結果
問題 | No.409 ダイエット |
ユーザー | ngtkana |
提出日時 | 2021-12-21 21:26:33 |
言語 | Rust (1.77.0 + proconio) |
結果 |
AC
|
実行時間 | 399 ms / 2,000 ms |
コード長 | 20,747 bytes |
コンパイル時間 | 15,073 ms |
コンパイル使用メモリ | 379,732 KB |
実行使用メモリ | 29,872 KB |
最終ジャッジ日時 | 2024-09-15 15:38:48 |
合計ジャッジ時間 | 27,417 ms |
ジャッジサーバーID (参考情報) |
judge4 / judge6 |
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テストケース
テストケース表示入力 | 結果 | 実行時間 実行使用メモリ |
---|---|---|
testcase_00 | AC | 1 ms
5,248 KB |
testcase_01 | AC | 2 ms
5,248 KB |
testcase_02 | AC | 2 ms
5,376 KB |
testcase_03 | AC | 2 ms
5,376 KB |
testcase_04 | AC | 2 ms
5,376 KB |
testcase_05 | AC | 2 ms
5,376 KB |
testcase_06 | AC | 2 ms
5,376 KB |
testcase_07 | AC | 2 ms
5,376 KB |
testcase_08 | AC | 2 ms
5,376 KB |
testcase_09 | AC | 2 ms
5,376 KB |
testcase_10 | AC | 2 ms
5,376 KB |
testcase_11 | AC | 1 ms
5,376 KB |
testcase_12 | AC | 2 ms
5,376 KB |
testcase_13 | AC | 2 ms
5,376 KB |
testcase_14 | AC | 2 ms
5,376 KB |
testcase_15 | AC | 2 ms
5,376 KB |
testcase_16 | AC | 2 ms
5,376 KB |
testcase_17 | AC | 2 ms
5,376 KB |
testcase_18 | AC | 2 ms
5,376 KB |
testcase_19 | AC | 2 ms
5,376 KB |
testcase_20 | AC | 2 ms
5,376 KB |
testcase_21 | AC | 2 ms
5,376 KB |
testcase_22 | AC | 1 ms
5,376 KB |
testcase_23 | AC | 1 ms
5,376 KB |
testcase_24 | AC | 2 ms
5,376 KB |
testcase_25 | AC | 2 ms
5,376 KB |
testcase_26 | AC | 2 ms
5,376 KB |
testcase_27 | AC | 1 ms
5,376 KB |
testcase_28 | AC | 2 ms
5,376 KB |
testcase_29 | AC | 2 ms
5,376 KB |
testcase_30 | AC | 2 ms
5,376 KB |
testcase_31 | AC | 2 ms
5,376 KB |
testcase_32 | AC | 2 ms
5,376 KB |
testcase_33 | AC | 2 ms
5,376 KB |
testcase_34 | AC | 1 ms
5,376 KB |
testcase_35 | AC | 6 ms
5,376 KB |
testcase_36 | AC | 6 ms
5,376 KB |
testcase_37 | AC | 5 ms
5,376 KB |
testcase_38 | AC | 5 ms
5,376 KB |
testcase_39 | AC | 5 ms
5,376 KB |
testcase_40 | AC | 5 ms
5,376 KB |
testcase_41 | AC | 11 ms
5,376 KB |
testcase_42 | AC | 6 ms
5,376 KB |
testcase_43 | AC | 5 ms
5,376 KB |
testcase_44 | AC | 5 ms
5,376 KB |
testcase_45 | AC | 5 ms
5,376 KB |
testcase_46 | AC | 6 ms
5,376 KB |
testcase_47 | AC | 6 ms
5,376 KB |
testcase_48 | AC | 5 ms
5,376 KB |
testcase_49 | AC | 5 ms
5,376 KB |
testcase_50 | AC | 5 ms
5,376 KB |
testcase_51 | AC | 5 ms
5,376 KB |
testcase_52 | AC | 6 ms
5,376 KB |
testcase_53 | AC | 6 ms
5,376 KB |
testcase_54 | AC | 4 ms
5,376 KB |
testcase_55 | AC | 187 ms
15,128 KB |
testcase_56 | AC | 45 ms
19,332 KB |
testcase_57 | AC | 399 ms
29,872 KB |
testcase_58 | AC | 160 ms
13,620 KB |
testcase_59 | AC | 247 ms
16,736 KB |
testcase_60 | AC | 143 ms
12,304 KB |
testcase_61 | AC | 351 ms
26,444 KB |
testcase_62 | AC | 360 ms
27,948 KB |
testcase_63 | AC | 349 ms
24,764 KB |
testcase_64 | AC | 181 ms
13,820 KB |
testcase_65 | AC | 373 ms
21,184 KB |
testcase_66 | AC | 398 ms
28,248 KB |
testcase_67 | AC | 289 ms
22,548 KB |
testcase_68 | AC | 241 ms
16,556 KB |
