#630915 (Rust) No.119 旅行のツアーの問題

• 問題: No.119 旅行のツアーの問題
• ユーザー: nebocco
• 提出日時: 2021-03-17 19:00:59
• 言語: Rust (1.77.0 + proconio)
• 結果: AC
• 実行時間: 1 ms / 5,000 ms
• コード長: 13,894 bytes
• コンパイル時間: 12,926 ms
• コンパイル使用メモリ: 405,872 KB
• 実行使用メモリ: 6,944 KB
• 最終ジャッジ日時: 2024-04-27 11:17:39
• 合計ジャッジ時間: 13,958 ms
• ジャッジサーバーID （参考情報）: judge1 / judge2

入力	結果	実行時間; 実行使用メモリ
testcase_00	AC	1 ms; 6,812 KB
testcase_01	AC	1 ms; 6,940 KB
testcase_02	AC	1 ms; 6,944 KB
testcase_03	AC	1 ms; 6,940 KB
testcase_04	AC	1 ms; 6,944 KB
testcase_05	AC	1 ms; 6,944 KB
testcase_06	AC	1 ms; 6,940 KB
testcase_07	AC	1 ms; 6,940 KB
testcase_08	AC	1 ms; 6,940 KB
testcase_09	AC	1 ms; 6,944 KB
testcase_10	AC	0 ms; 6,940 KB
testcase_11	AC	1 ms; 6,940 KB
testcase_12	AC	0 ms; 6,940 KB
testcase_13	AC	1 ms; 6,940 KB
testcase_14	AC	1 ms; 6,940 KB
testcase_15	AC	1 ms; 6,944 KB
testcase_16	AC	1 ms; 6,944 KB
testcase_17	AC	1 ms; 6,940 KB
testcase_18	AC	1 ms; 6,944 KB
testcase_19	AC	1 ms; 6,940 KB
testcase_20	AC	1 ms; 6,940 KB
testcase_21	AC	1 ms; 6,940 KB
testcase_22	AC	1 ms; 6,940 KB

ソースコード

fn main() {
	let mut io = IO::new();
    input!{ from io,
		n: usize,
		plans: [(i32, i32); n],
		m: usize,
		cl: [(usize, usize); m]
    }
    const INF: i32 = 1_000_000;
    let u = |i| { 2 * i };
    let v = |i| { 2 * i + 1 };
    let source = u(n);
    let sink = v(n);
	let mut ans = 0;
	let mut din = Dinic::new();
	for (i, &(b, c)) in plans.iter().enumerate() {
		ans += b + c;
        din.add_edge(source, u(i), b);
        din.add_edge(u(i), v(i), INF);
        din.add_edge(v(i), sink, c);
	}
	for &(i, j) in &cl {
		din.add_edge(u(i), v(j), INF);
	}
	ans -= din.max_flow(source, sink).0;
    io.println(ans);
}

use std::fmt::Display;

pub trait Cost:
	Element
    + Display
    + Clone
    + Copy
    + Eq
    + Ord
    + Zero
    + One
    + Add<Output = Self>
    + AddAssign
    + Sub<Output = Self>
    + Mul<Output = Self>
    + Neg<Output = Self>
{
    fn is_positive(&self) -> bool {
        self > &Self::zero()
    }
    fn is_negative(&self) -> bool {
        self < &Self::zero()
    }

    const MAX: Self;
}

pub trait Flow: Cost + SubAssign {
    fn abs(&self) -> Self {
        if self.is_negative() {
            -*self
        } else {
            *self
        }
    }
}

macro_rules! impl_flow {
    ($($T:ident,)*) => {
		$(
            impl Flow for $T {}

			impl Cost for $T {
                const MAX: Self = std::$T::MAX;
            }
		)*
    };
}

impl_flow!(
	i8, i16, i32, i64, i128, isize,
);

// ------------ Dinic's algorithm start ------------
use std::cmp::{max, min};

struct Edge<F> {
    dst: usize,
    rev: usize,
    flow: F,
    upper: F,
}

#[derive(Copy, Clone, Ord, PartialOrd, Eq, PartialEq, Debug, Hash)]
pub struct EdgeId(usize, usize);

struct TemporaryData {
    n: usize,
    s: usize,
    t: usize,
    label: Vec<usize>,
    current_edge: Vec<usize>,
    buffer: Vec<usize>,
}
#[derive(Default)]
pub struct Dinic<F: Flow> {
    edges: Vec<Vec<Edge<F>>>,
}
impl<F: Flow> Dinic<F> {
    pub fn new() -> Self {
        Self { edges: Vec::new() }
    }

