#1113770 (Rust) No.3207 Digital Font

• 問題: No.3207 Digital Font
• ユーザー: koba-e964
• 提出日時: 2025-08-19 11:09:41
• 言語: Rust (1.83.0 + proconio)
• 結果: AC
• 実行時間: 2,007 ms / 3,000 ms
• コード長: 14,437 bytes
• コンパイル時間: 13,384 ms
• コンパイル使用メモリ: 402,464 KB
• 実行使用メモリ: 45,140 KB
• 最終ジャッジ日時: 2025-08-19 11:10:38
• 合計ジャッジ時間: 50,600 ms
• ジャッジサーバーID （参考情報）: judge5 / judge3

ファイルパターン	結果
sample	AC * 2
other	AC * 38

ソースコード

use std::io::{Write, BufWriter};
// 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, $t)).collect::<Vec<_>>()
    };
    ($next:expr, usize1) => (read_value!($next, usize) - 1);
    ($next:expr, $t:ty) => ($next().parse::<$t>().expect("Parse error"));
}

/// Verified by https://atcoder.jp/contests/abc198/submissions/21774342
mod mod_int {
    use std::ops::*;
    pub trait Mod: Copy { fn m() -> i64; }
    #[derive(Copy, Clone, Hash, PartialEq, Eq, PartialOrd, Ord)]
    pub struct ModInt<M> { pub x: i64, phantom: ::std::marker::PhantomData<M> }
    impl<M: Mod> ModInt<M> {
        // x >= 0
        pub fn new(x: i64) -> Self { ModInt::new_internal(x % M::m()) }
        fn new_internal(x: i64) -> Self {
            ModInt { x: x, phantom: ::std::marker::PhantomData }
        }
        pub fn pow(self, mut e: i64) -> Self {
            debug_assert!(e >= 0);
            let mut sum = ModInt::new_internal(1);
            let mut cur = self;
            while e > 0 {
                if e % 2 != 0 { sum *= cur; }
                cur *= cur;
                e /= 2;
            }
            sum
        }
        #[allow(dead_code)]
        pub fn inv(self) -> Self { self.pow(M::m() - 2) }
    }
    impl<M: Mod> Default for ModInt<M> {
        fn default() -> Self { Self::new_internal(0) }
    }
    impl<M: Mod, T: Into<ModInt<M>>> Add<T> for ModInt<M> {
        type Output = Self;
        fn add(self, other: T) -> Self {
            let other = other.into();
            let mut sum = self.x + other.x;
            if sum >= M::m() { sum -= M::m(); }
            ModInt::new_internal(sum)
        }
    }
    impl<M: Mod, T: Into<ModInt<M>>> Sub<T> for ModInt<M> {
        type Output = Self;
        fn sub(self, other: T) -> Self {
            let other = other.into();
            let mut sum = self.x - other.x;
            if sum < 0 { sum += M::m(); }
            ModInt::new_internal(sum)
        }
    }
    impl<M: Mod, T: Into<ModInt<M>>> Mul<T> for ModInt<M> {
        type Output = Self;
        fn mul(self, other: T) -> Self { ModInt::new(self.x * other.into().x % M::m()) }
    }
    impl<M: Mod, T: Into<ModInt<M>>> AddAssign<T> for ModInt<M> {
        fn add_assign(&mut self, other: T) { *self = *self + other; }
    }
    impl<M: Mod, T: Into<ModInt<M>>> SubAssign<T> for ModInt<M> {
        fn sub_assign(&mut self, other: T) { *self = *self - other; }
    }
    impl<M: Mod, T: Into<ModInt<M>>> MulAssign<T> for ModInt<M> {
        fn mul_assign(&mut self, other: T) { *self = *self * other; }
    }
    impl<M: Mod> Neg for ModInt<M> {
        type Output = Self;
        fn neg(self) -> Self { ModInt::new(0) - self }
    }
    impl<M> ::std::fmt::Display for ModInt<M> {
        fn fmt(&self, f: &mut ::std::fmt::Formatter) -> ::std::fmt::Result {
            self.x.fmt(f)
        }
    }
    impl<M: Mod> ::std::fmt::Debug for ModInt<M> {
        fn fmt(&self, f: &mut ::std::fmt::Formatter) -> ::std::fmt::Result {
            let (mut a, mut b, _) = red(self.x, M::m());
            if b < 0 {
                a = -a;
                b = -b;
            }
            write!(f, "{}/{}", a, b)
        }
    }
    impl<M: Mod> From<i64> for ModInt<M> {
        fn from(x: i64) -> Self { Self::new(x) }
    }
    // Finds the simplest fraction x/y congruent to r mod p.
    // The return value (x, y, z) satisfies x = y * r + z * p.
    fn red(r: i64, p: i64) -> (i64, i64, i64) {
        if r.abs() <= 10000 {
            return (r, 1, 0);
        }
        let mut nxt_r = p % r;
        let mut q = p / r;
        if 2 * nxt_r >= r {
            nxt_r -= r;
            q += 1;
        }
        if 2 * nxt_r <= -r {
            nxt_r += r;
            q -= 1;
        }
        let (x, z, y) = red(nxt_r, r);
        (x, y - q * z, z)
    }
} // mod mod_int

