//https://qiita.com/tanakh/items/0ba42c7ca36cd29d0ac8 macro_rules! input { (source = $s:expr, $($r:tt)*) => { let mut iter = $s.split_whitespace(); input_inner!{iter, $($r)*} }; ($($r:tt)*) => { let s = { use std::io::Read; let mut s = String::new(); std::io::stdin().read_to_string(&mut s).unwrap(); s }; let mut iter = s.split_whitespace(); input_inner!{iter, $($r)*} }; } macro_rules! input_inner { ($iter:expr) => {}; ($iter:expr, ) => {}; ($iter:expr, $var:ident : $t:tt $($r:tt)*) => { let $var = read_value!($iter, $t); input_inner!{$iter $($r)*} }; } macro_rules! read_value { ($iter:expr, ( $($t:tt),* )) => { ( $(read_value!($iter, $t)),* ) }; ($iter:expr, [ $t:tt ; $len:expr ]) => { (0..$len).map(|_| read_value!($iter, $t)).collect::>() }; ($iter:expr, chars) => { read_value!($iter, String).chars().collect::>() }; ($iter:expr, usize1) => { read_value!($iter, usize) - 1 }; ($iter:expr, $t:ty) => { $iter.next().unwrap().parse::<$t>().expect("Parse error") }; } // // おためしLi Chao Tree // 最小値習得 struct LiChaoTree { seg: Vec<(i64, i64)>, bit: usize, z: Vec, } const INF_LINE: (i64, i64) = (0, 2_000_000_000_000_000_001); impl LiChaoTree { fn new(z: &Vec) -> Self { let mut z = z.clone(); z.sort(); z.dedup(); let mut k = 0; while (1 << k) < z.len() { k += 1; } let p = *z.last().unwrap(); while z.len() < (1 << k) { z.push(p); } LiChaoTree { seg: vec![INF_LINE; 2 << k], bit: k, z: z, } } //直線ax + b を追加 fn update(&mut self, a: i64, b: i64) { let mut state = ((a, b), 1, 0, (1 << self.bit)); loop { let ((a, b), k, l, r) = state; let (c, d) = self.seg[k]; let fl = a * self.z[l] + b; let fr = a * self.z[r - 1] + b; let gl = c * self.z[l] + d; let gr = c * self.z[r - 1] + d; if fl >= gl && fr >= gr { break; } if fl <= gl && fr <= gr { self.seg[k] = (a, b); break; } let m = (l + r) / 2; let fm = a * self.z[m] + b; let gm = c * self.z[m] + d; state = if fr >= gr && fm >= gm { ((a, b), 2 * k, l, m) } else if fr >= gr { self.seg[k] = (a, b); ((c, d), 2 * k + 1, m, r) } else if fm >= gm { ((a, b), 2 * k + 1, m, r) } else { self.seg[k] = (a, b); ((c, d), 2 * k, l, m) }; } } fn find(&self, x: i64) -> i64 { let k = self.z.binary_search(&x).unwrap(); let mut y = k + (1 << self.bit); let mut res = std::i64::MAX; while y >= 1 { let (a, b) = self.seg[y]; res = std::cmp::min(res, a * x + b); y >>= 1; } res } } fn run() { input! { n: usize, a: i64, b: i64, w: i64, d: [i64; n], } let (a, b, w) = (2 * a, 2 * b, 2 * w); let mut d = d; for d in &mut d { *d *= 2; } let z: Vec = (0..=n).map(|k| k as i64).collect(); let mut cht = LiChaoTree::new(&z); cht.update(0, w); let mut dp = vec![w; n + 1]; for i in 1..=n { let k = i as i64; dp[i] = d[i - 1] + -a * (k - 1) + b / 2 * k * (k - 1) + cht.find(k); cht.update(-b * k, dp[i] + a * k + b * k * k / 2 + b / 2 * k); } let mut ans = dp[n]; for i in 0..n { let k = (n - i) as i64; let v = dp[i] - a * k + b / 2 * k * (k + 1); ans = std::cmp::min(ans, v); } ans /= 2; println!("{}", ans); } fn main() { run(); }