2021/04/06
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() } }