macro_rules! define_mod {
    ($struct_name: ident, $modulo: expr) => {
        #[derive(Copy, Clone, PartialEq, Eq, PartialOrd, Ord, Hash)]
        pub struct $struct_name {}
        impl mod_int::Mod for $struct_name { fn m() -> i64 { $modulo } }
    }
}
const MOD: i64 = 1_000_000_007;
define_mod!(P, MOD);
type MInt = mod_int::ModInt<P>;

struct Rng {
    x: u64,
}

impl Rng {
    fn new() -> Self {
        use std::hash::{Hasher, BuildHasher};
        let hm = std::collections::HashMap::<i32, i32>::new();
        let mut hash = hm.hasher().build_hasher();
        hash.write_u32(8128);
        Rng {
            x: hash.finish(),
        }
    }
    fn next(&mut self) -> u32 {
        let a = 0xdead_c0de_0013_3331u64;
        let b = 2457;
        self.x = self.x.wrapping_mul(a).wrapping_add(b);
        let x = self.x;
        ((x ^ x << 10) >> 32) as _
    }
}

// Lazy Segment Tree. This data structure is useful for fast folding and updating on intervals of an array
// whose elements are elements of monoid T. Note that constructing this tree requires the identity
// element of T and the operation of T. This is monomorphised, because of efficiency. T := i64, biop = max, upop = (+)
// Reference: https://github.com/atcoder/ac-library/blob/master/atcoder/lazysegtree.hpp
// Verified by: https://judge.yosupo.jp/submission/68794
//              https://atcoder.jp/contests/joisc2021/submissions/27734236
pub trait ActionRing {
    type T: Clone + Copy; // data
    type U: Clone + Copy + PartialEq + Eq; // action
    fn biop(x: Self::T, y: Self::T) -> Self::T;
    fn update(x: Self::T, a: Self::U) -> Self::T;
    fn upop(fst: Self::U, snd: Self::U) -> Self::U;
    fn e() -> Self::T;
    fn upe() -> Self::U; // identity for upop
}
pub struct LazySegTree<R: ActionRing> {
    n: usize,
    dep: usize,
    dat: Vec<R::T>,
    lazy: Vec<R::U>,
}
impl<R: ActionRing> LazySegTree<R> {
    pub fn new(n_: usize) -> Self {
        let mut n = 1;
        let mut dep = 0;
        while n < n_ { n *= 2; dep += 1; } // n is a power of 2
        LazySegTree {
            n: n,
            dep: dep,
            dat: vec![R::e(); 2 * n],
            lazy: vec![R::upe(); n],
        }
    }
    #[allow(unused)]
    pub fn with(a: &[R::T]) -> Self {
        let mut ret = Self::new(a.len());
        let n = ret.n;
        for i in 0..a.len() {
            ret.dat[n + i] = a[i];
        }
        for i in (1..n).rev() {
            ret.update_node(i);
        }
        ret
    }
    #[inline]
    pub fn set(&mut self, idx: usize, x: R::T) {
        debug_assert!(idx < self.n);
        self.apply_any(idx, |_t| x);
    }
    #[inline]
    pub fn apply(&mut self, idx: usize, f: R::U) {
        debug_assert!(idx < self.n);
        self.apply_any(idx, |t| R::update(t, f));
    }
    pub fn apply_any<F: Fn(R::T) -> R::T>(&mut self, idx: usize, f: F) {
        debug_assert!(idx < self.n);
        let idx = idx + self.n;
        for i in (1..self.dep + 1).rev() {
