#725095 (Rust) No.409 ダイエット

• 問題: No.409 ダイエット
• ユーザー: ngtkana
• 提出日時: 2021-12-19 14:17:02
• 言語: Rust (1.77.0 + proconio)
• 結果: AC
• 実行時間: 409 ms / 2,000 ms
• コード長: 18,185 bytes
• コンパイル時間: 14,265 ms
• コンパイル使用メモリ: 388,748 KB
• 実行使用メモリ: 29,744 KB
• 最終ジャッジ日時: 2024-09-15 14:32:21
• 合計ジャッジ時間: 27,435 ms
• ジャッジサーバーID （参考情報）: judge6 / judge5

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	1 ms; 5,248 KB
testcase_02	AC	1 ms; 5,248 KB
testcase_03	AC	1 ms; 5,376 KB
testcase_04	AC	1 ms; 5,376 KB
testcase_05	AC	1 ms; 5,376 KB
testcase_06	AC	1 ms; 5,376 KB
testcase_07	AC	1 ms; 5,376 KB
testcase_08	AC	1 ms; 5,376 KB
testcase_09	AC	1 ms; 5,376 KB
testcase_10	AC	1 ms; 5,376 KB
testcase_11	AC	1 ms; 5,376 KB
testcase_12	AC	1 ms; 5,376 KB
testcase_13	AC	1 ms; 5,376 KB
testcase_14	AC	1 ms; 5,376 KB
testcase_15	AC	1 ms; 5,376 KB
testcase_16	AC	1 ms; 5,376 KB
testcase_17	AC	1 ms; 5,376 KB
testcase_18	AC	1 ms; 5,376 KB
testcase_19	AC	1 ms; 5,376 KB
testcase_20	AC	1 ms; 5,376 KB
testcase_21	AC	1 ms; 5,376 KB
testcase_22	AC	1 ms; 5,376 KB
testcase_23	AC	1 ms; 5,376 KB
testcase_24	AC	1 ms; 5,376 KB
testcase_25	AC	1 ms; 5,376 KB
testcase_26	AC	1 ms; 5,376 KB
testcase_27	AC	1 ms; 5,376 KB
testcase_28	AC	1 ms; 5,376 KB
testcase_29	AC	1 ms; 5,376 KB
testcase_30	AC	1 ms; 5,376 KB
testcase_31	AC	1 ms; 5,376 KB
testcase_32	AC	1 ms; 5,376 KB
testcase_33	AC	1 ms; 5,376 KB
testcase_34	AC	1 ms; 5,376 KB
testcase_35	AC	3 ms; 5,376 KB
testcase_36	AC	4 ms; 5,376 KB
testcase_37	AC	4 ms; 5,376 KB
testcase_38	AC	4 ms; 5,376 KB
testcase_39	AC	4 ms; 5,376 KB
testcase_40	AC	4 ms; 5,376 KB
testcase_41	AC	4 ms; 5,376 KB
testcase_42	AC	4 ms; 5,376 KB
testcase_43	AC	4 ms; 5,376 KB
testcase_44	AC	3 ms; 5,376 KB
testcase_45	AC	4 ms; 5,376 KB
testcase_46	AC	4 ms; 5,376 KB
testcase_47	AC	4 ms; 5,376 KB
testcase_48	AC	4 ms; 5,376 KB
testcase_49	AC	4 ms; 5,376 KB
testcase_50	AC	4 ms; 5,376 KB
testcase_51	AC	4 ms; 5,376 KB
testcase_52	AC	4 ms; 5,376 KB
testcase_53	AC	4 ms; 5,376 KB
testcase_54	AC	4 ms; 5,376 KB
testcase_55	AC	191 ms; 15,128 KB
testcase_56	AC	43 ms; 19,360 KB
testcase_57	AC	405 ms; 29,744 KB
testcase_58	AC	162 ms; 13,620 KB
testcase_59	AC	253 ms; 16,480 KB
testcase_60	AC	146 ms; 12,296 KB
testcase_61	AC	354 ms; 26,392 KB
testcase_62	AC	370 ms; 27,944 KB
testcase_63	AC	356 ms; 24,908 KB
testcase_64	AC	184 ms; 13,688 KB
testcase_65	AC	380 ms; 20,928 KB
testcase_66	AC	409 ms; 28,248 KB
testcase_67	AC	296 ms; 22,552 KB
testcase_68	AC	244 ms; 16,556 KB
testcase_69	AC	353 ms; 24,128 KB
testcase_70	AC	328 ms; 23,792 KB
testcase_71	AC	175 ms; 14,268 KB
testcase_72	AC	403 ms; 29,328 KB
testcase_73	AC	384 ms; 23,404 KB
testcase_74	AC	222 ms; 17,664 KB
testcase_75	AC	386 ms; 25,380 KB
testcase_76	AC	259 ms; 20,076 KB
testcase_77	AC	179 ms; 12,012 KB
testcase_78	AC	190 ms; 15,728 KB
testcase_79	AC	157 ms; 12,560 KB
testcase_80	AC	376 ms; 27,672 KB
testcase_81	AC	384 ms; 24,344 KB
testcase_82	AC	268 ms; 20,288 KB
testcase_83	AC	295 ms; 21,380 KB
testcase_84	AC	244 ms; 15,164 KB
testcase_85	AC	24 ms; 5,376 KB
testcase_86	AC	235 ms; 15,680 KB
testcase_87	AC	327 ms; 24,212 KB
testcase_88	AC	132 ms; 10,000 KB
testcase_89	AC	270 ms; 14,296 KB
testcase_90	AC	121 ms; 7,520 KB
testcase_91	AC	290 ms; 14,896 KB