    pub fn add_edge(&mut self, src: usize, dst: usize, capacity: F) -> EdgeId {
        let n = max(max(src, dst) + 1, self.edges.len());
        self.edges.resize_with(n, || Vec::with_capacity(4));
        let e = self.edges[src].len();
        let re = self.edges[dst].len() + if src == dst { 1 } else { 0 };

        self.edges[src].push(Edge {
            dst,
            rev: re,
            flow: F::zero(),
            upper: capacity,
        });
        self.edges[dst].push(Edge {
            dst: src,
            rev: e,
            flow: capacity,
            upper: capacity,
        });
        EdgeId(src, e)
    }

    fn prepare_data(&mut self, s: usize, t: usize) -> TemporaryData {
        let n = max(max(s, t) + 1, self.edges.len());
        self.edges.resize_with(n, Default::default);
        TemporaryData {
            n,
            s,
            t,
            label: vec![0; n],
            current_edge: vec![0; n],
            buffer: Vec::with_capacity(n),
        }
    }

    fn dual(&self, data: &mut TemporaryData) -> bool {
        let n = data.n;
        data.label.iter_mut().for_each(|v| *v = n);
        data.current_edge.iter_mut().for_each(|v| *v = 0);
        let mut queue = std::mem::take(&mut data.buffer);
        queue.clear();
        queue.push(data.s);
        data.label[data.s] = 0;
        let mut q_pos = 0;
        'new_node: while q_pos < queue.len() {
            let u = queue[q_pos];
            q_pos += 1;
            let next_label = data.label[u] + 1;
            for e in &self.edges[u] {
                if e.flow < e.upper && data.label[e.dst] == data.n {
                    data.label[e.dst] = next_label;
                    if e.dst == data.t {
                        break 'new_node;
                    }
                    queue.push(e.dst);
                }
            }
        }
        data.buffer = queue;
        data.label[data.t] < n
    }

    #[allow(clippy::many_single_char_names)]
    fn primal_dfs(&mut self, u: usize, data: &mut TemporaryData, mut limit: F) -> F {
        if u == data.s {
            return limit;
        }
        let mut total = F::zero();
        let mut i = data.current_edge[u];
        while i < self.edges[u].len() {
            let e = &self.edges[u][i];
            if e.flow.is_positive() && data.label[e.dst] < data.label[u] {
                let new_limit = min(limit, e.flow);
                let v = e.dst;
                let f = self.primal_dfs(v, data, new_limit);
                if !f.is_zero() {
                    let e = &mut self.edges[u][i];
                    let v = e.dst;
                    let r = e.rev;
                    e.flow -= f;
                    self.edges[v][r].flow += f;
                    total += f;
                    limit -= f;
                    if limit.is_zero() {
                        if self.edges[u][i].flow.is_zero() {
                            i += 1;
                        }
                        data.current_edge[u] = i;
                        return total;
                    }
                }
            }
            i += 1;
        }
        data.current_edge[u] = !0;
        data.label[u] = data.n;
        total
    }

    pub fn augment(&mut self, s: usize, t: usize, limit: F) -> F {
        assert_ne!(s, t, "Source and sink vertex should be different");
        let mut data = self.prepare_data(s, t);
        let mut flow = F::zero();
        while self.dual(&mut data) {
            flow += self.primal_dfs(data.t, &mut data, limit - flow);
            if flow == limit {
                break;
            }
        }
        flow
    }

    pub fn max_flow(&mut self, s: usize, t: usize) -> (F, Vec<usize>) {
        assert_ne!(s, t, "Source and sink vertex should be different");
        let mut data = self.prepare_data(s, t);
        let inf = self.edges[s]
            .iter()
            .map(|e| e.upper - e.flow)
            .fold(F::zero(), |a, b| a + b);
        let mut flow = F::zero();
        while self.dual(&mut data) {
            flow += self.primal_dfs(data.t, &mut data, inf);
        }
        let label = std::mem::take(&mut data.label);
        let cut = label
            .into_iter()
            .enumerate()
            .filter(|(_, l)| l < &data.n)
            .map(|(i, _)| i)
            .collect();
        (flow, cut)
    }

    pub fn get_flow(&self, e: &EdgeId) -> F {
        self.edges[e.0][e.1].flow
    }
}

// ------------ Dinic's algorithm start ------------

// ------------ algebraic traits start ------------
use std::marker::Sized;
use std::ops::*;

/// 元
pub trait Element: Sized + Clone + PartialEq {}
impl<T: Sized + Clone + PartialEq> Element for T {}

/// 結合性
pub trait Associative: Magma {}

/// マグマ
pub trait Magma: Element + Add<Output=Self> {}
impl<T: Element + Add<Output=Self>> Magma for T {}