testcase_69 | AC | 345 ms
24,256 KB |
testcase_70 | AC | 321 ms
23,788 KB |
testcase_71 | AC | 171 ms
14,396 KB |
testcase_72 | AC | 393 ms
29,332 KB |
testcase_73 | AC | 378 ms
23,404 KB |
testcase_74 | AC | 218 ms
17,536 KB |
testcase_75 | AC | 380 ms
25,252 KB |
testcase_76 | AC | 252 ms
20,208 KB |
testcase_77 | AC | 174 ms
11,880 KB |
testcase_78 | AC | 186 ms
15,852 KB |
testcase_79 | AC | 153 ms
12,560 KB |
testcase_80 | AC | 369 ms
27,676 KB |
testcase_81 | AC | 376 ms
24,344 KB |
testcase_82 | AC | 263 ms
20,412 KB |
testcase_83 | AC | 291 ms
21,252 KB |
testcase_84 | AC | 238 ms
15,288 KB |
testcase_85 | AC | 23 ms
5,376 KB |
testcase_86 | AC | 231 ms
15,676 KB |
testcase_87 | AC | 318 ms
24,208 KB |
testcase_88 | AC | 128 ms
9,864 KB |
testcase_89 | AC | 264 ms
14,296 KB |
testcase_90 | AC | 118 ms
7,516 KB |
testcase_91 | AC | 284 ms
15,020 KB |
コンパイルメッセージ
warning: unused imports: `Leaf`, `Tuple`, `VecLen` --> src/main.rs:360:27 | 360 | multi_token::{Leaf, Parser, ParserTuple, RawTuple, Tuple, VecLen}, | ^^^^ ^^^^^ ^^^^^^ | = note: `#[warn(unused_imports)]` on by default warning: unused import: `with_str` --> src/main.rs:598:35 | 598 | pub use self::i::{with_stdin, with_str}; | ^^^^^^^^ warning: unused imports: `ParserTuple`, `Parser`, `RawTuple`, `Token`, `Usize1` --> src/main.rs:600:28 | 600 | pub use super::i::{Parser, ParserTuple, RawTuple, Token, Usize1}; | ^^^^^^ ^^^^^^^^^^^ ^^^^^^^^ ^^^^^ ^^^^^^
ソースコード
use cht_integer::{Concave, ConvexHullTrick, X}; #[allow(unused_imports)] #[cfg(feature = "dbg")] use dbg::lg; use crate::cht_integer::Quadratic; fn main() { let mut buf = ngtio::with_stdin(); let n = buf.usize(); let a = buf.i64(); let b = buf.i64(); let w = buf.i64(); let d = buf.vec::<i64>(n); let mut cht = ConvexHullTrick::<Concave>::new(); cht.add(2 * Quadratic::from(w) - 2 * a * X + b * X * (X + 1)); for (i, &d) in d.iter().enumerate() { let i = i as i64; let value = cht.eval(i) + 2 * d; cht.add(value - 2 * a * (X - i - 1) + b * (X - 1 - i) * (X - i)); } let ans = cht.eval(n as i64) / 2; println!("{}", ans); } // cht_integer {{{ #[allow(dead_code)] mod cht_integer { use std::{ borrow::Borrow, collections::BTreeSet, fmt::Debug, i64::{MAX, MIN}, marker::PhantomData, ops::{Add, Mul, Sub}, }; pub trait ConvexOrConcave {} pub enum Convex {} pub enum Concave {} impl ConvexOrConcave for Convex {} impl ConvexOrConcave for Concave {} #[derive(Clone, Debug, Default, Hash, PartialEq)] pub struct ConvexHullTrick<C: ConvexOrConcave> { base: ConvexHullTrickBase, coeff_at_two: i64, __marker: PhantomData<fn(C) -> C>, } impl ConvexHullTrick<Convex> { pub fn new() -> Self { Self { base: Default::default(), coeff_at_two: 0, __marker: PhantomData, } } pub fn multieval(&self, xs: impl Iterator<Item = i64>) -> Vec<i64> { xs.map(|x| self.eval(x)).collect() } pub fn collect_lines(&self) -> Vec<(i64, i64)> { self.base .set .iter() .map(|&seg| (seg.line.p, -seg.line.q)) .collect() } pub fn eval(&self, x: i64) -> i64 { self.base.eval(x) + self.coeff_at_two * x * x } pub fn add(&mut self, quadratic: Quadratic) { let Quadratic([zeroth, first, second]) = quadratic; if self.base.set.is_empty() { self.coeff_at_two = second; } else { assert_eq!