair<int, int> Query(int l, int r, int pos, int ql, int qr, int qval)
{
// first is the smallest accessible element
// second is whether the range has become inaccessible or not?
if(ql > r || l > qr)
{
// cout << "(" << l << ", " << r << ") returns: {" << 0 << ", " << 0 << "}\n";
return {-1, 0};
}
if(ql <= l && r <= qr && seg[pos] <= qval)
{
// cout << "(" << l << ", " << r << ") returns: {" << seg[pos] << ", " << seg[pos] << "}\n";
return {seg[pos], seg[pos]};
}
if(l == r && seg[pos] > qval)
{
// cout << "(" << l << ", " << r << ") returns: {" << -1 << ", " << -1 << "}\n";
return {-1, -1};
}
int mid = (l + r) / 2;
pair<int, int> ans1 = Query(mid + 1, r, pos * 2 + 1, ql, qr, qval);
if(ans1.second == -1)
{
// cout << "(" << l << ", " << r << ") returns: {" << ans1.first << ", " << ans1.second << "}\n";
return ans1;
}
pair<int, int> ans2 = Query(l, mid, pos * 2, ql, qr, qval);
if(ans2.second == -1)
{
// cout << "(" << l << ", " << r << ") returns: {" << max(ans1.first, ans2.first) << ", " << -1 << "}\n";
return {max(ans1.first, ans2.first), -1};
}
// cout << "(" << l << ", " << r << ") returns: {" << max(ans1.first, ans2.first) << ", " << max(ans1.second, ans2.second) << "}\n";
return {max(ans1.first, ans2.first), max(ans1.second, ans2.second)};
}
void init(int n, std::vector<int> h)
{
stack<int> s;
N = n;
REV.resize(N + 1);
for(int i = 0; i < h.size(); i++)
{
H.push_back(h[i]);
REV[H[i]] = i;
}
Build(0, N - 1, 1);
for(int i = 0; i < N; i++)
{
while(!s.empty() && H[s.top()] < H[i])
{
s.pop();
}
if(s.empty())
{
dp_min[0][i] = -1;
}
else
{
dp_min[0][i] = s.top();
}
s.push(i);
}
while(!s.empty())
{
s.pop();
}
for(int i = N - 1; i >= 0; i--)
{
while(!s.empty() && H[s.top()] < H[i])
{
s.pop();
}
if(s.empty())
{
dp_max[0][i] = -1;
}
else
{
dp_max[0][i] = s.top();
}
s.push(i);
if(dp_min[0][i] == -1 || (dp_max[0][i] != -1 && H[dp_max[0][i]] < H[dp_min[0][i]]))
{
swap(dp_min[0][i], dp_max[0][i]);
}
}
for(int i = 1; i < 19; i++)
{
for(int j = 0; j < N; j++)
{
dp_min[i][j] = (dp_min[i - 1][j] == -1) ? -1 : dp_min[i - 1][dp_min[i - 1][j]];
dp_max[i][j] = (dp_max[i - 1][j] == -1) ? -1 : dp_max[i - 1][dp_max[i - 1][j]];
assert(dp_max[i][j] == -1 || H[dp_max[i][j]] >= H[dp_min[i][j]]);
}
}
// for(int i = 0; i < N; i++)
// {
// for(int j = 0; j < 19; j++)
// {
// cout << "val: " << min_max_node[j][i] << ", " << max_max_node[j][i] << "\n";
// cout << "dp: " << dp_min[j][i] << ", " << dp_max[j][i] << "\n";
// }
// }
}
int query(int l, int r, int pos, int ql, int qr, int qval)
{
if(ql > r || l > qr || seg[pos] <= qval)
{
return -1;
}
if(l == r)
{
return l;
}
int mid = (l + r) >> 1;
int ans1 = query(l, mid, pos * 2, ql, qr, qval);
if(ans1 != -1)
{
return ans1;
}
return query(mid + 1, r, pos * 2 + 1, ql, qr, qval);
}
int minimum_jumps(int A, int B, int C, int D)
{
// A = B && C = D
// cout << "---- ---- ---- ---- ----\n";
// cout << "A = " << A << ", B = " << B << "\n";
int HIGHEST = Query(0, N - 1, 1, C, D);
HIGHEST = REV[HIGHEST];
// cout << "HIGHEST = " << HIGHEST << "\n";
int query_result = Query(0, N - 1, 1, A, B, H[HIGHEST]).first;
// cout << "query_result = " << query_result << "\n";
if(query_result == -1)
{
return -1;
}
A = REV[query_result];
B = A;
// cout << "A = " << A << "\n";
C = query(0, N - 1, 1, C, D, H[A]); // query for the smallest element >= H[A]
// cout << "C = " << C << "\n";
if(C == -1)
{
return -1;
}
// C = REV[C];
D = C;
// cout << "A = " << A << ", B = " << B << "\n";
// cout << "---- ---- ---- ---- ----\n";
int ans = 0;
for(int i = 18; i >= 0; i--)
{
if(dp_max[i][A] != -1 && H[dp_max[i][A]] <= H[C])
{
ans += (1 << i);
A = dp_max[i][A];
}
}
// cout << "ans = " << ans << ", A = " << A << "\n";
for(int i = 18; i >= 0; i--)
{
if(dp_min[i][A] != -1 && H[dp_min[i][A]] <= H[C])
{
ans += (1 << i);
A = dp_min[i][A];
}
}
// cout << "ans = " << ans << ", A = " << A << "\n";
if(A == C)
{
return ans;
}
return -1;
}
