AOJ 3022: Cluster Network

問題

http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=3022

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);
        }
    }
}

ARC 039 D - 旅行会社高橋君

問題

https://beta.atcoder.jp/contests/arc039/tasks/arc039_d

解法

橋を2回通らずに A->B->C の移動が出来るかという問題になる。

まず橋を検出し、それらを取り除くと、グラフはいくつかの連結成分に分かれる。各連結成分内では頂点間を移動する経路が常に複数あるため、移動に制限がかからない。これらの連結成分をそれぞれ頂点とし、元のグラフの橋を辺とした木を考える。この木の上で dist(A,B)+dist(B,C)==dist(C,A) ならば A->B->C は同じ橋を 2 回通らずに移動可能である。

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::{BTreeMap, BTreeSet, VecDeque};

fn main() {
    input!(
        n: usize,
        m: usize,
        edges: [(usize1, usize1); m],
        q: usize,
        queries: [(usize1, usize1, usize1); q]
    );
    solve(n, &edges, &queries);
}

fn solve(n: usize, edges: &Vec<(usize, usize)>, queries: &Vec<(usize, usize, usize)>) {
    let bridges = {
        let mut graph = vec![vec![]; n];
        for &(u, v) in edges.iter() {
            graph[u].push(v);
            graph[v].push(u);
        }

        let mut bridge_detector = BridgeDetector::new(n);
        bridge_detector.run(&graph);

        let mut bridges = BTreeSet::new();
        for &(a, b) in bridge_detector.bridges.iter() {
            bridges.insert((a, b));
            bridges.insert((b, a));
        }
        bridges
    };

    let mut uf = UnionFind::new(n);
    for &(a, b) in edges.iter() {
        if bridges.contains(&(a, b)) {
            continue;
        }
        uf.unite(a, b);
    }

    let mut set = BTreeSet::new();
    let mut find = vec![0; n];
    for i in 0..n {
        let f = uf.find(i);
        let cur = set.len();
        set.insert(f);
        if cur == set.len() {
            find[i] = find[f];
        } else {
            find[f] = cur;
            find[i] = find[f];
        }
    }

    let super_tree = {
        let mut super_tree = vec![vec![]; set.len()];
        for &(a, b) in edges.iter() {
            let a = find[a];
            let b = find[b];
            if a == b {
                continue;
            }
            super_tree[a].push(b);
            super_tree[b].push(a);
        }
        super_tree
    };

    let lca = LowestCommonAncestor::new(&super_tree);
    for &(a, b, c) in queries.iter() {
        let (a, b, c) = (find[a], find[b], find[c]);

        if lca.get_dist(a, b) + lca.get_dist(b, c) == lca.get_dist(a, c) {
            println!("OK");
        } else {
            println!("NG");
        }
    }
}

struct BridgeDetector {
    articulations: Vec<usize>,
    bridges: Vec<(usize, usize)>,
    visit: Vec<bool>,
    ord: Vec<usize>,
    low: Vec<usize>,
    k: usize,
}

impl BridgeDetector {
    fn new(n: usize) -> Self {
        BridgeDetector {
            articulations: vec![],
            bridges: vec![],
            visit: vec![false; n],
            ord: vec![0; n],
            low: vec![0; n],
            k: 0,
        }
    }

    fn run(&mut self, graph: &Vec<Vec<usize>>) {
        let n = graph.len();
        for i in 0..n {
            if !self.visit[i] {
                self.dfs(i, None, graph);
            }
        }
    }
    fn dfs(&mut self, v: usize, p: Option<usize>, graph: &Vec<Vec<usize>>) {
        self.visit[v] = true;
        self.ord[v] = self.k;
        self.k += 1;
        self.low[v] = self.ord[v];