( self.coeff_at_two, second, "added a expression with different `second` from the before.", ) } self.base.insert(first, zeroth) } } impl ConvexHullTrick<Concave> { pub fn new() -> Self { Self { base: Default::default(), coeff_at_two: 0, __marker: PhantomData, } } pub fn multieval(&self, xs: impl Iterator<Item = i64>) -> Vec<i64> { xs.map(|x| self.eval(x)).collect() } pub fn collect_lines(&self) -> Vec<(i64, i64)> { self.base .set .iter() .map(|&seg| (-seg.line.p, seg.line.q)) .collect() } pub fn eval(&self, x: i64) -> i64 { -self.base.eval(x) + self.coeff_at_two * x * x } pub fn add(&mut self, quadratic: Quadratic) { let Quadratic([zeroth, first, second]) = quadratic; if self.base.set.is_empty() { self.coeff_at_two = second; } else { assert_eq!( self.coeff_at_two, second, "added a expression with different `second` from the before.", ) } self.base.insert(-first, -zeroth) } } #[derive(Clone, Debug, Default, Hash, PartialEq)] struct ConvexHullTrickBase { set: BTreeSet<Segment>, } impl ConvexHullTrickBase { fn eval(&self, x: i64) -> i64 { assert!( !self.set.is_empty(), "empty maximum is the negative infinity" ); self.set.range(Max(x)..).next().unwrap().line.eval(x) } fn lave(&self, p: i64) -> Option<i64> { assert!( !self.set.is_empty(), "empty maximum is the negative infinity" ); let &Segment { line: Line { p: p1, q: q1 }, min: Min(min), max: _, } = self.set.range(p..).next()?; if min == MIN { if p1 == p { Some(q1) } else { None } } else { Some(q1 - (p1 - p) * min) } } pub fn insert(&mut self, tilt: i64, intercept: i64) { let q = -intercept; let p = tilt; if !self.set.is_empty() && self.lave(p).map_or(false, |c| c <= q) { return; } self.set.take(&p); let line = Line { p, q }; while let Some(&seg1) = self.set.range(..p).next_back() { if seg1.min.0 == MIN || line.eval(seg1.min.0) < seg1.line.eval(seg1.min.0) { break; } self.set.remove(&seg1); } while let Some(&seg1) = self.set.range(p..).next() { if seg1.max.0 == MAX || line.eval(seg1.max.0) < seg1.line.eval(seg1.max.0) { break; } self.set.remove(&seg1); } if let Some(&seg1) = self.set.range(..p).next_back() { self.set.remove(&seg1); match seg1.line.brace(line) { Err(x) => { debug_assert!(seg1.min.0 < x); self.set.insert(Segment { max: Max(x), ..seg1 }); } Ok(brace) => { if seg1.min.0 < brace.min.0 { self.set.insert(Segment { max: Max(brace.min.0), ..seg1 }); } self.set.insert(brace); } } } if let Some(&seg1) = self.set.range(p..).next() { self.set.remove(&seg1); match line.brace(seg1.line) { Err(x) => { debug_assert!