AOJ 3022: Cluster Network
解法
雰囲気から、関節点を求める機運が高まるが、実際の問題はその後に最後の答えを出力するパートである。
http://web-ext.u-aizu.ac.jp/circles/acpc/commentary/ACPC2017Day2/J.pdf
解説 PDF にあるとおり、 DFS Tree において、頂点 i と、その子 v について lowlink[v] < order[i] が成り立つならば、 v を根とする部分木と i の親は後退辺によって連結である、という性質を利用する。
コード
/// Thank you tanakh!!! /// https://qiita.com/tanakh/items/0ba42c7ca36cd29d0ac8 macro_rules! input { (source = $s:expr, $($r:tt)*) => { let mut iter = $s.split_whitespace(); input_inner!{iter, $($r)*} }; ($($r:tt)*) => { let mut s = { use std::io::Read; let mut s = String::new(); std::io::stdin().read_to_string(&mut s).unwrap(); s }; let mut iter = s.split_whitespace(); input_inner!{iter, $($r)*} }; } macro_rules! input_inner { ($iter:expr) => {}; ($iter:expr, ) => {}; ($iter:expr, $var:ident : $t:tt $($r:tt)*) => { let $var = read_value!($iter, $t); input_inner!{$iter $($r)*} }; } macro_rules! read_value { ($iter:expr, ( $($t:tt),* )) => { ( $(read_value!($iter, $t)),* ) }; ($iter:expr, [ $t:tt ; $len:expr ]) => { (0..$len).map(|_| read_value!($iter, $t)).collect::<Vec<_>>() }; ($iter:expr, chars) => { read_value!($iter, String).chars().collect::<Vec<char>>() }; ($iter:expr, usize1) => { read_value!($iter, usize) - 1 }; ($iter:expr, $t:ty) => { $iter.next().unwrap().parse::<$t>().expect("Parse error") }; } use std::cmp; use std::collections::{BTreeSet, VecDeque}; const INF: usize = 1e15 as usize; fn main() { input!( n: usize, m: usize, power: [usize; n], edges: [(usize1, usize1); m] ); let mut graph = vec![vec![]; n]; for &(u, v) in edges.iter() { graph[v].push(u); graph[u].push(v); } let bridge_detector = BridgeDetector::new(&graph); let total: usize = power.iter().sum(); let mut is_articulation = vec![false; n]; for &v in bridge_detector.articulations.iter() { is_articulation[v] = true; } let mut dp = vec![INF; n]; let tree = bridge_detector.dfs_tree; let low_link = bridge_detector.low_link; let order = bridge_detector.order; for i in 0..n { if is_articulation[i] { let mut max_child = 0; let mut connected_to_parent = 0; for &child in tree[i].iter() { let dp_child = dfs(child, &tree, &mut dp, &power); max_child = cmp::max(max_child, dp_child); if low_link[child] < order[i] { connected_to_parent += dp_child; } } let dp_parent = total - (dfs(i, &tree, &mut dp, &power) - connected_to_parent); println!("{}", cmp::max(dp_parent, max_child)); } else { println!("{}", total - power[i]); } } } fn dfs(v: usize, tree: &Vec<Vec<usize>>, dp: &mut Vec<usize>, power: &Vec<usize>) -> usize { if dp[v] != INF { return dp[v]; } dp[v] = power[v]; for &next in tree[v].iter() { dp[v] += dfs(next, tree, dp, power); } dp[v] } pub struct BridgeDetector { articulations: Vec<usize>, bridges: Vec<(usize, usize)>, visit: Vec<bool>, order: Vec<usize>, low_link: Vec<usize>, k: usize, dfs_tree: Vec<Vec<usize>>, } impl BridgeDetector { pub fn new(graph: &Vec<Vec<usize>>) -> Self { let n = graph.len(); let mut d = BridgeDetector { articulations: vec![], bridges: vec![], visit: vec![false; n], order: vec![0; n], low_link: vec![0; n], k: 0, dfs_tree: vec![vec![]; n], }; d.run(graph); d } fn run(&mut self, graph: &Vec<Vec<usize>>) { let n = graph.len(); for i in 0..n { if !self.visit[i] { self.dfs(i, 0, graph, i); } } } fn dfs(&mut self, v: usize, previous: usize, graph: &Vec<Vec<usize>>, root: usize) { self.visit[v] = true; self.order[v] = self.k; self.k += 1; self.low_link[v] = self.order[v]; let mut is_articulation = false; let mut dimension = 0; for &next in graph[v].iter() { if !self.visit[next] { // The edge (v->next) is not a backedge. self.dfs_tree[v].push(next); dimension += 1; self.dfs(next, v, graph, root); self.low_link[v] = cmp::min(self.low_link[v], self.low_link[next]); if v != root && self.order[v] <= self.low_link[next] { is_articulation = true; } if self.order[v] < self.low_link[next] { let min = cmp::min(v, next); let max = cmp::max(v, next); self.bridges.push((min, max)); } } else if v == root || next != previous { // The edge (v->next) is a backedge. self.low_link[v] = cmp::min(self.low_link[v], self.order[next]); } } if v == root && dimension > 1 { is_articulation = true; } if is_articulation { self.articulations.push(v); } } }