        let mut is_articulation = false;
        let mut count = 0;
        for &next in graph[v].iter() {
            if !self.visit[next] {
                count += 1;
                self.dfs(next, Some(v), graph);
                if self.low[v] > self.low[next] {
                    self.low[v] = self.low[next];
                }
                if p.is_some() && self.ord[v] <= self.low[next] {
                    is_articulation = true;
                }
                if self.ord[v] < self.low[next] {
                    let (v, next) = if v < next { (v, next) } else { (next, v) };
                    self.bridges.push((v, next));
                }
            } else if p.is_none() || next != p.unwrap() && self.low[v] > self.ord[next] {
                self.low[v] = self.ord[next];
            }
        }

        if p.is_none() && count > 1 {
            is_articulation = true;
        }
        if is_articulation {
            self.articulations.push(v);
        }
    }
}

const MAX_PARENT: usize = 1 << 50;
pub struct LowestCommonAncestor {
    parent: Vec<Vec<usize>>,
    depth: Vec<usize>,
    log_v: usize,
}

impl LowestCommonAncestor {
    pub fn new(graph: &Vec<Vec<usize>>) -> Self {
        let num_v = graph.len();
        let root = 0;
        let mut depth = vec![0; num_v];

        let mut log_v = 1;
        let mut i = 1;
        while i <= num_v {
            i *= 2;
            log_v += 1;
        }
        let mut parent: Vec<Vec<usize>> = vec![vec![0; num_v]; log_v];

        let mut depth_vis = vec![false; num_v];
        let mut stack = VecDeque::new();
        stack.push_front(root);
        parent[0][root] = MAX_PARENT;
        depth[root] = 0;
        depth_vis[root] = true;
        while !stack.is_empty() {
            let v = stack.pop_front().unwrap();
            stack.push_front(v);
            for &u in &graph[v] {
                if depth_vis[u] {
                    continue;
                }
                parent[0][u] = v;
                depth[u] = depth[v] + 1;
                depth_vis[u] = true;
                stack.push_front(u);
            }

            let head = stack.pop_front().unwrap();
            if head != v {
                stack.push_front(head);
            }
        }

        for k in 0..(log_v - 1) {
            for u in 0..num_v {
                parent[k + 1][u] = if parent[k][u] == MAX_PARENT {
                    MAX_PARENT
                } else {
                    parent[k][parent[k][u]]
                };
            }
        }

        LowestCommonAncestor {
            parent: parent,
            depth: depth,
            log_v: log_v,
        }
    }

    pub fn get_lca(&self, u: usize, v: usize) -> usize {
        let (mut u, mut v) = if self.depth[u] <= self.depth[v] {
            (u, v)
        } else {
            (v, u)
        };
        for k in 0..self.log_v {
            if ((self.depth[v] - self.depth[u]) & (1 << k)) != 0 {
                v = self.parent[k][v];
            }
        }
        if u == v {
            return u;
        }

        for k in (0..self.log_v).rev() {
            if self.parent[k][u] != self.parent[k][v] {
                u = self.parent[k][u];
                v = self.parent[k][v];
            }
        }
        return self.parent[0][u];
    }

    pub fn get_dist(&self, u: usize, v: usize) -> usize {
        let lca = self.get_lca(u, v);
        self.depth[u] + self.depth[v] - self.depth[lca] * 2
    }
}

pub struct UnionFind {
    parent: Vec<usize>,
    sizes: Vec<usize>,
    size: usize,
}

impl UnionFind {
    pub fn new(n: usize) -> UnionFind {
        UnionFind {
            parent: (0..n).map(|i| i).collect::<Vec<usize>>(),
            sizes: vec![1; n],
            size: n,
        }
    }

    pub fn find(&mut self, x: usize) -> usize {
        if x == self.parent[x] {
            x
        } else {
            let px = self.parent[x];
            self.parent[x] = self.find(px);
            self.parent[x]
        }
    }

    pub fn unite(&mut self, x: usize, y: usize) -> bool {
        let parent_x = self.find(x);
        let parent_y = self.find(y);
        if parent_x == parent_y {
            return false;
        }

        let (large, small) = if self.sizes[parent_x] < self.sizes[parent_y] {
            (parent_y, parent_x)
        } else {
            (parent_x, parent_y)
        };

        self.parent[small] = large;
        self.sizes[large] += self.sizes[small];
        self.sizes[small] = 0;
        self.size -= 1;
        return true;
    }
}