(x < seg1.max.0); self.set.insert(Segment { min: Min(x), ..seg1 }); } Ok(brace) => { if brace.max.0 < seg1.max.0 { self.set.insert(Segment { min: Min(brace.max.0), ..seg1 }); } self.set.insert(brace); } } } let min = Min(self .set .range(..p) .next_back() .map_or(MIN, |seg1| seg1.max.0)); let max = Max(self.set.range(p..).next().map_or(MAX, |seg1| seg1.min.0)); if min.0 < max.0 { self.set.insert(Segment { line, min, max }); } } } pub const X: Quadratic = Quadratic([0, 1, 0]); #[derive(Clone, Debug, Default, Hash, PartialEq, Copy)] pub struct Quadratic([i64; 3]); impl Quadratic { pub fn eval(self, x: i64) -> i64 { self.0[0] + (self.0[1] + self.0[2] * x) * x } } impl From<i64> for Quadratic { fn from(x: i64) -> Self { Self([x, 0, 0]) } } impl<T: Into<Self>> Add<T> for Quadratic { type Output = Self; fn add(self, rhs: T) -> Self::Output { let rhs = rhs.into(); Self([ self.0[0] + rhs.0[0], self.0[1] + rhs.0[1], self.0[2] + rhs.0[2], ]) } } impl Add<Quadratic> for i64 { type Output = Quadratic; fn add(self, rhs: Quadratic) -> Self::Output { rhs.add(self) } } impl<T: Into<Self>> Sub<T> for Quadratic { type Output = Self; fn sub(self, rhs: T) -> Self::Output { let rhs = rhs.into(); Self([ self.0[0] - rhs.0[0], self.0[1] - rhs.0[1], self.0[2] - rhs.0[2], ]) } } impl Sub<Quadratic> for i64 { type Output = Quadratic; fn sub(self, rhs: Quadratic) -> Self::Output { let lhs: Quadratic = self.into(); Quadratic([ lhs.0[0] - rhs.0[0], lhs.0[1] - rhs.0[1], lhs.0[2] - rhs.0[2], ]) } } impl<T: Into<Self>> Mul<T> for Quadratic { type Output = Self; fn mul(self, rhs: T) -> Self::Output { let rhs = rhs.into(); assert_eq!(self.0[1] * rhs.0[2] + self.0[2] * rhs.0[1], 0); assert_eq!(self.0[2] * rhs.0[2], 0); Self([ self.0[0] * rhs.0[0], self.0[0] * rhs.0[1] + self.0[1] * rhs.0[0], self.0[0] * rhs.0[2] + self.0[1] * rhs.0[1] + self.0[2] * rhs.0[0], ]) } } impl Mul<Quadratic> for i64 { type Output = Quadratic; fn mul(self, rhs: Quadratic) -> Self::Output { rhs.mul(self) } } #[derive(Clone, Debug, Default, Hash, PartialEq, Eq, PartialOrd, Ord, Copy)] struct Min(i64); #[derive(Clone, Debug, Default, Hash, PartialEq, Eq, PartialOrd, Ord, Copy)] struct Max(i64); #[derive(Clone, Debug, Default, Hash, PartialEq, Eq, PartialOrd, Ord, Copy)] struct Line { p: i64, q: i64, } impl Line { fn eval(&self, x: i64) -> i64 { self.p * x - self.q } fn brace(self, other: Self) -> Result<Segment, i64> { let Self { p: p0, q: q0 } = self; let Self { p: p1, q: q1 } = other; debug_assert!(p0 < p1); let x0 = (q1 - q0).div_euclid(p1 - p0); if x0 * (p1 - p0) == (q1 - q0) { return Err(x0); } let x1 = x0 + 1; let p = (p1 * x1 - p0 * x0) - (q1 - q0); let q = (p1 - p0) * x0 * x1 - q1 * x0 + q0 * x1; debug_assert_eq!(p * x0 - q, p0 * x0 - q0); debug_assert_eq!