#ifndef LOCAL #define FAST_IO #endif // ============ #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #define OVERRIDE(a, b, c, d, ...) d #define REP2(i, n) for (i32 i = 0; i < (i32)(n); ++i) #define REP3(i, m, n) for (i32 i = (i32)(m); i < (i32)(n); ++i) #define REP(...) OVERRIDE(__VA_ARGS__, REP3, REP2)(__VA_ARGS__) #define PER(i, n) for (i32 i = (i32)(n) - 1; i >= 0; --i) #define ALL(x) begin(x), end(x) using namespace std; using u32 = unsigned int; using u64 = unsigned long long; using i32 = signed int; using i64 = signed long long; using f64 = double; using f80 = long double; template using Vec = vector; template bool chmin(T &x, const T &y) { if (x > y) { x = y; return true; } return false; } template bool chmax(T &x, const T &y) { if (x < y) { x = y; return true; } return false; } #ifdef INT128 using u128 = __uint128_t; using i128 = __int128_t; istream &operator>>(istream &is, i128 &x) { i64 v; is >> v; x = v; return is; } ostream &operator<<(ostream &os, i128 x) { os << (i64)x; return os; } istream &operator>>(istream &is, u128 &x) { u64 v; is >> v; x = v; return is; } ostream &operator<<(ostream &os, u128 x) { os << (u64)x; return os; } #endif [[maybe_unused]] constexpr i32 INF = 1000000100; [[maybe_unused]] constexpr i64 INF64 = 3000000000000000100; struct SetUpIO { SetUpIO() { #ifdef FAST_IO ios::sync_with_stdio(false); cin.tie(nullptr); #endif cout << fixed << setprecision(15); } } set_up_io; // ============ #ifdef DEBUGF #else #define DBG(x) (void)0 #endif // いつもありがとうございます // https://github.com/kth-competitive-programming/kactl/blob/main/content/data-structures/LineContainer.h /** * Author: Simon Lindholm * Date: 2017-04-20 * License: CC0 * Source: own work * Description: Container where you can add lines of the form kx+m, and query maximum values at points x. * Useful for dynamic programming (``convex hull trick''). * Time: O(\log N) * Status: stress-tested */ using ll = i64; #include struct Line { mutable ll k, m, p; bool operator<(const Line& o) const { return k < o.k; } bool operator<(ll x) const { return p < x; } }; struct LineContainer : multiset> { // (for doubles, use inf = 1/.0, div(a,b) = a/b) static const ll inf = LLONG_MAX; ll div(ll a, ll b) { // floored division return a / b - ((a ^ b) < 0 && a % b); } bool isect(iterator x, iterator y) { if (y == end()) return x->p = inf, 0; if (x->k == y->k) x->p = x->m > y->m ? inf : -inf; else x->p = div(y->m - x->m, x->k - y->k); return x->p >= y->p; } void add(ll k, ll m) { auto z = insert({k, m, 0}), y = z++, x = y; while (isect(y, z)) z = erase(z); if (x != begin() && isect(--x, y)) isect(x, y = erase(y)); while ((y = x) != begin() && (--x)->p >= y->p) isect(x, erase(y)); } ll query(ll x) { assert(!empty()); auto l = *lower_bound(x); return l.k * x + l.m; } }; int main() { i32 n; cin >> n; Vec a(n); REP(i, n) { cin >> a[i]; } LineContainer cht; Vec dp(n, 0LL); REP(i, n) { if (i > 0) { chmax(dp[i], cht.query(a[i])); } cht.add(a[i], dp[i]); } cout << *max_element(ALL(dp)) << '\n'; }