CS Academy: Growing Segment

問題と解法

記憶力があれなので同じ問題を何度も解く。

kenkoooo.hatenablog.com

コード

use std::cmp;
use std::collections::BTreeSet;

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")
    };
}

fn main() {
    input!{
        n: usize,
        q: usize,
        x: [i64; n],
        l: [i64; q],
    }
    let mut l: Vec<(i64, usize)> = (0..q).map(|i| (l[i], i)).collect();
    l.sort();

    let mut x = {
        let mut v: Vec<i64> = vec![0];
        for &x in x.iter() {
            while v.len() >= 2 && (v[v.len() - 2] < v[v.len() - 1]) == (v[v.len() - 1] < x) {
                v.pop();
            }
            v.push(x);
        }
        v
    };

    let mut offset = 0;
    if x.len() >= 2 && x[1] < 0 {
        offset = -x[1];
        x.remove(0);
        for x in x.iter_mut() {
            *x += offset;
        }
    }

    let mut point_set = BTreeSet::new();
    for i in 0..x.len() {
        point_set.insert(i);
    }

    let mut edge_set = EdgeSet::new(offset);
    for i in 1..x.len() {
        edge_set.insert(i - 1, i, &x);
    }

    let mut ans = vec![0; q];
    for &(length, ans_id) in l.iter() {
        while let Some(&(distance, i1, i2)) = edge_set.first() {
            if distance >= length {
                break;
            }

            if edge_set.set.len() == 1 {
                break;
            }

            if i1 == 0 {
                let &i3 = point_set.range((i2 + 1)..).next().unwrap();

                edge_set.remove(i1, i2, &x);
                edge_set.remove(i2, i3, &x);

                x[i2] = length;
                edge_set.insert(i1, i2, &x);
                edge_set.insert(i2, i3, &x);
                continue;
            }

            let i3 = point_set.range((i2 + 1)..).next().cloned();
            if i3.is_none() {
                edge_set.remove(i1, i2, &x);
                point_set.remove(&i2);
                continue;
            }

            let &i0 = point_set.range(..i1).next_back().unwrap();
            let i3 = i3.unwrap();
            assert!((x[i0] < x[i1]) != (x[i1] < x[i2]));
            assert!((x[i1] < x[i2]) != (x[i2] < x[i3]));

            // remove i2
            edge_set.remove(i1, i2, &x);
            edge_set.remove(i2, i3, &x);
            point_set.remove(&i2);

            if (x[i0] - x[i1]).abs() > (x[i0] - x[i3]).abs() {
                // remove i3
                let &i4 = point_set.range((i3 + 1)..).next_back().unwrap();
                point_set.remove(&i3);
                edge_set.remove(i3, i4, &x);
                edge_set.insert(i1, i4, &x);
            } else {
                // remove i1
                point_set.remove(&i1);
                edge_set.remove(i0, i1, &x);
                edge_set.insert(i0, i3, &x);
            }
        }

        ans[ans_id] = cmp::max(0, edge_set.total - (edge_set.set.len() as i64) * length);
    }
    for &ans in ans.iter() {
        println!("{}", ans);
    }
}

#[derive(Debug)]
struct EdgeSet {
    set: BTreeSet<(i64, usize, usize)>,
    total: i64,
}

impl EdgeSet {
    fn new(offset: i64) -> Self {
        EdgeSet {
            set: BTreeSet::new(),
            total: offset,
        }
    }

    fn insert(&mut self, from: usize, to: usize, x: &Vec<i64>) {
        assert!(from < to);
        let distance = (x[from] - x[to]).abs();
        self.set.insert((distance, from, to));
        self.total += distance;
    }

    fn remove(&mut self, from: usize, to: usize, x: &Vec<i64>) {
        assert!(from < to);
        let distance = (x[from] - x[to]).abs();
        self.set.remove(&(distance, from, to));
        self.total -= distance;
    }

    fn first(&self) -> Option<&(i64, usize, usize)> {
        self.set.iter().next()
    }
}