            self.push(idx >> i);
        }
        self.dat[idx] = f(self.dat[idx]);
        for i in 1..self.dep + 1 {
            self.update_node(idx >> i);
        }
    }
    pub fn get(&mut self, idx: usize) -> R::T {
        debug_assert!(idx < self.n);
        let idx = idx + self.n;
        for i in (1..self.dep + 1).rev() {
            self.push(idx >> i);
        }
        self.dat[idx]
    }
    /* [l, r) (note: half-inclusive) */
    #[inline]
    pub fn query(&mut self, rng: std::ops::Range<usize>) -> R::T {
        let (l, r) = (rng.start, rng.end);
        debug_assert!(l <= r && r <= self.n);
        if l == r { return R::e(); }
        let mut l = l + self.n;
        let mut r = r + self.n;
        for i in (1..self.dep + 1).rev() {
            if ((l >> i) << i) != l { self.push(l >> i); }
            if ((r >> i) << i) != r { self.push((r - 1) >> i); }
        }
        let mut sml = R::e();
        let mut smr = R::e();
        while l < r {
            if (l & 1) != 0 {
                sml = R::biop(sml, self.dat[l]);
                l += 1;
            }
            if (r & 1) != 0 {
                r -= 1;
                smr = R::biop(self.dat[r], smr);
            }
            l >>= 1;
            r >>= 1;
        }
        R::biop(sml, smr)
    }
    /* ary[i] = upop(ary[i], v) for i in [l, r) (half-inclusive) */
    #[inline]
    pub fn update(&mut self, rng: std::ops::Range<usize>, f: R::U)  {
        let (l, r) = (rng.start, rng.end);
        debug_assert!(l <= r && r <= self.n);
        if l == r { return; }
        let mut l = l + self.n;
        let mut r = r + self.n;
        for i in (1..self.dep + 1).rev() {
            if ((l >> i) << i) != l { self.push(l >> i); }
            if ((r >> i) << i) != r { self.push((r - 1) >> i); }
        }
        {
            let l2 = l;
            let r2 = r;
            while l < r {
                if (l & 1) != 0 {
                    self.all_apply(l, f);
                    l += 1;
                }
                if (r & 1) != 0 {
                    r -= 1;
                    self.all_apply(r, f);
                }
                l >>= 1;
                r >>= 1;
            }
            l = l2;
            r = r2;
        }
        for i in 1..self.dep + 1 {
            if ((l >> i) << i) != l { self.update_node(l >> i); }
            if ((r >> i) << i) != r { self.update_node((r - 1) >> i); }
        }
    }
    #[inline]
    fn update_node(&mut self, k: usize) {
        self.dat[k] = R::biop(self.dat[2 * k], self.dat[2 * k + 1]);
    }
    fn all_apply(&mut self, k: usize, f: R::U) {
        self.dat[k] = R::update(self.dat[k], f);
        if k < self.n {
            self.lazy[k] = R::upop(self.lazy[k], f);
        }
    }
    fn push(&mut self, k: usize) {
        let val = self.lazy[k];
        self.all_apply(2 * k, val);
        self.all_apply(2 * k + 1, val);
        self.lazy[k] = R::upe();
    }
}

