#include "obstacles.h"
#include <bits/stdc++.h>
using namespace std;
using vi = vector<int>;
using pi = pair<int, int>;
struct SegTree {
int n; vi arr; vector<pi> st;
SegTree() {}
SegTree(int N, vi &Arr) {
n = N; arr = Arr; st.assign(4*n, {-1, -1});
build(0, 0, n);
}
pi combine(pi x, pi y) {
pi r = {-1, -1};
if (x.first < 0) r.first = y.first;
else if (y.first < 0) r.first = x.first;
else r.first = arr[x.first] < arr[y.first] ? x.first : y.first;
if (x.second < 0) r.second = y.second;
else if (y.second < 0) r.second = x.second;
else r.second = arr[x.second] > arr[y.second] ? x.second : y.second;
return r;
}
pi build(int i, int l, int r) {
if (l+1==r) return st[i] = {l, l};
int m = l + (r- l)/2;
return st[i] = combine(build(2*i+1, l, m), build(2*i+2, m, r));
}
pi query(int i, int l, int r, int ql, int qr) {
if (qr <= l || r <= ql) return {-1, -1};
if (ql <= l && r <= qr) return st[i];
int m = l + (r - l) / 2;
return combine(query(2*i+1, l, m, ql, qr), query(2*i+2, m, r, ql, qr));
}
// max i in [l, r] such that max([l, i]) < T or min([l, i]) > T
int right(int i, int l, int r, int ql, int qr, int T, bool mx) {
if (r <= ql || qr <= l) return -1;
if (ql <= l && r <= qr) {
if ((mx && (st[i].second >= 0 && arr[st[i].second] < T)) || (!mx && (st[i].first >= 0 && arr[st[i].first] > T))) return -1;
}
if (l + 1 == r) return ((mx && arr[l] >= T) || (!mx && arr[l] <= T)) ? l : -1;
int m = l + (r - l) / 2;
int left = right(2*i+1, l, m, ql, qr, T, mx);
if (left != -1) return left;
return right(2*i+2, m, r, ql, qr, T, mx);
}
// min i in [l, r] such that max([i, r]) < T or min([i, r]) > T
int left(int i, int l, int r, int ql, int qr, int T, bool mx) {
if (r <= ql || qr <= l) return -1;
if (ql <= l && r <= qr) {
if ((mx && (st[i].second >= 0 && arr[st[i].second] < T)) || (!mx && (st[i].first >= 0 && arr[st[i].first] > T))) return -1;
}
if (l + 1 == r) return ((mx && arr[l] >= T) || (!mx && arr[l] <= T)) ? l : -1;
int m = l + (r - l) / 2;
int right = left(2*i+2, m, r, ql, qr, T, mx);
if (right != -1) return right;
return left(2*i+1, l, m, ql, qr, T, mx);
}
};
int r, c;
SegTree row, col;
vi t, h, depth, L, R;
void initialize(vi T, vi H) {
r = T.size(); c = H.size();
t = T; h = H; depth.assign(c, 0); L.assign(c, 0); R.assign(c, 0); for (int i = 0; i < c; i++) L[i] = R[i] = i;
row = SegTree(r, T); col = SegTree(c, H);
return;
}
bool can_reach(int lower, int upper, int s, int d) {
if (s>d) swap(s, d);
int mx = h[col.query(0, 0, c, s, d+1).second];
int lo = 0, hi = r;
while (lo < hi) {
int mid = lo + (hi - lo) / 2;
if (t[row.query(0, 0, r, 0, mid+1).second] > mx) hi = mid;
else lo = mid + 1;
}
int first = lo;
if (first >= r || t[first] <= mx) return false;
auto get_range = [&](int i, int x, int ca, int cb) {
int a = col.left(0, 0, c, 0, ca+1, t[i], true), b = col.right(0, 0, c, cb, c, t[i], true);
a = (a == -1) ? 0 : a+1; b = (b == -1) ? c-1 : b-1;
return make_pair(a, b);
};
int S = s, D = d;
int ra = depth[s], rb = depth[d];
int ca = L[s], cb = R[s], da = L[d], db = R[d];
while (ra < first || rb < first) {
if (ra < first) {
s = col.query(0, 0, c, ca, cb+1).first;
int posx = row.right(0, 0, r, ra, r, h[s], false);
if (posx == -1) posx = r-1;
if (posx == ra) {
L[S] = min(L[S], ca); R[S] = max(R[S], cb);
depth[S] = max(depth[S], ra);
return false;
}
ra = posx;
int maxy = row.query(0, 0, r, 0, posx+1).second;
auto range = get_range(maxy, s, ca, cb);
ca = range.first, cb = range.second;
}
if (rb < first) {
d = col.query(0, 0, c, da, db+1).first;
int posx = row.right(0, 0, r, rb, r, h[d], false);
if (posx == -1) posx = r-1;
if (posx == rb) {
L[D] = min(L[D], da); R[D] = max(R[D], db);
depth[D] = max(depth[D], rb);
return false;
}
rb = posx;
int maxy = row.query(0, 0, r, 0, posx+1).second;
auto range = get_range(maxy, d, da, db);
da = range.first, db = range.second;
}
}
L[S] = min(L[S], ca); R[S] = max(R[S], cb);
L[D] = min(L[D], da); R[D] = max(R[D], db);
depth[S] = max(depth[S], ra); depth[D] = max(depth[D], rb);
return true;
}
