#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); } }; struct DSU { int n; vector<int> par; DSU(int N = 0) : n(N), par(N) {iota(par.begin(), par.end(), 0);} int find(int v) {return par[v] == v ? v : par[v] = find(par[v]);} void unite(int a, int b) {if (find(a) != find(b)) par[find(b)] = find(a);} }; int r, c; SegTree row, col; vi t, h, depth; DSU dsu; 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 initialize(vi T, vi H) { r = T.size(); c = H.size(); t = T; h = H; depth.assign(c, -1); row = SegTree(r, T); col = SegTree(c, H); dsu = DSU(c); vector<int> idx(c); iota(idx.begin(), idx.end(), 0); sort(idx.begin(), idx.end(), [&](int i, int j) {return h[i] < h[j];}); set<int> done; 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, i, i); auto it = done.lower_bound(i); if (it != done.end() && *it <= range.second) depth[i] = max(depth[i], depth[*it]), dsu.unite(i, *it); if (it != done.begin() && (it != done.end() || (done.end() != done.begin()))) { --it; if (*it >= range.first) depth[i] = max(depth[i], depth[*it]), dsu.unite(i, *it); } done.insert(i); } } 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 first = row.right(0, 0, r, 0, r, mx+1, true); if (first >= r || t[first] <= mx) return false; return dsu.find(s) == dsu.find(d); }