AtCoder Regular Contest 083 E - Bichrome Tree

問題

https://beta.atcoder.jp/contests/arc083/tasks/arc083_c

解法

いつもありがとうございます。

頂点 v を根とする部分木で、頂点 v と同じ色の頂点の重みの合計は x[v] だが、同じ色でない頂点の重みの合計は小さければ小さいほどよい。よって、「頂点 v を根とする部分木の、頂点 v と異なる色の頂点の、重みの合計値の最小値」を求めていく。

コード

use std::cmp;

const INF: usize = 1e18 as usize;

fn dfs(v: usize, parent: usize, x: &Vec<usize>, graph: &Vec<Vec<usize>>) -> usize {
    let mut dp = vec![INF; x[v] + 1];
    dp[0] = 0;

    for &child in graph[v].iter() {
        if child == parent {
            continue;
        }
        let white = dfs(child, v, x, graph);
        let black = x[child];
        let mut next = vec![INF; x[v] + 1];
        for i in 0..(x[v] + 1) {
            if dp[i] != INF {
                if i + white <= x[v] {
                    next[i + white] = cmp::min(next[i + white], dp[i] + black);
                }
                if i + black <= x[v] {
                    next[i + black] = cmp::min(next[i + black], dp[i] + white);
                }
            }
        }
        dp = next;
    }

    *dp.iter().min().unwrap()
}

fn main() {
    let mut sc = Scanner::new();
    let n = sc.read();
    let mut graph = vec![vec![]; n];
    for i in 0..(n - 1) {
        let p = sc.read::<usize>() - 1;
        graph[p].push(i + 1);
        graph[i + 1].push(p);
    }
    let x = sc.read_vec(n);

    if dfs(0, INF, &x, &graph) != INF {
        println!("POSSIBLE");
    } else {
        println!("IMPOSSIBLE");
    }
}

struct Scanner {
    ptr: usize,
    length: usize,
    buf: Vec<u8>,
    small_cache: Vec<u8>,
}

#[allow(dead_code)]
impl Scanner {
    fn new() -> Scanner {
        Scanner {
            ptr: 0,
            length: 0,
            buf: vec![0; 1024],
            small_cache: vec![0; 1024],
        }
    }

    fn load(&mut self) {
        use std::io::Read;
        let mut s = std::io::stdin();
        self.length = s.read(&mut self.buf).unwrap();
    }

    fn byte(&mut self) -> u8 {
        if self.ptr >= self.length {
            self.ptr = 0;
            self.load();
            if self.length == 0 {
                self.buf[0] = b'\n';
                self.length = 1;
            }
        }

        self.ptr += 1;
        return self.buf[self.ptr - 1];
    }

    fn is_space(b: u8) -> bool {
        b == b'\n' || b == b'\r' || b == b'\t' || b == b' '
    }

    fn read_vec<T>(&mut self, n: usize) -> Vec<T>
    where
        T: std::str::FromStr,
        T::Err: std::fmt::Debug,
    {
        (0..n).map(|_| self.read()).collect()
    }

    fn usize_read(&mut self) -> usize {
        self.read()
    }

    fn read<T>(&mut self) -> T
    where
        T: std::str::FromStr,
        T::Err: std::fmt::Debug,
    {
        let mut b = self.byte();
        while Scanner::is_space(b) {
            b = self.byte();
        }

        for pos in 0..self.small_cache.len() {
            self.small_cache[pos] = b;
            b = self.byte();
            if Scanner::is_space(b) {
                return String::from_utf8_lossy(&self.small_cache[0..(pos + 1)])
                    .parse()
                    .unwrap();
            }
        }

        let mut v = self.small_cache.clone();
        while !Scanner::is_space(b) {
            v.push(b);
            b = self.byte();
        }
        return String::from_utf8_lossy(&v).parse().unwrap();
    }
}

