2021/11/16

ABC155E - Payment

atcoder.jp

桁DPは前の桁から、という思い込みがあって全然見えなかった…頭が固い……

const INF: usize = 1 << 60;
fn main() {
    let (r, w) = (std::io::stdin(), std::io::stdout());
    let mut sc = IO::new(r.lock(), w.lock());

    let n: Vec<usize> = sc
        .read::<String>()
        .bytes()
        .map(|b| b as usize - b'0' as usize)
        .collect();

    let mut dp = vec![0, INF];
    for d in n.into_iter().rev() {
        let mut next = vec![INF; 2];
        for carry in 0..2 {
            let pay = carry + d;
            if pay < 10 {
                next[0] = next[0].min(dp[carry] + pay);
            }
            next[1] = next[1].min(dp[carry] + 10 - pay);
        }
        dp = next;
    }

    let ans = dp[0].min(dp[1] + 1);
    println!("{}", ans);
}

pub struct IO<R, W: std::io::Write>(R, std::io::BufWriter<W>);

impl<R: std::io::Read, W: std::io::Write> IO<R, W> {
    pub fn new(r: R, w: W) -> IO<R, W> {
        IO(r, std::io::BufWriter::new(w))
    }
    pub fn write<S: ToString>(&mut self, s: S) {
        use std::io::Write;
        self.1.write_all(s.to_string().as_bytes()).unwrap();
    }
    pub fn read<T: std::str::FromStr>(&mut self) -> T {
        use std::io::Read;
        let buf = self
            .0
            .by_ref()
            .bytes()
            .map(|b| b.unwrap())
            .skip_while(|&b| b == b' ' || b == b'\n' || b == b'\r' || b == b'\t')
            .take_while(|&b| b != b' ' && b != b'\n' && b != b'\r' && b != b'\t')
            .collect::<Vec<_>>();
        unsafe { std::str::from_utf8_unchecked(&buf) }
            .parse()
            .ok()
            .expect("Parse error.")
    }
    pub fn usize0(&mut self) -> usize {
        self.read::<usize>() - 1
    }
    pub fn vec<T: std::str::FromStr>(&mut self, n: usize) -> Vec<T> {
        (0..n).map(|_| self.read()).collect()
    }
    pub fn chars(&mut self) -> Vec<char> {
        self.read::<String>().chars().collect()
    }
}

AGC037D - Sorting a Grid

atcoder.jp

各列ごとに順番にマッチングをしていくと終盤で詰んでしまわないか?というところから先に進まなかった。具体的に詰むような終盤の状態を構築しようとするとできないことはすぐに分かるので、具体例を考えてみるべきだった。

use crate::dinitz::Dinitz;

fn main() {
    let (r, w) = (std::io::stdin(), std::io::stdout());
    let mut sc = IO::new(r.lock(), w.lock());

    let n: usize = sc.read();
    let m: usize = sc.read();
    let mut a: Vec<Vec<usize>> = vec![vec![0; m]; n];
    for i in 0..n {
        for j in 0..m {
            a[i][j] = sc.usize0();
        }
    }

    let mut used = vec![vec![false; m]; n];
    let mut edge_id = vec![vec![0; m]; n];
    let mut columns = vec![];
    for _ in 0..m {
        let mut graph = Dinitz::new(2 * n + 2);
        let source = 2 * n;
        let sink = 2 * n + 1;
        for i in 0..n {
            graph.add_edge(source, i, 1);
            graph.add_edge(i + n, sink, 1);
        }

        for i in 0..n {
            for j in 0..m {
                if used[i][j] {
                    continue;
                }

                let target_row = a[i][j] / m;
                edge_id[i][j] = graph.g[i].len();
                graph.add_edge(i, target_row + n, 1);
            }
        }

        let flow = graph.max_flow(source, sink);
        assert_eq!(flow as usize, n);

        let mut column = vec![];
        for i in 0..n {
            for j in 0..m {
                if used[i][j] {
                    continue;
                }

                let ej = edge_id[i][j];
                if graph.g[i][ej].cap == 0 {
                    used[i][j] = true;
                    column.push(a[i][j]);
                }
            }
        }

        assert_eq!(column.len(), n);
        columns.push(column);
    }

    for i in 0..n {
        for j in 0..m {
            if j > 0 {
                sc.write(' ');
            }
            sc.write(columns[j][i] + 1);
        }
        sc.write('\n');
    }

