#include #include #include #include using namespace std; #define Inf 1e15 #define maxn 300010 long long d[maxn]; long long dp[maxn][2]; // dp[i][0]: sleep at i day, dp[i][1]: read at i day struct line { // y = mx + b long long m; // slope long long b; // intercept line(long long m, long long b): m(m), b(b) {} }; long long foo(line l, long long i, long long a, long long b) { // return dp[i][1] from line l(j) return l.m * i + l.b + b * i * (i + 1) / 2 - a * i; } double vertex(line l1, line l2) { // the intersection of l1 and l2 return 1.0 * (l2.b - l1.b) / (l1.m - l2.m); } // reamin: w // days: n // study 1 day: -a // study for x days: + x * b // sleep in i day: + d[i] int main() { long long n, a, b, w; cin >> n >> a >> b >> w; for (int i = 1; i <= n; i++) cin >> d[i]; dp[0][0] = dp[0][1] = w; deque dq; dq.push_front(line(0, w)); // sine dp[j][0] = w for (long long i = 1; i <= n; i++) { dp[i][0] = min(dp[i - 1][0], dp[i - 1][1]) + d[i]; // sleep // consider the value of dp[i][1] by subtituting i into dq[0] while (dq.size() > 1 && (foo(dq[1], i, a, b) < foo(dq[0], i, a, b))) dq.pop_front(); // we no longer need dq[0], pop out dp[i][1] = foo(dq[0], i, a, b); // cout << dp[i][0] << " " << dp[i][1] << " " << dq.size() << '\n'; // add line "i" into dq line tmp = line(0, 0); tmp.m = -1 * i * b; // since this line will be treat as j in the future, the slope's j = i now tmp.b = dp[i][0] + b * i * (i - 1) / 2 + i * a; while (dq.size() >= 2 && (vertex(dq[dq.size() - 1], dq[dq.size() - 2]) > vertex(tmp, dq[dq.size() - 2]))) dq.pop_back(); dq.push_back(tmp); } cout << min(dp[n][1], dp[n][0]) << '\n'; return 0; }