Battle Conference U30 - Programming Battle F - 数列と計算

問題

https://beta.atcoder.jp/contests/bcu30/tasks/bcu30_f

解法

全く同じ問題が CodeChef で出ている。

https://ei1333.hateblo.jp/entry/2017/06/04/151131

コード

use std::ops::*;

const MOD: usize = 1e9 as usize + 7;

fn main() {
    let mut sc = Scanner::new();
    let n = sc.read();
    let a: Vec<usize> = sc.read_vec(n);

    let mut pow2 = vec![ModInt::new(1); n + 1];
    for i in 1..(n + 1) {
        pow2[i] = pow2[i - 1] * 2;
    }

    let mut dp = vec![ModInt::new(0); n + 1];
    let mut sum = ModInt::new(0);
    let mut mul = ModInt::new(a[0]);
    for i in 0..n {
        dp[i + 1] = sum + mul;
        sum += dp[i + 1];
        if i < n - 1 {
            mul = (mul + pow2[i]) * a[i + 1];
        }
    }
    println!("{}", dp[n].value);
}

#[derive(Copy)]
pub struct ModInt<T> {
    value: T,
    modulo: T,
}

impl<T> Clone for ModInt<T>
where
    T: Copy,
{
    fn clone(&self) -> Self {
        ModInt {
            value: self.value,
            modulo: self.modulo,
        }
    }

    fn clone_from(&mut self, source: &ModInt<T>) {
        self.value = source.value;
        self.modulo = source.modulo;
    }
}

impl<T> Add<ModInt<T>> for ModInt<T>
where
    T: Add<Output = T> + Sub<Output = T> + Copy + PartialOrd,
{
    type Output = ModInt<T>;
    fn add(self, rhs: ModInt<T>) -> ModInt<T> {
        self + rhs.value
    }
}

impl<T> Add<T> for ModInt<T>
where
    T: Add<Output = T> + Sub<Output = T> + Copy + PartialOrd,
{
    type Output = ModInt<T>;
    fn add(self, rhs: T) -> ModInt<T> {
        let m = self.modulo;
        let mut t = rhs + self.value;
        if t >= m {
            t = t - m;
        }
        ModInt {
            value: t,
            modulo: self.modulo,
        }
    }
}

impl<T> Sub<T> for ModInt<T>
where
    T: PartialOrd + Copy + Add<Output = T> + Sub<Output = T> + Rem<Output = T>,
{
    type Output = ModInt<T>;
    fn sub(self, rhs: T) -> ModInt<T> {
        let rhs = if rhs >= self.modulo {
            rhs % self.modulo
        } else {
            rhs
        };
        let value = if self.value < rhs {
            self.value + self.modulo
        } else {
            self.value
        };
        ModInt {
            value: value - rhs,
            modulo: self.modulo,
        }
    }
}

impl<T> Sub<ModInt<T>> for ModInt<T>
where
    T: PartialOrd + Copy + Add<Output = T> + Sub<Output = T> + Rem<Output = T>,
{
    type Output = ModInt<T>;
    fn sub(self, rhs: ModInt<T>) -> ModInt<T> {
        self - rhs.value
    }
}

impl<T> AddAssign<T> for ModInt<T>
where
    T: Add<Output = T> + Sub<Output = T> + Copy + PartialOrd,
{
    fn add_assign(&mut self, other: T) {
        *self = *self + other;
    }
}
impl<T> AddAssign<ModInt<T>> for ModInt<T>
where
    T: Add<Output = T> + Sub<Output = T> + Copy + PartialOrd,
{
    fn add_assign(&mut self, other: ModInt<T>) {
        *self = *self + other;
    }
}