enum AffineRolling3207 {}

type AffineInt = MInt; // Change here to change type
impl ActionRing for AffineRolling3207 {
    type T = (AffineInt, AffineInt, AffineInt); // data, bias, cumulative sum of bias^?
    type U = (AffineInt, AffineInt); // action, (a, b) |-> x |-> ax + b
    fn biop((x, s, t): Self::T, (y, u, v): Self::T) -> Self::T {
        (x * u + y, s * u, t * u + v)
    }
    fn update((x, bias, s): Self::T, (a, b): Self::U) -> Self::T {
        (x * a + b * s, bias, s)
    }
    fn upop(fst: Self::U, snd: Self::U) -> Self::U {
        let (a, b) = fst;
        let (c, d) = snd;
        (a * c, b * c + d)
    }
    fn e() -> Self::T {
        (0.into(), 1.into(), 0.into())
    }
    fn upe() -> Self::U { // identity for upop
        (1.into(), 0.into())
    }
}

fn hashes(
    h: usize, w: usize,
    ijx: &[(usize, usize, i8)],
    ldru: &[(usize, usize, usize, usize)],
    bases: &[MInt; 2],
    letters: &[MInt; 10],
) -> Vec<MInt> {
    let q = ldru.len();
    let mut st = LazySegTree::<AffineRolling3207>::new(h);
    for i in 0..h {
        st.set(i, (0.into(), bases[0], 1.into()));
    }
    let mut ev = vec![vec![]; w + 1];
    for &(i, j, x) in ijx {
        ev[j].push((2, i, letters[x as usize]));
    }
    for i in 0..w {
        ev[i].push((1, 0, 0.into()));
    }
    for i in 0..q {
        let (_, d, _, u) = ldru[i];
        ev[d].push((0, i, -bases[1].pow((u - d) as i64)));
        ev[u].push((0, i, MInt::new(1)));
    }
    for i in 0..w + 1 {
        ev[i].sort();
    }
    let mut hashes = vec![MInt::new(0); q];
    for i in 0..w + 1 {
        for &(ty, idx, x) in &ev[i] {
            if ty == 0 {
                let (l, _, r, _) = ldru[idx];
                hashes[idx] += x * st.query(l..r).0;
            } else if ty == 1 {
                st.update(0..h, (bases[1], 0.into()));
            } else {
                st.apply(idx, (1.into(), x));
            }
        }
    }
    hashes
}

// ​​https://yukicoder.me/problems/no/3207 (3.5)
// 上下それぞれの方向から平面走査して rolling hash を計算すればよい。
// 二つの方向で計算する時、rolling hash の bases と文字に対する乱数が同じになるようにすること。
// -> サンプルが合わずに困ったが、d のときのハッシュ値は単に -1 倍するのではなく bases[1]^{u-d} 倍する必要があることに気づいた。
fn main() {
    let out = std::io::stdout();
    let mut out = BufWriter::new(out.lock());
    macro_rules! puts {($($format:tt)*) => (let _ = write!(out,$($format)*););}
    input! {
        h: usize, w: usize,
        n: usize,
        ijx: [(usize1, usize1, i8); n],
        q: usize,
        ldru: [(usize1, usize1, usize, usize); q],
    }
    let mut rng = Rng::new();
    let mut ok = vec![true; q];
    for _ in 0..2 {
        let mut bases = [MInt::new(0); 2];
        let mut letters = [MInt::new(0); 10];
        for i in 0..2 {
            bases[i] = MInt::new(rng.next() as i64);
            bases[i] = MInt::new(10);
        }
        for i in 1..10 {
            letters[i] = MInt::new(rng.next() as i64);
            letters[i] = MInt::new(i as i64);
        }
        let hashes1 = hashes(h, w, &ijx, &ldru, &bases, &letters);
        let ijx = ijx.iter().map(|&(i, j, x)| {
            let y = match x {
                6 => 9,
                9 => 6,
                _ => x,
            };
            (h - 1 - i, w - 1 - j, y)
        }).collect::<Vec<_>>();
        let ldru = ldru.iter().map(|&(l, d, r, u)| {
            (h - r, w - u, h - l, w - d)
        }).collect::<Vec<_>>();
        let hashes2 = hashes(h, w, &ijx, &ldru, &bases, &letters);
        for i in 0..q {
            ok[i] &= hashes1[i] == hashes2[i];
        }
    }
    for i in 0..q {
        puts!("{}\n", if ok[i] { "Yes" } else { "No" });
    }
}