//#pragma GCC target("sse,sse2,sse3,ssse3,sse4,popcnt,abm,mmx,avx,avx2,avx512f") #pragma GCC target("sse,sse2,sse3,ssse3,sse4,popcnt,abm,mmx,avx") #pragma GCC optimize("O3") #pragma GCC optimize("unroll-loops") #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #ifdef DEBUG #include "./CompetitiveProgrammingCpp/Utils/debug.hpp" #include "./CompetitiveProgrammingCpp/Utils/Timer.hpp" #include "./CompetitiveProgrammingCpp/Utils/sample.hpp" #else #define dump(...) templateconstexpr inline auto d_val(T a, T b) { return a; } #endif /* macro */ #define FOR(i, b, e) for(ll i = (ll)(b); i < (ll)(e); ++i) #define RFOR(i, b, e) for(ll i = (ll)((e)-1); i >= (ll)(b); --i) #define REP(i, n) FOR(i, 0, (n)) #define RREP(i, n) RFOR(i, 0, (n)) #define REPC(x,c) for(const auto& x:(c)) #define REPI2(it,b,e) for(auto it = (b); it != (e); ++it) #define REPI(it,c) REPI2(it, (c).begin(), (c).end()) #define RREPI(it,c) REPI2(it, (c).rbegin(), (c).rend()) #define REPI_ERACE2(it, b, e) for(auto it = (b); it != (e);) #define REPI_ERACE(it, c) REPI_ERACE2(it, (c).begin(), (c).end()) #define ALL(x) (x).begin(),(x).end() #define cauto const auto& /* macro func */ template inline auto sort(T& t) { std::sort(ALL(t)); } template inline auto rsort(T& t) { std::sort((t).rbegin(), (t).rend()); } template inline auto unique(T& t) { (t).erase(unique((t).begin(), (t).end()), (t).end()); } template inline auto chmax(T& t, const S& s) { if(s > t) { t = s; return true; } return false; } template inline auto chmin(T& t, const S& s) { if(s < t) { t = s; return true; } return false; } inline auto BR() { std::cout << "\n"; } /* type define */ using ll = long long; using VS = std::vector; using VL = std::vector; using VVL = std::vector; using VVVL = std::vector; using VVVVL = std::vector; using VVVVVL = std::vector; using VD = std::vector; template using V = std::vector; template using P = std::pair; using PAIR = P; /* using std */ using std::cout; constexpr char endl = '\n'; using std::cin; using std::pair; using std::string; using std::stack; using std::queue; using std::deque; using std::vector; using std::list; using std::map; using std::unordered_map; using std::multimap; using std::unordered_multimap; using std::set; using std::unordered_set; using std::unordered_multiset; using std::multiset; using std::bitset; using std::priority_queue; /* Initial processing */ struct Preprocessing { Preprocessing() { std::cin.tie(0); std::ios::sync_with_stdio(0); }; }_Preprocessing; /* Remove the source of the bug */ auto pow(signed, signed) { assert(false); } /* define hash */ namespace std { template <> class hash> { public: size_t operator()(const std::pair& x) const { return hash()(1000000000 * x.first + x.second); } }; } /* input */ template std::istream& operator >> (std::istream& is, vector& vec) { for(T& x : vec) is >> x; return is; } /* constant value */ // constexpr ll MOD = 1000000007; constexpr ll MOD = 998244353; //============================================================================================= class ConvexHullTrick { using T = long long; std::deque> lines; static auto func(const std::pair& line, const T& x) { return x * line.first + line.second; } static auto check(const std::pair& line1, const std::pair& line2, const std::pair& line3) { auto [a1, b1] = line1; auto [a2, b2] = line2; auto [a3, b3] = line3; return (a2 - a1) * (b3 - b2) >= (b2 - b1) * (a3 - a2); } public: ConvexHullTrick() {} auto add(const std::pair& line) { while(lines.size() > 1 && check(*std::next(lines.rbegin()), *lines.rbegin(), line)) { lines.pop_back(); } lines.emplace_back(line); } auto add(const T& a, const T& b) { add({a,b}); } auto query(const T& x) { while(lines.size() > 1 && func(*lines.begin(), x) > func(*std::next(lines.begin()), x)) { lines.pop_front(); } return func(*lines.begin(), x); } }; signed main() { ll n, a, b, w; cin >> n >> a >> b >> w; VL d(n); cin >> d; constexpr ll mx = 1e18; auto cht = ConvexHullTrick(); VL dp(n + 1, mx); auto update = [&](ll i, ll x) { chmin(dp[i], x); auto pa = -b * i; auto pb = a * i + i * (i + 1) / 2 * b + dp[i]; cht.add(pa, pb); }; update(0, w); FOR(i, 1, n + 1) { auto ad = d[i - 1] - a * i + a + i * (i - 1) / 2 * b; auto min = cht.query(i); update(i, ad + min); } ll ans = dp[n]; REP(i, n) { ll k = n - i; chmin(ans, dp[i] + -a * k + k * (k + 1) / 2 * b); } cout << ans << endl; dump(dp); }