impl<T> Mul<ModInt<T>> for ModInt<T>
where
    T: Mul<Output = T> + Rem<Output = T> + Copy,
{
    type Output = ModInt<T>;

    fn mul(self, rhs: ModInt<T>) -> ModInt<T> {
        self * rhs.value
    }
}
impl<T> Mul<T> for ModInt<T>
where
    T: Mul<Output = T> + Rem<Output = T> + Copy,
{
    type Output = ModInt<T>;

    fn mul(self, rhs: T) -> ModInt<T> {
        let t = (self.value * rhs) % self.modulo;
        ModInt {
            value: t,
            modulo: self.modulo,
        }
    }
}

impl<T> MulAssign<T> for ModInt<T>
where
    T: Mul<Output = T> + Rem<Output = T> + Copy,
{
    fn mul_assign(&mut self, rhs: T) {
        *self = *self * rhs;
    }
}

impl<T> MulAssign<ModInt<T>> for ModInt<T>
where
    T: Mul<Output = T> + Rem<Output = T> + Copy,
{
    fn mul_assign(&mut self, rhs: ModInt<T>) {
        *self = *self * rhs;
    }
}

impl ModInt<usize> {
    fn new(x: usize) -> Self {
        ModInt {
            value: x,
            modulo: MOD,
        }
    }
}

struct Scanner {
    ptr: usize,
    length: usize,
    buf: Vec<u8>,
    small_cache: Vec<u8>,
}

#[allow(dead_code)]
impl Scanner {
    fn new() -> Scanner {
        Scanner {
            ptr: 0,
            length: 0,
            buf: vec![0; 1024],
            small_cache: vec![0; 1024],
        }
    }

    fn load(&mut self) {
        use std::io::Read;
        let mut s = std::io::stdin();
        self.length = s.read(&mut self.buf).unwrap();
    }

    fn byte(&mut self) -> u8 {
        if self.ptr >= self.length {
            self.ptr = 0;
            self.load();
            if self.length == 0 {
                self.buf[0] = b'\n';
                self.length = 1;
            }
        }

        self.ptr += 1;
        return self.buf[self.ptr - 1];
    }

    fn is_space(b: u8) -> bool {
        b == b'\n' || b == b'\r' || b == b'\t' || b == b' '
    }

    fn read_vec<T>(&mut self, n: usize) -> Vec<T>
    where
        T: std::str::FromStr,
        T::Err: std::fmt::Debug,
    {
        (0..n).map(|_| self.read()).collect()
    }

    fn usize_read(&mut self) -> usize {
        self.read()
    }

    fn read<T>(&mut self) -> T
    where
        T: std::str::FromStr,
        T::Err: std::fmt::Debug,
    {
        let mut b = self.byte();
        while Scanner::is_space(b) {
            b = self.byte();
        }

        for pos in 0..self.small_cache.len() {
            self.small_cache[pos] = b;
            b = self.byte();
            if Scanner::is_space(b) {
                return String::from_utf8_lossy(&self.small_cache[0..(pos + 1)])
                    .parse()
                    .unwrap();
            }
        }

        let mut v = self.small_cache.clone();
        while !Scanner::is_space(b) {
            v.push(b);
            b = self.byte();
        }
        return String::from_utf8_lossy(&v).parse().unwrap();
    }
}

AtCoder Regular Contest 081 F - Flip and Rectangles

問題

https://beta.atcoder.jp/contests/arc081/tasks/arc081_d

解法

解説の通り。最大長方形を求めるのは AOJ で学べた。

http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=DPL_3_B

コード

use std::cmp;
use std::collections::VecDeque;

trait TopQueue<T> {
    fn top(&self) -> &T;
}

impl<T> TopQueue<T> for VecDeque<T> {
    fn top(&self) -> &T {
        self.iter().next().unwrap()
    }
}

fn calc_area(height: usize, width: usize) -> usize {
    (height + 1) * (width + 1)
}

