2021/04/06

atcoder.jp

Project Selection Problem なのだけど、そこへの帰着が初心者には難しい。慣れている人には自明かもしれない。

use crate::dinitz::Dinitz;
const INF: i64 = 1 << 60;

const DI: [usize; 4] = [0, 0, 1, !0];
const DJ: [usize; 4] = [1, !0, 0, 0];

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 mut board: Vec<Vec<char>> = (0..n).map(|_| sc.chars()).collect();
    for i in 0..n {
        for j in 0..n {
            board[i][j] = if (i + j) % 2 == 0 {
                match board[i][j] {
                    'B' => 'W',
                    'W' => 'B',
                    '?' => '?',
                    _ => unreachable!(),
                }
            } else {
                board[i][j]
            };
        }
    }

    let mut graph = Dinitz::new(n * n + 2);
    let black = n * n;
    let white = black + 1;
    for i in 0..n {
        for j in 0..n {
            let v = i * n + j;
            match board[i][j] {
                'B' => {
                    graph.add_edge(black, v, 0);
                    graph.add_edge(v, white, INF);
                }
                'W' => {
                    graph.add_edge(black, v, INF);
                    graph.add_edge(v, white, 0);
                }
                '?' => {
                    graph.add_edge(black, v, 0);
                    graph.add_edge(v, white, 0);
                }
                _ => unreachable!(),
            }

            for d in 0..4 {
                let ni = i.wrapping_add(DI[d]);
                let nj = j.wrapping_add(DJ[d]);
                if ni >= n || nj >= n {
                    continue;
                }

                let next = ni * n + nj;
                graph.add_edge(v, next, 1);
            }
        }
    }

    let penalty = graph.max_flow(black, white);
    let ans = n * (n - 1) * 2 - penalty as usize;
    println!("{}", ans);
}
pub mod dinitz {
    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, std::i64::MAX, &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()
    }
}