#include "meetings.h"
#include <bits/stdc++.h>
using namespace std;
template<typename T>
using min_heap = priority_queue<T, vector<T>, greater<T>>;
template<typename T>
using max_heap = priority_queue<T, vector<T>, less<T>>;
using int64 = long long;
using ld = long double;
constexpr int kInf = 1e9 + 10;
constexpr int64 kInf64 = 1e15 + 10;
constexpr int kMod = 1e9 + 7;
constexpr int kMaxHeight = 20;
template<class node, class F = std::function<node(const node &, const node &)>>
class SegTree {
int n = 0;
std::vector<node> t;
F unite;
void build(const int x, const int l, const int r, const std::vector<node> &a) {
if (l == r) {
t[x] = a[l];
return;
}
const int mid = (l + r) / 2;
const int y = 2 * (mid - l + 1) + x;
build(x + 1, l, mid, a);
build(y, mid + 1, r, a);
t[x] = unite(t[x + 1], t[y]);
}
void update(const int x, const int l, const int r, const int p, const node &v) {
if (l == p and p == r) {
t[x] = v;
return;
}
const int mid = (l + r) / 2;
const int y = 2 * (mid - l + 1) + x;
if (p <= mid) {
update(x + 1, l, mid, p, v);
} else {
update(y, mid + 1, r, p, v);
}
t[x] = unite(t[x + 1], t[y]);
}
node query(const int x, const int l, const int r, const int ql, const int qr) const {
if (ql <= l and r <= qr) {
return t[x];
}
const int mid = (l + r) / 2;
const int y = 2 * (mid - l + 1) + x;
if (qr <= mid) {
return query(x + 1, l, mid, ql, qr);
} else if (mid < ql) {
return query(y, mid + 1, r, ql, qr);
} else {
return unite(query(x + 1, l, mid, ql, qr), query(y, mid + 1, r, ql, qr));
}
}
void debug_node(const int x, const vector<int> &path) const {
for (int i = 0; i < path.size(); i++) {
cerr << path[i] << (i == path.size() - 1 ? ": " : " -> ");
}
cerr << t[x] << '\n';
}
void debug(const int x, const int l, const int r, vector<int> path) const {
path.push_back(x);
if (l == r) {
debug_node(x, path);
return;
}
const int mid = (l + r) / 2;
const int y = 2 * (mid - l + 1) + x;
debug(x + 1, l, mid, path);
debug(y, mid + 1, r, path);
debug_node(x, path);
}
public:
SegTree() = default;
explicit SegTree(const int n, const node e, F f) : n(n), t(2 * n - 1, e), unite(std::move(f)) {
vector<node> a(n, e);
build(0, 0, n - 1, a);
}
explicit SegTree(const std::vector<node> &a, F f) : n(a.size()), t(2 * (a.size()) - 1), unite(std::move(f)) {
build(0, 0, n - 1, a);
}
void set(const int p, const node &v) {
assert(0 <= p and p < n);
update(0, 0, n - 1, p, v);
}
[[nodiscard]] node get(const int l, const int r) const {
assert(0 <= l and l <= r and r < n);
return query(0, 0, n - 1, l, r);
}
void debug() const {
debug(0, 0, n - 1, {});
cerr << "----------\n\n";
}
};
struct node {
int peak{};
vector<int> left;
vector<int> right;
vector<int> costl;
vector<int> costr;
node() = default;
explicit node(const int h) : left(h + 1), right(h + 1),
costl(h + 1, kInf), costr(h + 1, kInf) {}
};
std::vector<long long> minimum_costs(std::vector<int> H, std::vector<int> L, std::vector<int> R) {
const int n = H.size(), q = L.size();
vector<node> leaves(n, node(kMaxHeight));
for (int i = 0; i < n; i++) {
node &x = leaves[i];
x.peak = H[i];
for (int h = 0; h <= kMaxHeight; h++) {
x.left[h] = max(h, H[i]);
x.right[h] = max(h, H[i]);
}
x.costl[H[i]] = H[i];
x.costr[H[i]] = H[i];
}
SegTree<node> st(leaves, [](const node &l, const node &r) {
node ans(kMaxHeight);
ans.peak = max(l.peak, r.peak);
for (int i = 0; i <= kMaxHeight; i++) {
ans.left[i] = l.left[i] + r.left[max(l.peak, i)];
ans.right[i] = l.right[max(r.peak, i)] + r.right[i];
}
auto update = [&](const int max_left, const int max_right, const int cost) {
if (max_left == ans.peak) {
ans.costl[max_right] = min(ans.costl[max_right], cost);
}
if (max_right == ans.peak) {
ans.costr[max_left] = min(ans.costr[max_left], cost);
}
};
for (int i = 0; i <= kMaxHeight; i++) {
//meetings point is in l
update(l.peak, max(i, r.peak), l.costl[i] + r.left[i]);
update(i, ans.peak, l.costr[i] + r.left[l.peak]);
//meeting point is in r
update(ans.peak, i, l.right[r.peak] + r.costl[i]);
update(max(l.peak, i), r.peak, l.right[i] + r.costr[i]);
}
return ans;
});
vector<int64> ans(q);
for (int i = 0; i < q; i++) {
const node x = st.get(L[i], R[i]);
ans[i] = min(*min_element(x.costl.begin(), x.costl.end()),
*min_element(x.costr.begin(), x.costr.end()));
}
return ans;
}