fn calc_max_rectangle(hist: &Vec<usize>) -> usize {
    let n = hist.len();
    let mut ans = 0;
    let mut stack: VecDeque<(usize, usize)> = VecDeque::new();

    for i in 0..n {
        let mut reachable_min = i;
        while !stack.is_empty() && stack.top().1 > hist[i] {
            let (pos, height) = stack.pop_front().unwrap();
            reachable_min = pos;

            let area = calc_area(height, i - reachable_min);
            ans = cmp::max(ans, area);
        }

        if stack.is_empty() || stack.top().1 < hist[i] {
            stack.push_front((reachable_min, hist[i]));
        }
    }

    while !stack.is_empty() {
        let (pos, height) = stack.pop_front().unwrap();

        let area = calc_area(n - pos, height);
        ans = cmp::max(ans, area);
    }
    ans
}

fn main() {
    let mut sc = Scanner::new();
    let h = sc.read();
    let w: usize = sc.read();
    let a: Vec<Vec<usize>> = (0..h)
        .map(|_| {
            sc.read::<String>()
                .chars()
                .map(|c| if c == '#' { 1 } else { 0 })
                .collect()
        }).collect();

    let w = w - 1;
    let h = h - 1;
    let mut map = vec![vec![false; w]; h];

    for i in 0..h {
        for j in 0..w {
            let s = a[i][j] + a[i][j + 1] + a[i + 1][j] + a[i + 1][j + 1];
            map[i][j] = s % 2 == 0;
        }
    }

    let mut hist = vec![vec![0; w]; h];
    for i in 0..h {
        for j in 0..w {
            if !map[i][j] {
                continue;
            }
            if i == 0 {
                hist[i][j] = 1;
            } else {
                hist[i][j] = hist[i - 1][j] + 1;
            }
        }
    }

    let mut ans = cmp::max(w + 1, h + 1);
    for i in 0..h {
        ans = cmp::max(ans, calc_max_rectangle(&hist[i]));
    }
    println!("{}", ans);
}

trait CppDeque<S> {
    fn top(&mut self) -> S;
}

struct Scanner {
    ptr: usize,
    length: usize,
    buf: Vec<u8>,
    small_cache: Vec<u8>,
}

#[allow(dead_code)]
impl Scanner {
    fn new() -> Scanner {
        Scanner {
            ptr: 0,
            length: 0,
            buf: vec![0; 1024],
            small_cache: vec![0; 1024],
        }
    }

    fn load(&mut self) {
        use std::io::Read;
        let mut s = std::io::stdin();
        self.length = s.read(&mut self.buf).unwrap();
    }

    fn byte(&mut self) -> u8 {
        if self.ptr >= self.length {
            self.ptr = 0;
            self.load();
            if self.length == 0 {
                self.buf[0] = b'\n';
                self.length = 1;
            }
        }

        self.ptr += 1;
        return self.buf[self.ptr - 1];
    }

    fn is_space(b: u8) -> bool {
        b == b'\n' || b == b'\r' || b == b'\t' || b == b' '
    }

    fn read_vec<T>(&mut self, n: usize) -> Vec<T>
    where
        T: std::str::FromStr,
        T::Err: std::fmt::Debug,
    {
        (0..n).map(|_| self.read()).collect()
    }

    fn usize_read(&mut self) -> usize {
        self.read()
    }

    fn read<T>(&mut self) -> T
    where
        T: std::str::FromStr,
        T::Err: std::fmt::Debug,
    {
        let mut b = self.byte();
        while Scanner::is_space(b) {
            b = self.byte();
        }

        for pos in 0..self.small_cache.len() {
            self.small_cache[pos] = b;
            b = self.byte();
            if Scanner::is_space(b) {
                return String::from_utf8_lossy(&self.small_cache[0..(pos + 1)])
                    .parse()
                    .unwrap();
            }
        }

        let mut v = self.small_cache.clone();
        while !Scanner::is_space(b) {
            v.push(b);
            b = self.byte();
        }
        return String::from_utf8_lossy(&v).parse().unwrap();
    }
}

