#1132691 (Rust) No.3345 Reducible Sequence

• 問題: No.3345 Reducible Sequence
• ユーザー: rhoo
• 提出日時: 2025-11-13 22:34:27
• 言語: Rust (1.83.0 + proconio)
• 結果: AC
• 実行時間: 282 ms / 2,000 ms
• コード長: 11,175 bytes
• コンパイル時間: 12,994 ms
• コンパイル使用メモリ: 399,620 KB
• 実行使用メモリ: 25,720 KB
• 最終ジャッジ日時: 2025-11-13 22:34:45
• 合計ジャッジ時間: 17,587 ms
• ジャッジサーバーID （参考情報）: judge5 / judge1

ファイルパターン	結果
sample	AC * 3
other	AC * 26

ソースコード

#![allow(unused_imports,non_snake_case,dead_code)]
use std::{cmp::Reverse as Rev,ops::Range,collections::*,iter::*,mem::swap};
use proconio::{marker::*,*};



#[fastout]
fn main(){
    input!{
        n:usize,
        a:[usize;n],
    }

    let mut g=vec![vec![];n];
    for i in 0..n{
        for j in 0..n{
            if a[j]%(i+1)==0{
                g[i].push(j);
            }
        }
    }

    let ans=binary_search(0,n+1,|x|{
        let mut flow=MfGraph::new(n*2+2);
        let s=n*2;
        let t=s+1;
        for i in 0..n{
            flow.add_edge(s,i,1);
            flow.add_edge(i+n,t,1);
        }
        for u in 0..x{
            for &v in &g[u]{
                flow.add_edge(u,v+n,1);
            }
        }
        flow.flow(s,t)>=x
    });
    println!("{ans}");
}



use std::cmp::min;
use std::iter;

impl<Cap> MfGraph<Cap>
where
    Cap: Integral,
{
    pub fn new(n: usize) -> MfGraph<Cap> {
        MfGraph {
            _n: n,
            pos: Vec::new(),
            g: iter::repeat_with(Vec::new).take(n).collect(),
        }
    }

    pub fn add_edge(&mut self, from: usize, to: usize, cap: Cap) -> usize {
        assert!(from < self._n);
        assert!(to < self._n);
        assert!(Cap::zero() <= cap);
        let m = self.pos.len();
        self.pos.push((from, self.g[from].len()));
        let rev = self.g[to].len() + usize::from(from == to);
        self.g[from].push(_Edge { to, rev, cap });
        let rev = self.g[from].len() - 1;
        self.g[to].push(_Edge {
            to: from,
            rev,
            cap: Cap::zero(),
        });
        m
    }
}

#[derive(Debug, PartialEq, Eq)]
pub struct Edge<Cap: Integral> {
    pub from: usize,
    pub to: usize,
    pub cap: Cap,
    pub flow: Cap,
}

impl<Cap> MfGraph<Cap>
where
    Cap: Integral,
{
    pub fn get_edge(&self, i: usize) -> Edge<Cap> {
        let m = self.pos.len();
        assert!(i < m);
        let _e = &self.g[self.pos[i].0][self.pos[i].1];
        let _re = &self.g[_e.to][_e.rev];
        Edge {
            from: self.pos[i].0,
            to: _e.to,
            cap: _e.cap + _re.cap,
            flow: _re.cap,
        }
    }
    pub fn edges(&self) -> Vec<Edge<Cap>> {
        let m = self.pos.len();
        (0..m).map(|i| self.get_edge(i)).collect()
    }
    pub fn change_edge(&mut self, i: usize, new_cap: Cap, new_flow: Cap) {
        let m = self.pos.len();
        assert!(i < m);
        assert!(Cap::zero() <= new_flow && new_flow <= new_cap);
        let (to, rev) = {
            let _e = &mut self.g[self.pos[i].0][self.pos[i].1];
            _e.cap = new_cap - new_flow;
            (_e.to, _e.rev)
        };
        let _re = &mut self.g[to][rev];
        _re.cap = new_flow;
    }

