#include #include #include using namespace std; typedef long long ll; template class ConvexHullTrick { private: typedef pair P; vector

lines; bool isMonotonic; function comp; public: ConvexHullTrick(bool M = false, function c = [](T l, T r) { return l >= r; }) : isMonotonic(M), comp(c) {} bool check(P l1, P l2, P l3) { if (l1 < l3) swap(l1, l3); return (l3.second - l2.second) * (l2.first - l1.first) >= (l2.second - l1.second) * (l3.first - l2.first); } void add(T a, T b) { P line = P(a, b); while (lines.size() >= 2 && check(*(lines.end() - 2), lines.back(), line)) lines.pop_back(); lines.push_back(line); } T f(int k, T x) { return lines[k].first * x + lines[k].second; } T f(P line, T x) { return line.first * x + line.second; } T get(T x) { if (isMonotonic) { static int head = 0; while (lines.size() - head >= 2 && comp(f(head, x), f(head + 1, x))) head++; return f(head, x); } else { int lb = -1, ub = lines.size() - 1; while (ub - lb > 1) { int md = (ub + lb) / 2; if (comp(f(md, x), f(md + 1, x))) lb = md; else ub = md; } return f(ub, x); } } }; // verified // https://atcoder.jp/contests/colopl2018-final/tasks/colopl2018_final_c void AtCoder_2018_1_20_C() { ll N, a; cin >> N; ConvexHullTrick CHT(true); for (ll i = 0; i < N; i++) { cin >> a; CHT.add(-2 * i, a + i * i); } for (ll i = 0; i < N; i++) cout << CHT.get(i) + i * i << '\n'; } // verified // https://yukicoder.me/problems/no/409 void yuki409() { ll n, a, b, w; cin >> n >> a >> b >> w; vector d(n); for (int i = 0; i < n; i++) cin >> d[i]; ConvexHullTrick CHT(true); vector dp(n + 1); // i日目に食べた時の体重の最大の変化量 CHT.add(0, 0); for (ll i = 1; i <= n; i++) { dp[i] = CHT.get(i - 1) - a * (i - 1) + b * i * (i - 1) / 2 + d[i - 1]; CHT.add(-i * b, dp[i] + a * i + b * i * (i - 1) / 2); } ll ans = dp[n]; for (ll i = 0; i < n; i++) { ans = min(ans, dp[i] - a * (n - i) + b * (n - i) * (n - i + 1) / 2); } cout << ans + w << '\n'; } int main() { // AtCoder_2018_1_20_C(); yuki409(); return 0; }