AOJ Largest Rectangle

問題

http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=DPL_3_B

解法

各列についてヒストグラムに内接する最大長方形を求める。

コード

use std::cmp;
use std::collections::VecDeque;

trait TopQueue<T> {
    fn top(&self) -> &T;
}

impl<T> TopQueue<T> for VecDeque<T> {
    fn top(&self) -> &T {
        assert!(!self.is_empty());
        self.iter().next().unwrap()
    }
}

fn f(hist: &Vec<usize>) -> usize {
    let n = hist.len();
    let mut ans = 0;
    let mut q: VecDeque<(usize, usize)> = VecDeque::new();

    for i in 0..n {
        let mut reachable_min = i;
        while !q.is_empty() && q.top().1 > hist[i] {
            let (pos, height) = q.pop_front().unwrap();
            reachable_min = pos;
            ans = cmp::max(ans, (i - reachable_min) * height);
        }

        if q.is_empty() || q.top().1 < hist[i] {
            q.push_front((reachable_min, hist[i]));
        }
    }
    while !q.is_empty() {
        let (pos, height) = q.pop_front().unwrap();
        ans = cmp::max(ans, (n - pos) * height);
    }
    ans
}

fn main() {
    let mut sc = Scanner::new();
    let h = sc.read();
    let w = sc.read();
    let mut c = vec![vec![false; w]; h];
    for i in 0..h {
        for j in 0..w {
            c[i][j] = sc.read::<usize>() == 0;
        }
    }

    let mut hist = vec![vec![0; w]; h];
    for i in 0..h {
        for j in 0..w {
            if !c[i][j] {
                continue;
            }
            if i == 0 {
                hist[i][j] = 1;
            } else {
                hist[i][j] = hist[i - 1][j] + 1;
            }
        }
    }

    let mut ans = 0;
    for i in 0..h {
        ans = cmp::max(ans, f(&hist[i]));
    }
    println!("{}", ans);
}

struct Scanner {
    ptr: usize,
    length: usize,
    buf: Vec<u8>,
    small_cache: Vec<u8>,
}

#[allow(dead_code)]
impl Scanner {
    fn new() -> Scanner {
        Scanner {
            ptr: 0,
            length: 0,
            buf: vec![0; 1024],
            small_cache: vec![0; 1024],
        }
    }

    fn load(&mut self) {
        use std::io::Read;
        let mut s = std::io::stdin();
        self.length = s.read(&mut self.buf).unwrap();
    }

    fn byte(&mut self) -> u8 {
        if self.ptr >= self.length {
            self.ptr = 0;
            self.load();
            if self.length == 0 {
                self.buf[0] = b'\n';
                self.length = 1;
            }
        }

        self.ptr += 1;
        return self.buf[self.ptr - 1];
    }

    fn is_space(b: u8) -> bool {
        b == b'\n' || b == b'\r' || b == b'\t' || b == b' '
    }

    fn read_vec<T>(&mut self, n: usize) -> Vec<T>
    where
        T: std::str::FromStr,
        T::Err: std::fmt::Debug,
    {
        (0..n).map(|_| self.read()).collect()
    }

    fn usize_read(&mut self) -> usize {
        self.read()
    }

    fn read<T>(&mut self) -> T
    where
        T: std::str::FromStr,
        T::Err: std::fmt::Debug,
    {
        let mut b = self.byte();
        while Scanner::is_space(b) {
            b = self.byte();
        }

        for pos in 0..self.small_cache.len() {
            self.small_cache[pos] = b;
            b = self.byte();
            if Scanner::is_space(b) {
                return String::from_utf8_lossy(&self.small_cache[0..(pos + 1)])
                    .parse()
                    .unwrap();
            }
        }

        let mut v = self.small_cache.clone();
        while !Scanner::is_space(b) {
            v.push(b);
            b = self.byte();
        }
        return String::from_utf8_lossy(&v).parse().unwrap();
    }
}