    /// `s != t` must hold, otherwise it panics.
    pub fn flow(&mut self, s: usize, t: usize) -> Cap {
        self.flow_with_capacity(s, t, Cap::max_value())
    }
    /// # Parameters
    /// * `s != t` must hold, otherwise it panics.
    /// * `flow_limit >= 0`
    pub fn flow_with_capacity(&mut self, s: usize, t: usize, flow_limit: Cap) -> Cap {
        let n_ = self._n;
        assert!(s < n_);
        assert!(t < n_);
        // By the definition of max flow in appendix.html, this function should return 0
        // when the same vertices are provided.  On the other hand, it is reasonable to
        // return infinity-like value too, which is what the original implementation
        // (and this implementation without the following assertion) does.
        // Since either return value is confusing, we'd rather deny the parameters
        // of the two same vertices.
        // For more details, see https://github.com/rust-lang-ja/ac-library-rs/pull/24#discussion_r485343451
        // and https://github.com/atcoder/ac-library/issues/5 .
        assert_ne!(s, t);
        // Additional constraint
        assert!(Cap::zero() <= flow_limit);

        let mut calc = FlowCalculator {
            graph: self,
            s,
            t,
            flow_limit,
            level: vec![0; n_],
            iter: vec![0; n_],
            que: SimpleQueue::default(),
        };

        let mut flow = Cap::zero();
        while flow < flow_limit {
            calc.bfs();
            if calc.level[t] == -1 {
                break;
            }
            calc.iter.iter_mut().for_each(|e| *e = 0);
            while flow < flow_limit {
                let f = calc.dfs(t, flow_limit - flow);
                if f == Cap::zero() {
                    break;
                }
                flow += f;
            }
        }
        flow
    }

    pub fn min_cut(&self, s: usize) -> Vec<bool> {
        let mut visited = vec![false; self._n];
        let mut que = SimpleQueue::default();
        que.push(s);
        while let Some(&p) = que.pop() {
            visited[p] = true;
            for e in &self.g[p] {
                if e.cap != Cap::zero() && !visited[e.to] {
                    visited[e.to] = true;
                    que.push(e.to);
                }
            }
        }
        visited
    }
}

struct FlowCalculator<'a, Cap> {
    graph: &'a mut MfGraph<Cap>,
    s: usize,
    t: usize,
    flow_limit: Cap,
    level: Vec<i32>,
    iter: Vec<usize>,
    que: SimpleQueue<usize>,
}

impl<Cap> FlowCalculator<'_, Cap>
where
    Cap: Integral,
{
    fn bfs(&mut self) {
        self.level.iter_mut().for_each(|e| *e = -1);
        self.level[self.s] = 0;
        self.que.clear();
        self.que.push(self.s);
        while !self.que.empty() {
            let v = *self.que.front().unwrap();
            self.que.pop();
            for e in &self.graph.g[v] {
                if e.cap == Cap::zero() || self.level[e.to] >= 0 {
                    continue;
                }
                self.level[e.to] = self.level[v] + 1;
                if e.to == self.t {
                    return;
                }
                self.que.push(e.to);
            }
        }
    }
    fn dfs(&mut self, v: usize, up: Cap) -> Cap {
        if v == self.s {
            return up;
        }
        let mut res = Cap::zero();
        let level_v = self.level[v];
        for i in self.iter[v]..self.graph.g[v].len() {
            self.iter[v] = i;
            let &_Edge {
                to: e_to,
                rev: e_rev,
                ..
            } = &self.graph.g[v][i];
            if level_v <= self.level[e_to] || self.graph.g[e_to][e_rev].cap == Cap::zero() {
                continue;
            }
            let d = self.dfs(e_to, min(up - res, self.graph.g[e_to][e_rev].cap));
            if d <= Cap::zero() {
                continue;
            }
            self.graph.g[v][i].cap += d;
            self.graph.g[e_to][e_rev].cap -= d;
            res += d;
            if res == up {
                return res;
            }
        }
        self.iter[v] = self.graph.g[v].len();
        res
    }
}