/// 半群
pub trait SemiGroup: Magma + Associative {}
impl<T: Magma + Associative> SemiGroup for T {}

/// モノイド
pub trait Monoid: SemiGroup + Zero {}
impl<T: SemiGroup + Zero> Monoid for T {}

pub trait ComMonoid: Monoid + AddAssign {}
impl<T: Monoid + AddAssign> ComMonoid for T {}

/// 群
pub trait Group: Monoid + Neg<Output=Self> {}
impl<T: Monoid + Neg<Output=Self>> Group for T {}

pub trait ComGroup: Group + ComMonoid {}
impl<T: Group + ComMonoid> ComGroup for T {}

/// 半環
pub trait SemiRing: ComMonoid + Mul<Output=Self> + One {}
impl<T: ComMonoid + Mul<Output=Self> + One> SemiRing for T {}

/// 環
pub trait Ring: ComGroup + SemiRing {}
impl<T: ComGroup + SemiRing> Ring for T {}

pub trait ComRing: Ring + MulAssign {}
impl<T: Ring + MulAssign> ComRing for T {}

/// 体
pub trait Field: ComRing + Div<Output=Self> + DivAssign {}
impl<T: ComRing + Div<Output=Self> + DivAssign> Field for T {}

/// 加法単元
pub trait Zero: Element {
    fn zero() -> Self;
    fn is_zero(&self) -> bool {
        *self == Self::zero()
    }
}

/// 乗法単元
pub trait One: Element {
    fn one() -> Self;
    fn is_one(&self) -> bool {
        *self == Self::one()
    }
}

macro_rules! impl_integer {
    ($($T:ty,)*) => {
        $(
            impl Associative for $T {}

            impl Zero for $T {
                fn zero() -> Self { 0 }
                fn is_zero(&self) -> bool { *self == 0 }
            }

            impl<'a> Zero for &'a $T {
                fn zero() -> Self { &0 }
                fn is_zero(&self) -> bool { *self == &0 }
            }

            impl One for $T {
                fn one() -> Self { 1 }
                fn is_one(&self) -> bool { *self == 1 }
            }

            impl<'a> One for &'a $T {
                fn one() -> Self { &1 }
                fn is_one(&self) -> bool { *self == &1 }
            }
        )*
    };
}

impl_integer! {
    i8, i16, i32, i64, i128, isize,
    u8, u16, u32, u64, u128, usize,
}
// ------------ algebraic traits end ------------



// ------------ io module start ------------
use std::io::{stdout, BufWriter, Read, StdoutLock, Write};

pub struct IO {
	iter: std::str::SplitAsciiWhitespace<'static>,
	buf: BufWriter<StdoutLock<'static>>,
}

impl IO {
	pub fn new() -> Self {
		let mut input = String::new();
		std::io::stdin().read_to_string(&mut input).unwrap();
		let input = Box::leak(input.into_boxed_str());
		let out = Box::new(stdout());
		IO {
			iter: input.split_ascii_whitespace(),
			buf: BufWriter::new(Box::leak(out).lock()),
		}
	}
	fn scan_str(&mut self) -> &'static str {
		self.iter.next().unwrap()
	}
	pub fn scan<T: Scan>(&mut self) -> <T as Scan>::Output {
		<T as Scan>::scan(self)
	}
	pub fn scan_vec<T: Scan>(&mut self, n: usize) -> Vec<<T as Scan>::Output> {
		(0..n).map(|_| self.scan::<T>()).collect()
	}
	pub fn print<T: Print>(&mut self, x: T) {
		<T as Print>::print(self, x);
	}
	pub fn println<T: Print>(&mut self, x: T) {
		self.print(x);
		self.print("\n");
	}
	pub fn iterln<T: Print, I: Iterator<Item = T>>(&mut self, mut iter: I, delim: &str) {
		if let Some(v) = iter.next() {
			self.print(v);
			for v in iter {
				self.print(delim);
				self.print(v);
			}
		}
		self.print("\n");
	}
	pub fn flush(&mut self) {
		self.buf.flush().unwrap();
	}
}

impl Default for IO {
	fn default() -> Self {
		Self::new()
	}
}

pub trait Scan {
	type Output;
	fn scan(io: &mut IO) -> Self::Output;
}

macro_rules! impl_scan {
	($($t:tt),*) => {
		$(
			impl Scan for $t {
				type Output = Self;
				fn scan(s: &mut IO) -> Self::Output {
					s.scan_str().parse().unwrap()
				}
			}
		)*
	};
}

impl_scan!(i16, i32, i64, isize, u16, u32, u64, usize, String, f32, f64);

