use std::collections::*; use std::cmp::*; // https://qiita.com/tanakh/items/0ba42c7ca36cd29d0ac8 macro_rules! input { ($($r:tt)*) => { let stdin = std::io::stdin(); let mut bytes = std::io::Read::bytes(std::io::BufReader::new(stdin.lock())); let mut next = move || -> String{ bytes.by_ref().map(|r|r.unwrap() as char) .skip_while(|c|c.is_whitespace()) .take_while(|c|!c.is_whitespace()) .collect() }; input_inner!{next, $($r)*} }; } macro_rules! input_inner { ($next:expr) => {}; ($next:expr,) => {}; ($next:expr, $var:ident : $t:tt $($r:tt)*) => { let $var = read_value!($next, $t); input_inner!{$next $($r)*} }; } macro_rules! read_value { ($next:expr, [ $t:tt ; $len:expr ]) => { (0..$len).map(|_| read_value!($next, $t)).collect::>() }; ($next:expr, $t:ty) => ($next().parse::<$t>().expect("Parse error")); } trait Change { fn chmax(&mut self, x: Self); fn chmin(&mut self, x: Self); } impl Change for T { fn chmax(&mut self, x: T) { if *self < x { *self = x; } } fn chmin(&mut self, x: T) { if *self > x { *self = x; } } } fn calc(n: usize, acc: &[i64], m: usize, x: i64) -> (i64, usize) { let mut dp = vec![(0, 0); n + 1]; for i in 1..n + 1 { let mut me = (dp[i - 1].0 + acc[i] - acc[i - 1] - x, dp[i - 1].1 + 1); for j in 1..min(i, m) + 1 { me.chmax((dp[i - j].0 + (acc[i] - acc[i - j]).abs() - x, dp[i - j].1 + 1)); } dp[i] = me; } dp[n] } const INF: i64 = 1 << 50; fn prog(n: usize, acc: &[i64], m: usize, dp: &[i64], ep: &mut [i64]) { let mut st = VecDeque::new(); st.push_back((0, dp[0])); for i in 1..n + 1 { let pre = st[0]; ep[i] = pre.1 + acc[i]; if pre.0 + m <= i { st.pop_front(); } while let Some(v) = st.pop_back() { if v.1 <= dp[i] - acc[i] { continue; } st.push_back(v); break; } st.push_back((i, dp[i] - acc[i])); } let mut st = VecDeque::new(); st.push_back((0, dp[0])); for i in 1..n + 1 { let pre = st[0]; ep[i].chmax(pre.1 - acc[i]); if pre.0 + m <= i { st.pop_front(); } while let Some(v) = st.pop_back() { if v.1 <= dp[i] + acc[i] { continue; } st.push_back(v); break; } st.push_back((i, dp[i] + acc[i])); } } // Tags: sliding-window-technique fn main() { // Lagrange relaxation seems not to work. input! { n: usize, k: usize, m: usize, a: [i64; n], } let mut acc = vec![0; n + 1]; for i in 0..n { acc[i + 1] = acc[i] + a[i]; } let mut dp = vec![-INF; n + 1]; dp[0] = 0; for _ in 0..k { let mut ep = vec![-INF; n + 1]; prog(n, &acc, m, &dp, &mut ep); dp = ep; // eprintln!("{:?}", dp); } println!("{}", dp[n]); }