(p * x1 - q, p1 * x1 - q1); Ok(Segment { line: Self { p, q }, min: Min(x0), max: Max(x1), }) } } #[derive(Clone, Default, Debug, Hash, PartialEq, Eq, PartialOrd, Ord, Copy)] struct Segment { line: Line, min: Min, max: Max, } impl Borrow<i64> for Segment { fn borrow(&self) -> &i64 { &self.line.p } } impl Borrow<Min> for Segment { fn borrow(&self) -> &Min { &self.min } } impl Borrow<Max> for Segment { fn borrow(&self) -> &Max { &self.max } } } // }}} // template {{{ #[cfg(not(feature = "dbg"))] #[allow(unused_macros)] #[macro_export] macro_rules! lg { ($($expr:expr),*) => {}; } #[allow(dead_code)] mod ngtio { mod i { pub use self::{ multi_token::{Leaf, Parser, ParserTuple, RawTuple, Tuple, VecLen}, token::{Token, Usize1}, }; use std::{ io::{self, BufRead}, iter, }; pub fn with_stdin() -> Tokenizer<io::BufReader<io::Stdin>> { io::BufReader::new(io::stdin()).tokenizer() } pub fn with_str(src: &str) -> Tokenizer<&[u8]> { src.as_bytes().tokenizer() } pub struct Tokenizer<S: BufRead> { queue: Vec<String>, // FIXME: String のみにすると速そうです。 scanner: S, } macro_rules! prim_method { ($name:ident: $T:ty) => { pub fn $name(&mut self) -> $T { <$T>::leaf().parse(self) } }; ($name:ident) => { prim_method!($name: $name); }; } macro_rules! prim_methods { ($name:ident: $T:ty; $($rest:tt)*) => { prim_method!($name:$T); prim_methods!($($rest)*); }; ($name:ident; $($rest:tt)*) => { prim_method!($name); prim_methods!($($rest)*); }; () => () } impl<S: BufRead> Tokenizer<S> { pub fn token(&mut self) -> String { self.load(); self.queue.pop().expect("入力が終了したのですが。") } pub fn new(scanner: S) -> Self { Self { queue: Vec::new(), scanner, } } fn load(&mut self) { while self.queue.is_empty() { let mut s = String::new(); let length = self.scanner.read_line(&mut s).unwrap(); // 入力が UTF-8 でないときにエラーだそうです。 if length == 0 { break; } self.queue = s.split_whitespace().rev().map(str::to_owned).collect(); } } pub fn skip_line(&mut self) { assert!( self.queue.is_empty(), "行の途中で呼ばないでいただきたいです。現在のトークンキュー: {:?}", &self.queue ); self.load(); } pub fn end(&mut self) { self.load(); assert!(self.queue.is_empty(), "入力はまだあります!"); } pub fn parse<T: Token>(&mut self) -> T::Output { T::parse(&self.token()) } pub fn parse_collect<T: Token, B>(&mut self, n: usize) -> B where B: iter::FromIterator<T::Output>, { iter::repeat_with(|| self.parse::<T>()).take(n).collect() } pub fn tuple<T: RawTuple>(&mut self) -> <T::LeafTuple as Parser>::Output { T::leaf_tuple().parse(self) } pub fn vec<T: Token>(&mut self, len: usize) -> Vec<T::Output> { T::leaf().vec(len).parse(self) } pub fn vec_tuple<T: RawTuple>( &mut self, len: usize, ) -> Vec<<T::LeafTuple as Parser>::Output> { T::leaf_tuple().vec(len).parse(self) } pub fn vec2<T: Token>(&mut self, height: usize, width: usize) -> Vec<Vec<T::Output>> { T::leaf().vec(width).vec(height).parse(self) } pub fn vec2_tuple<T>( &mut self, height: usize, width: usize, ) -> Vec<Vec<<T::LeafTuple as Parser>::Output>> where T: RawTuple, { T::leaf_tuple().vec(width).vec(height).parse(self) } prim_methods! { u8; u16; u32; u64; u128; usize; i8; i16; i32; i64; i128; isize; f32; f64; char; string: String; } } mod token { use super::multi_token::Leaf; use std::{any, fmt, marker, str}; pub trait Token: Sized { type Output; fn parse(s: &str) -> Self::Output; fn leaf() -> Leaf<Self> { Leaf(marker::PhantomData) } } impl<T> Token for T where T: str::FromStr, <Self as str::FromStr>::Err: fmt::Debug, { type Output = Self; fn parse(s: &str) -> Self::Output { s.parse().unwrap_or_else(|_| { panic!