#[derive(Default)]
pub struct MfGraph<Cap> {
    _n: usize,
    pos: Vec<(usize, usize)>,
    g: Vec<Vec<_Edge<Cap>>>,
}

struct _Edge<Cap> {
    to: usize,
    rev: usize,
    cap: Cap,
}



#[derive(Default)]
pub(crate) struct SimpleQueue<T> {
    payload: Vec<T>,
    pos: usize,
}

impl<T> SimpleQueue<T> {
    pub(crate) fn reserve(&mut self, n: usize) {
        if n > self.payload.len() {
            self.payload.reserve(n - self.payload.len());
        }
    }

    pub(crate) fn size(&self) -> usize {
        self.payload.len() - self.pos
    }

    pub(crate) fn empty(&self) -> bool {
        self.pos == self.payload.len()
    }

    pub(crate) fn push(&mut self, t: T) {
        self.payload.push(t);
    }

    // Do we need mutable version?
    pub(crate) fn front(&self) -> Option<&T> {
        if self.pos < self.payload.len() {
            Some(&self.payload[self.pos])
        } else {
            None
        }
    }

    pub(crate) fn clear(&mut self) {
        self.payload.clear();
        self.pos = 0;
    }

    pub(crate) fn pop(&mut self) -> Option<&T> {
        if self.pos < self.payload.len() {
            self.pos += 1;
            Some(&self.payload[self.pos - 1])
        } else {
            None
        }
    }
}


use std::{
    fmt,
    iter::{Product, Sum},
    ops::{
        Add, AddAssign, BitAnd, BitAndAssign, BitOr, BitOrAssign, BitXor, BitXorAssign, Div,
        DivAssign, Mul, MulAssign, Not, Rem, RemAssign, Shl, ShlAssign, Shr, ShrAssign, Sub,
        SubAssign,
    },
};

// Skipped:
//
// - `is_signed_int_t<T>`   (probably won't be used directly in `modint.rs`)
// - `is_unsigned_int_t<T>` (probably won't be used directly in `modint.rs`)
// - `to_unsigned_t<T>`     (not used in `fenwicktree.rs`)

/// Corresponds to `std::is_integral` in C++.
// We will remove unnecessary bounds later.
//
// Maybe we should rename this to `PrimitiveInteger` or something, as it probably won't be used in the
// same way as the original ACL.
pub trait Integral:
    'static
    + Send
    + Sync
    + Copy
    + Ord
    + Not<Output = Self>
    + Add<Output = Self>
    + Sub<Output = Self>
    + Mul<Output = Self>
    + Div<Output = Self>
    + Rem<Output = Self>
    + AddAssign
    + SubAssign
    + MulAssign
    + DivAssign
    + RemAssign
    + Sum
    + Product
    + BitOr<Output = Self>
    + BitAnd<Output = Self>
    + BitXor<Output = Self>
    + BitOrAssign
    + BitAndAssign
    + BitXorAssign
    + Shl<Output = Self>
    + Shr<Output = Self>
    + ShlAssign
    + ShrAssign
    + fmt::Display
    + fmt::Debug
    + fmt::Binary
    + fmt::Octal
    + Zero
    + One
    + BoundedBelow
    + BoundedAbove
{
}

/// Class that has additive identity element
pub trait Zero {
    /// The additive identity element
    fn zero() -> Self;
}

/// Class that has multiplicative identity element
pub trait One {
    /// The multiplicative identity element
    fn one() -> Self;
}

pub trait BoundedBelow {
    fn min_value() -> Self;
}

pub trait BoundedAbove {
    fn max_value() -> Self;
}

macro_rules! impl_integral {
    ($($ty:ty),*) => {
        $(
            impl Zero for $ty {
                #[inline]
                fn zero() -> Self {
                    0
                }
            }

            impl One for $ty {
                #[inline]
                fn one() -> Self {
                    1
                }
            }

            impl BoundedBelow for $ty {
                #[inline]
                fn min_value() -> Self {
                    Self::min_value()
                }
            }

            impl BoundedAbove for $ty {
                #[inline]
                fn max_value() -> Self {
                    Self::max_value()
                }
            }

            impl Integral for $ty {}
        )*
    };
}

impl_integral!(i8, i16, i32, i64, i128, isize, u8, u16, u32, u64, u128, usize);



// true,true,..,true,false,false で一番右のtrue
// ok>ngでも大丈夫
fn binary_search(mut ok:usize,mut ng:usize,mut f:impl FnMut(usize)->bool)->usize{
    assert!(ok!=ng);
    
    while 1<ok.abs_diff(ng){
        let m=ok.min(ng)+ok.abs_diff(ng)/2;
        if f(m){
            ok=m;
        } else{
            ng=m;
        }
    }
    ok
}