    for column in columns.iter_mut() {
        column.sort();
    }
    for i in 0..n {
        for j in 0..m {
            if j > 0 {
                sc.write(' ');
            }
            sc.write(columns[j][i] + 1);
        }
        sc.write('\n');
    }
}
pub mod dinitz {
    const INF: i64 = 1 << 60;
    pub struct Edge {
        pub to: usize,
        pub rev: usize,
        pub is_reversed: bool,
        pub cap: i64,
    }

    pub struct Dinitz {
        pub g: Vec<Vec<Edge>>,
    }

    impl Dinitz {
        pub fn new(v: usize) -> Dinitz {
            let mut g: Vec<Vec<Edge>> = Vec::new();
            for _ in 0..v {
                g.push(Vec::new());
            }
            Dinitz { g }
        }

        pub fn add_edge(&mut self, from: usize, to: usize, cap: i64) {
            let to_len = self.g[to].len();
            let from_len = self.g[from].len();
            self.g[from].push(Edge {
                to,
                rev: to_len,
                is_reversed: false,
                cap,
            });
            self.g[to].push(Edge {
                to: from,
                rev: from_len,
                is_reversed: true,
                cap: 0,
            });
        }

        fn dfs(
            &mut self,
            v: usize,
            sink: usize,
            flow: i64,
            level: &[i32],
            iter: &mut [usize],
        ) -> i64 {
            if v == sink {
                return flow;
            }
            while iter[v] < self.g[v].len() {
                let flow = std::cmp::min(flow, self.g[v][iter[v]].cap);
                let to = self.g[v][iter[v]].to;
                if flow > 0 && level[v] < level[to] {
                    let flowed = self.dfs(to, sink, flow, level, iter);
                    if flowed > 0 {
                        let rev = self.g[v][iter[v]].rev;
                        self.g[v][iter[v]].cap -= flowed;
                        self.g[to][rev].cap += flowed;
                        return flowed;
                    }
                }
                iter[v] += 1;
            }
            0
        }

        fn bfs(&self, s: usize) -> Vec<i32> {
            let v = self.g.len();
            let mut level = vec![-1; v];
            level[s] = 0;
            let mut deque = std::collections::VecDeque::new();
            deque.push_back(s);
            while let Some(v) = deque.pop_front() {
                for e in self.g[v].iter() {
                    if e.cap > 0 && level[e.to] < 0 {
                        level[e.to] = level[v] + 1;
                        deque.push_back(e.to);
                    }
                }
            }
            level
        }

        pub fn max_flow(&mut self, s: usize, t: usize) -> i64 {
            let v = self.g.len();
            let mut flow: i64 = 0;
            loop {
                let level = self.bfs(s);
                if level[t] < 0 {
                    return flow;
                }
                let mut iter = vec![0; v];
                loop {
                    let f = self.dfs(s, t, INF, &level, &mut iter);
                    if f == 0 {
                        break;
                    }
                    flow += f;
                }
            }
        }
    }
}

pub struct IO<R, W: std::io::Write>(R, std::io::BufWriter<W>);

impl<R: std::io::Read, W: std::io::Write> IO<R, W> {
    pub fn new(r: R, w: W) -> IO<R, W> {
        IO(r, std::io::BufWriter::new(w))
    }
    pub fn write<S: ToString>(&mut self, s: S) {
        use std::io::Write;
        self.1.write_all(s.to_string().as_bytes()).unwrap();
    }
    pub fn read<T: std::str::FromStr>(&mut self) -> T {
        use std::io::Read;
        let buf = self
            .0
            .by_ref()
            .bytes()
            .map(|b| b.unwrap())
            .skip_while(|&b| b == b' ' || b == b'\n' || b == b'\r' || b == b'\t')
            .take_while(|&b| b != b' ' && b != b'\n' && b != b'\r' && b != b'\t')
            .collect::<Vec<_>>();
        unsafe { std::str::from_utf8_unchecked(&buf) }
            .parse()
            .ok()
            .expect("Parse error.")
    }
    pub fn usize0(&mut self) -> usize {
        self.read::<usize>() - 1
    }
    pub fn vec<T: std::str::FromStr>(&mut self, n: usize) -> Vec<T> {
        (0..n).map(|_| self.read()).collect()
    }
    pub fn chars(&mut self) -> Vec<char> {
        self.read::<String>().chars().collect()
    }
}