("Parse error!: ({}: {})", s, any::type_name::<Self>(),) }) } } pub struct Usize1 {} impl Token for Usize1 { type Output = usize; fn parse(s: &str) -> Self::Output { usize::parse(s) .checked_sub(1) .expect("Parse error! (Zero substruction error of Usize1)") } } } mod multi_token { use super::{Token, Tokenizer}; use std::{io::BufRead, iter, marker}; pub trait Parser: Sized { type Output; fn parse<S: BufRead>(&self, server: &mut Tokenizer<S>) -> Self::Output; fn vec(self, len: usize) -> VecLen<Self> { VecLen { len, elem: self } } } pub struct Leaf<T>(pub(super) marker::PhantomData<T>); impl<T: Token> Parser for Leaf<T> { type Output = T::Output; fn parse<S: BufRead>(&self, server: &mut Tokenizer<S>) -> T::Output { server.parse::<T>() } } pub struct VecLen<T> { pub len: usize, pub elem: T, } impl<T: Parser> Parser for VecLen<T> { type Output = Vec<T::Output>; fn parse<S: BufRead>(&self, server: &mut Tokenizer<S>) -> Self::Output { iter::repeat_with(|| self.elem.parse(server)) .take(self.len) .collect() } } pub trait RawTuple { type LeafTuple: Parser; fn leaf_tuple() -> Self::LeafTuple; } pub trait ParserTuple { type Tuple: Parser; fn tuple(self) -> Self::Tuple; } pub struct Tuple<T>(pub T); macro_rules! impl_tuple { ($($t:ident: $T:ident),*) => { impl<$($T),*> Parser for Tuple<($($T,)*)> where $($T: Parser,)* { type Output = ($($T::Output,)*); #[allow(unused_variables)] fn parse<S: BufRead >(&self, server: &mut Tokenizer<S>) -> Self::Output { match self { Tuple(($($t,)*)) => { ($($t.parse(server),)*) } } } } impl<$($T: Token),*> RawTuple for ($($T,)*) { type LeafTuple = Tuple<($(Leaf<$T>,)*)>; fn leaf_tuple() -> Self::LeafTuple { Tuple(($($T::leaf(),)*)) } } impl<$($T: Parser),*> ParserTuple for ($($T,)*) { type Tuple = Tuple<($($T,)*)>; fn tuple(self) -> Self::Tuple { Tuple(self) } } }; } impl_tuple!(); impl_tuple!(t1: T1); impl_tuple!(t1: T1, t2: T2); impl_tuple!(t1: T1, t2: T2, t3: T3); impl_tuple!(t1: T1, t2: T2, t3: T3, t4: T4); impl_tuple!(t1: T1, t2: T2, t3: T3, t4: T4, t5: T5); impl_tuple!(t1: T1, t2: T2, t3: T3, t4: T4, t5: T5, t6: T6); impl_tuple!(t1: T1, t2: T2, t3: T3, t4: T4, t5: T5, t6: T6, t7: T7); impl_tuple!( t1: T1, t2: T2, t3: T3, t4: T4, t5: T5, t6: T6, t7: T7, t8: T8 ); } trait Scanner: BufRead + Sized { fn tokenizer(self) -> Tokenizer<Self> { Tokenizer::new(self) } } impl<R: BufRead> Scanner for R {} } pub use self::i::{with_stdin, with_str}; mod prelude { pub use super::i::{Parser, ParserTuple, RawTuple, Token, Usize1}; } } // }}}