コンパイルメッセージ

warning: unused imports: `Leaf`, `Tuple`, `VecLen`
   --> src/main.rs:278:27
    |
278 |             multi_token::{Leaf, Parser, ParserTuple, RawTuple, Tuple, VecLen},
    |                           ^^^^                                 ^^^^^  ^^^^^^
    |
    = note: `#[warn(unused_imports)]` on by default

warning: unused import: `with_str`
   --> src/main.rs:516:35
    |
516 |     pub use self::i::{with_stdin, with_str};
    |                                   ^^^^^^^^

warning: unused imports: `ParserTuple`, `Parser`, `RawTuple`, `Token`, `Usize1`
   --> src/main.rs:518:28
    |
518 |         pub use super::i::{Parser, ParserTuple, RawTuple, Token, Usize1};
    |                            ^^^^^^  ^^^^^^^^^^^  ^^^^^^^^  ^^^^^  ^^^^^^

ソースコード

use cht_integer::ConvexHullTrick;
#[allow(unused_imports)]
#[cfg(feature = "dbg")]
use dbg::lg;
use ngtio::with_stdin;
use std::iter::once;

use crate::cht_integer::Concave;

fn main() {
    let mut buf = 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.insert(0, 2 * w);
    for (i, d) in once(0).chain(d.iter().copied()).enumerate() {
        let x0 = i as i64;
        let y0 = (cht.eval(x0) + b * x0 * x0) / 2 + d;
        let tilt = -2 * a + (-2 * x0 - 1) * b;
        let intercept = 2 * y0 + 2 * (x0 + 1) * a + b * x0 * (x0 + 1);
        cht.insert(tilt, intercept);
    }
    let end = n as i64 + 1;
    let ans = (cht.eval(end) + b * end * end) / 2;
    println!("{}", ans);
}

// cht_integer {{{
#[allow(dead_code)]
mod cht_integer {
    use std::{
        borrow::Borrow,
        collections::BTreeSet,
        fmt::Debug,
        i64::{MAX, MIN},
        marker::PhantomData,
    };
    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,
        __marker: PhantomData<fn(C) -> C>,
    }
    impl ConvexHullTrick<Convex> {
        pub fn new() -> Self {
            Self {
                base: Default::default(),
                __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)
        }
        pub fn lave(&self, p: i64) -> Option<i64> {
            self.base.lave(p)
        }
        pub fn insert(&mut self, tilt: i64, intercept: i64) -> bool {
            self.base.insert(tilt, intercept)
        }
    }
    impl ConvexHullTrick<Concave> {
        pub fn new() -> Self {
            Self {
                base: Default::default(),
                __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)
        }
        pub fn lave(&self, p: i64) -> Option<i64> {
            assert_ne!(p, MIN);
            self.base.lave(-p).map(|q| -q)
        }
        pub fn insert(&mut self, tilt: i64, intercept: i64) -> bool {
            assert_ne!(tilt, MIN);
            assert_ne!(intercept, MIN);
            self.base.insert(-tilt, -intercept)
        }
    }
    #[derive(Clone, Debug, Default, Hash, PartialEq)]
    pub struct ConvexHullTrickBase {
        set: BTreeSet<Segment>,
    }
    impl ConvexHullTrickBase {
        pub fn new() -> Self {
            Self::default()
        }
        pub 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)
        }
        pub 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) -> bool {
            let q = -intercept;
            let p = tilt;
            if !self.set.is_empty() && self.lave(p).map_or(false, |c| c <= q) {
                return false;
            }
            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 });
            }
            true
        }
    }
    #[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
        }
    }
}
// }}}
// ngtio {{{
#[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};
    }
}
// }}}
// template {{{
#[cfg(not(feature = "dbg"))]
#[allow(unused_macros)]
#[macro_export]
macro_rules! lg {
    ($($expr:expr),*) => {};
}
// }}}