// ---------- begin Foldable Deque ---------- struct FoldableDeque { front: Vec<(T, T)>, back: Vec<(T, T)>, op: F, } #[allow(dead_code)] impl FoldableDeque where T: Clone, F: Fn(&T, &T) -> T, { fn new(op: F) -> Self { FoldableDeque { front: Vec::new(), back: Vec::new(), op: op, } } fn find(&self) -> Option { match (self.front.last(), self.back.last()) { (Some(a), Some(b)) => Some((self.op)(&a.1, &b.1)), (Some(a), None) => Some(a.1.clone()), (None, Some(b)) => Some(b.1.clone()), (None, None) => None, } } fn clear(&mut self) { self.front.clear(); self.back.clear(); } fn len(&self) -> usize { self.front.len() + self.back.len() } fn push_back(&mut self, val: T) { let sum = self .back .last() .map_or_else(|| val.clone(), |p| (self.op)(&p.1, &val)); self.back.push((val, sum)); } fn push_front(&mut self, val: T) { let sum = self .front .last() .map_or_else(|| val.clone(), |p| (self.op)(&val, &p.1)); self.front.push((val, sum)); } fn pop_front(&mut self) -> Option { if self.len() == 0 { return None; } if self.front.is_empty() { let a = self.back.clone(); let m = (self.back.len() + 1) / 2; self.back.clear(); let (f, b) = a.split_at(m); for v in f.iter().rev() { self.push_front(v.0.clone()); } for v in b.iter() { self.push_back(v.0.clone()); } } self.front.pop().map(|p| p.0) } fn pop_back(&mut self) -> Option { if self.len() == 0 { return None; } if self.back.is_empty() { let a = self.front.clone(); let m = self.front.len() / 2; self.front.clear(); let (f, b) = a.split_at(m); for v in f.iter().rev() { self.push_front(v.0.clone()); } for v in b.iter() { self.push_back(v.0.clone()); } } self.back.pop().map(|p| p.0) } } // ---------- end Foldable Deque ---------- //https://qiita.com/tanakh/items/0ba42c7ca36cd29d0ac8 より 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, bytes) => { read_value!($iter, String).bytes().collect::>() }; ($iter:expr, usize1) => { read_value!($iter, usize) - 1 }; ($iter:expr, $t:ty) => { $iter.next().unwrap().parse::<$t>().expect("Parse error") }; } // fn run() { input! { n: usize, k: usize, m: usize, a: [f64; n], } let mut sum = a.clone(); sum.push(0f64); for i in (0..n).rev() { sum[i] += sum[i + 1]; } /* let inf = 1e14; let mut dp = vec![-inf; n + 1]; dp[n] = 0f64; for _ in 0..k { let mut next = vec![-inf; n + 1]; for i in (0..n).rev() { let mut val = -inf; for j in ((i + 1)..=n).take(m) { val = val.max(dp[j] + (sum[i] - sum[j]).abs()); } next[i] = val; } dp = next; } println!("{}", dp[0].round() as i64); */ type T = (f64, f64);// f = |x - a| + b let eval = |f: &T, x: f64| -> f64 { f.1 + (f.0 - x).abs() }; let merge = |a: &T, b: &T| -> T { let mut a = *a; let mut b = *b; if a.1 < b.1 { std::mem::swap(&mut a, &mut b); } if a.1 > eval(&b, a.0) { return a; } if a.0 > b.0 { std::mem::swap(&mut a, &mut b); } let x = (a.0 - a.1 + b.0 + b.1) * 0.5; assert!((eval(&b, x) - eval(&a, x)).abs() < 2f64); (x, eval(&a, x)) }; let mut deq = FoldableDeque::new(merge); let inf = 1e14; let mut dp = vec![-inf; n + 1]; dp[n] = 0f64; for _it in 0..k { let mut next = vec![-inf; n + 1]; deq.clear(); deq.push_front((sum[n], dp[n])); for i in (0..n).rev() { let v = eval(&deq.find().unwrap(), sum[i]); next[i] = v; deq.push_front((sum[i], dp[i])); if deq.len() > m { deq.pop_back(); } } dp = next; } let ans = dp[0].round() as i64; println!("{}", ans); } fn main() { run(); }