#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 update(int i, int l, int r, int k, int v) {
if (!(l <= k && k < r)) return st[i];
if (l+1==r) {arr[k] = v; return st[i] = {l, l};}
int m = l + (r- l)/2;
return st[i] = combine(update(2*i+1, l, m, k, v), update(2*i+2, m, r, k, v));
}
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);
}
};
struct DSU {
int n; vi par, L, R;
DSU(int N = 0) {n = N; for (int i = 0; i < 2*n; i++) par.push_back(i), L.push_back(i < n ? i : 3*n), R.push_back(i < n ? i : -1);}
int find(int v) {return par[v] == v ? v : par[v] = find(par[v]);}
void unite(int a, int b) {
a = find(a); b = find(b);
if (a != b) {
L[n] = min(L[a], L[b]); R[n] = max(R[a], R[b]);
par[a] = par[b] = n++;
}
}
};
int r, c;
SegTree row, col;
vi t, h, depth, L, R;
DSU dsu;
vector<bool> finished;
pi get_range(int i, 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);
};
void compute(int i, int maxdepth) {
if (t[0] <= h[i]) return;
if (depth[i] != -1 && (finished[i] || depth[i] >= maxdepth)) return;
if (depth[i] == -1) depth[i] = 0;
while (depth[i] < maxdepth && depth[i] < r-1) {
int mn = col.query(0, 0, c, L[i], R[i]+1).first;
int posx = row.right(0, 0, r, depth[i], r, h[mn], false);
if (posx == -1) posx = r-1;
if (depth[i] >= r-1 || posx == depth[i]) finished[i] = true;
if (posx == depth[i]) break;
depth[i] = posx;
int maxy = row.query(0, 0, r, 0, posx+1).second;
auto range = get_range(maxy, L[i], R[i]);
L[i] = range.first, R[i] = range.second;
}
}
void initialize(vi T, vi H) {
r = T.size(); c = H.size();
t = T; h = H; dsu = DSU(c);
depth.assign(c, -1); L.assign(c, 0); R.assign(c, 0); for (int i = 0; i < c; i++) L[i] = R[i] = i;
finished.assign(c, false); dsu = DSU(c);
row = SegTree(r, T); col = SegTree(c, H);
auto depthst = SegTree(c, depth);
vector<int> idx(c); iota(idx.begin(), idx.end(), 0);
sort(idx.begin(), idx.end(), [&](int i, int j) {return h[i] < h[j];});
for (int ix = 0; ix < c; ix++) {
int i = idx[ix];
depth[i] = row.right(0, 0, r, 0, r, h[i], false);
if (depth[i] == -1) depth[i] = r-1;
int maxy = row.query(0, 0, r, 0, depth[i]+1).second;
auto range = get_range(maxy, L[i], R[i]);
int x = depthst.right(0, 0, c, i, range.second+1, depth[i], true);
int y = depthst.right(0, 0, c, range.first, i+1, depth[i], true);
if (x != -1) dsu.unite(i, x);
else if (y != -1) dsu.unite(i, y);
depth[i] = max(depth[i], x == -1 ? (y == -1 ? -1 : depth[y]) : depth[x]);
depthst.update(0, 0, c, i, depth[i]);
}
}
bool can_reach(int lower, int upper, int s, int d) {
if (s>d) swap(s, d);
return dsu.find(s) == dsu.find(d);
// int mx = h[col.query(0, 0, c, s, d+1).second];
// int first = row.right(0, 0, r, 0, r, mx+1, true);
// if (first >= r || t[first] <= mx) return false;
// return depth[s] >= first && depth[d] >= first;
}