impl Scan for char {
	type Output = char;
	fn scan(s: &mut IO) -> Self::Output {
		s.scan_str().chars().next().unwrap()
	}
}

pub enum Bytes {}
impl Scan for Bytes {
	type Output = &'static [u8];
	fn scan(s: &mut IO) -> Self::Output {
		s.scan_str().as_bytes()
	}
}

pub enum Chars {}
impl Scan for Chars {
	type Output = Vec<char>;
	fn scan(s: &mut IO) -> Self::Output {
		s.scan_str().chars().collect()
	}
}

pub enum Usize1 {}
impl Scan for Usize1 {
	type Output = usize;
	fn scan(s: &mut IO) -> Self::Output {
		s.scan::<usize>().wrapping_sub(1)
	}
}

impl<T: Scan, U: Scan> Scan for (T, U) {
	type Output = (T::Output, U::Output);
	fn scan(s: &mut IO) -> Self::Output {
		(T::scan(s), U::scan(s))
	}
}

impl<T: Scan, U: Scan, V: Scan> Scan for (T, U, V) {
	type Output = (T::Output, U::Output, V::Output);
	fn scan(s: &mut IO) -> Self::Output {
		(T::scan(s), U::scan(s), V::scan(s))
	}
}

impl<T: Scan, U: Scan, V: Scan, W: Scan> Scan for (T, U, V, W) {
	type Output = (T::Output, U::Output, V::Output, W::Output);
	fn scan(s: &mut IO) -> Self::Output {
		(T::scan(s), U::scan(s), V::scan(s), W::scan(s))
	}
}

pub trait Print {
	fn print(w: &mut IO, x: Self);
}

macro_rules! impl_print_int {
	($($t:ty),*) => {
		$(
			impl Print for $t {
				fn print(w: &mut IO, x: Self) {
					w.buf.write_all(x.to_string().as_bytes()).unwrap();
				}
			}
		)*
	};
}

impl_print_int!(i16, i32, i64, isize, u16, u32, u64, usize, f32, f64);

impl Print for u8 {
	fn print(w: &mut IO, x: Self) {
		w.buf.write_all(&[x]).unwrap();
	}
}

impl Print for &[u8] {
	fn print(w: &mut IO, x: Self) {
		w.buf.write_all(x).unwrap();
	}
}

impl Print for &str {
	fn print(w: &mut IO, x: Self) {
		w.print(x.as_bytes());
	}
}

impl Print for String {
	fn print(w: &mut IO, x: Self) {
		w.print(x.as_bytes());
	}
}

impl<T: Print, U: Print> Print for (T, U) {
	fn print(w: &mut IO, (x, y): Self) {
		w.print(x);
		w.print(" ");
		w.print(y);
	}
}

impl<T: Print, U: Print, V: Print> Print for (T, U, V) {
	fn print(w: &mut IO, (x, y, z): Self) {
		w.print(x);
		w.print(" ");
		w.print(y);
		w.print(" ");
		w.print(z);
	}
}

mod neboccoio_macro {
	#[macro_export]
	macro_rules! input {
		(@start $io:tt @read @rest) => {};

		(@start $io:tt @read @rest, $($rest: tt)*) => {
			input!(@start $io @read @rest $($rest)*)
		};

		(@start $io:tt @read @rest mut $($rest:tt)*) => {
			input!(@start $io @read @mut [mut] @rest $($rest)*)
		};

		(@start $io:tt @read @rest $($rest:tt)*) => {
			input!(@start $io @read @mut [] @rest $($rest)*)
		};

		(@start $io:tt @read @mut [$($mut:tt)?] @rest $var:tt: [[$kind:tt; $len1:expr]; $len2:expr] $($rest:tt)*) => {
			let $($mut)* $var = (0..$len2).map(|_| $io.scan_vec::<$kind>($len1)).collect::<Vec<Vec<$kind>>>();
			input!(@start $io @read @rest $($rest)*)
		};

		(@start $io:tt @read @mut [$($mut:tt)?] @rest $var:tt: [$kind:tt; $len:expr] $($rest:tt)*) => {
			let $($mut)* $var = $io.scan_vec::<$kind>($len);
			input!(@start $io @read @rest $($rest)*)
		};

		(@start $io:tt @read @mut [$($mut:tt)?] @rest $var:tt: $kind:tt $($rest:tt)*) => {
			let $($mut)* $var = $io.scan::<$kind>();
			input!(@start $io @read @rest $($rest)*)
		};

		(from $io:tt $($rest:tt)*) => {
			input!(@start $io @read @rest $($rest)*)
		};
	}
}

// ------------ io module end ------------