#[allow(unused_imports)] use std::cmp::*; #[allow(unused_imports)] use std::collections::*; // https://qiita.com/tanakh/items/0ba42c7ca36cd29d0ac8 macro_rules! input { ($($r:tt)*) => { let stdin = std::io::stdin(); let mut bytes = std::io::Read::bytes(std::io::BufReader::new(stdin.lock())); let mut next = move || -> String{ bytes.by_ref().map(|r|r.unwrap() as char) .skip_while(|c|c.is_whitespace()) .take_while(|c|!c.is_whitespace()) .collect() }; input_inner!{next, $($r)*} }; } macro_rules! input_inner { ($next:expr) => {}; ($next:expr,) => {}; ($next:expr, $var:ident : $t:tt $($r:tt)*) => { let $var = read_value!($next, $t); input_inner!{$next $($r)*} }; } macro_rules! read_value { ($next:expr, ( $($t:tt),* )) => { ($(read_value!($next, $t)),*) }; ($next:expr, [ $t:tt ; $len:expr ]) => { (0..$len).map(|_| read_value!($next, $t)).collect::>() }; ($next:expr, $t:ty) => ($next().parse::<$t>().expect("Parse error")); } /** * Dinic's algorithm for maximum flow problem. * Verified by: yukicoder No.177 (http://yukicoder.me/submissions/148371) * Min-cut (the second element of max_flow's returned values) is not verified. */ #[derive(Clone)] struct Edge { to: usize, cap: T, rev: usize, // rev is the position of the reverse edge in graph[to] } struct Dinic { graph: Vec>>, iter: Vec, zero: T, } impl Dinic where T: Clone, T: Copy, T: Ord, T: std::ops::AddAssign, T: std::ops::SubAssign, { fn bfs(&self, s: usize, level: &mut [Option]) { let n = level.len(); for i in 0 .. n { level[i] = None; } let mut que = std::collections::VecDeque::new(); level[s] = Some(0); que.push_back(s); while let Some(v) = que.pop_front() { for e in self.graph[v].iter() { if e.cap > self.zero && level[e.to] == None { level[e.to] = Some(level[v].unwrap() + 1); que.push_back(e.to); } } } } /* search augment path by dfs. * if f == None, f is treated as infinity. */ fn dfs(&mut self, v: usize, t: usize, f: Option, level: &mut [Option]) -> T { if v == t { return f.unwrap(); } while self.iter[v] < self.graph[v].len() { let i = self.iter[v]; let e = self.graph[v][i].clone(); if e.cap > self.zero && level[v] < level[e.to] { let newf = std::cmp::min(f.unwrap_or(e.cap), e.cap); let d = self.dfs(e.to, t, Some(newf), level); if d > self.zero { self.graph[v][i].cap -= d; self.graph[e.to][e.rev].cap += d; return d; } } self.iter[v] += 1; } self.zero } pub fn new(n: usize, zero: T) -> Self { Dinic { graph: vec![Vec::new(); n], iter: vec![0; n], zero: zero, } } pub fn add_edge(&mut self, from: usize, to: usize, cap: T) { let added_from = Edge { to: to, cap: cap, rev: self.graph[to].len() }; let added_to = Edge { to: from, cap: self.zero, rev: self.graph[from].len() }; self.graph[from].push(added_from); self.graph[to].push(added_to); } pub fn max_flow(&mut self, s: usize, t: usize) -> (T, Vec) { let mut flow = self.zero; let n = self.graph.len(); let mut level = vec![None; n]; loop { self.bfs(s, &mut level); if level[t] == None { let ret = (0 .. n).filter(|&i| level[i] == None) .collect(); return (flow, ret); } self.iter.clear(); self.iter.resize(n, 0); loop { let f = self.dfs(s, t, None, &mut level); if f <= self.zero { break; } flow += f; } } } } // Submodular minimization (up to 2-variable constraints) // Ref: https://theory-and-me.hatenablog.com/entry/2020/03/17/180157 // Verified by: https://atcoder.jp/contests/abc259/submissions/33771580 // Depends on: graph/Dinic.rs struct SubmodMin(Dinic, i64); impl SubmodMin { fn new(n: usize) -> Self { let din = Dinic::new(2 + n, 0); SubmodMin(din, 0) } fn add1(&mut self, i: usize, cost: [i64; 2]) { let d = cost[1] - cost[0]; if cost[0] < cost[1] { self.0.add_edge(0, 2 + i, d); self.1 += cost[0]; } if cost[0] > cost[1] { self.0.add_edge(2 + i, 1, -d); self.1 += cost[1]; } if cost[0] == cost[1] { self.1 += cost[1]; } } fn add2(&mut self, i: usize, j: usize, c: [[i64; 2]; 2]) { assert!(c[0][0] + c[1][1] <= c[0][1] + c[1][0]); self.1 += c[0][0]; self.add1(i, [0, c[1][0] - c[0][0]]); self.add1(j, [0, c[1][1] - c[1][0]]); self.0.add_edge(2 + i, 2 + j, c[0][1] + c[1][0] - (c[0][0] + c[1][1])); } #[allow(unused)] fn calc(&mut self) -> i64 { let ans = self.0.max_flow(0, 1).0; ans + self.1 } } fn main() { // In order to avoid potential stack overflow, spawn a new thread. let stack_size = 104_857_600; // 100 MB let thd = std::thread::Builder::new().stack_size(stack_size); thd.spawn(|| solve()).unwrap().join().unwrap(); } fn solve() { input! { h: usize, w: usize, g: [[i64; w]; h], r: [i64; h], c: [i64; w], } let mut submodmin = SubmodMin::new(h + w); for i in 0..h { let mut row = r[i]; for j in 0..w { submodmin.add2(i, h + j, [[0, 0], [0, -g[i][j]]]); row -= g[i][j]; } submodmin.add1(i, [0, -row]); } for j in 0..w { let mut col = c[j]; for i in 0..h { col -= g[i][j]; } submodmin.add1(h + j, [0, -col]); } println!("{}", -submodmin.calc()); }