#962683 (Rust) No.2683 Two Sheets

• 問題: No.2683 Two Sheets
• ユーザー: naut3
• 提出日時: 2024-03-20 22:15:06
• 言語: Rust (1.83.0 + proconio)
• 結果: AC
• 実行時間: 23 ms / 2,000 ms
• コード長: 8,687 bytes
• コンパイル時間: 12,357 ms
• コンパイル使用メモリ: 377,852 KB
• 実行使用メモリ: 5,248 KB
• 最終ジャッジ日時: 2024-09-30 08:10:51
• 合計ジャッジ時間: 13,640 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 * 13

ソースコード

#![allow(non_snake_case, unused_imports, unused_must_use)]
use std::io::{self, prelude::*};
use std::str;

fn main() {
    let (stdin, stdout) = (io::stdin(), io::stdout());
    let mut scan = Scanner::new(stdin.lock());
    let mut out = io::BufWriter::new(stdout.lock());

    macro_rules! input {
        ($T: ty) => {
            scan.token::<$T>()
        };
        ($T: ty, $N: expr) => {
            (0..$N).map(|_| scan.token::<$T>()).collect::<Vec<_>>()
        };
    }

    let H = input!(usize);
    let W = input!(usize);
    let A = input!(usize);
    let B = input!(usize);

    let he = {
        let base = 200_005;
        let mut bit = BinaryIndexedTree::new(400_010);

        bit.add(base, MInt998244353::from(A));

        for d in 1..A {
            bit.add(base - d, MInt998244353::from(A - d));
            bit.add(base + d, MInt998244353::from(A - d));
        }

        let mut exp = MInt998244353::default();

        for i in 0..=H - A {
            let s = bit.sum(base - i..=base - i + H - A);
            exp += s;
        }

        exp /= MInt998244353::from((H - A + 1) * (H - A + 1));

        exp
    };

    let we = {
        let base = 200_005;
        let mut bit = BinaryIndexedTree::new(400_010);

        bit.add(base, MInt998244353::from(B));

        for d in 1..B {
            bit.add(base - d, MInt998244353::from(B - d));
            bit.add(base + d, MInt998244353::from(B - d));
        }

        let mut exp = MInt998244353::default();

        for i in 0..=W - B {
            let s = bit.sum(base - i..=base - i + W - B);
            exp += s;
        }

        exp /= MInt998244353::from((W - B + 1) * (W - B + 1));

        exp
    };

    let ans = MInt998244353::from(2 * A * B) - he * we;
    writeln!(out, "{}", ans);
}

pub struct BinaryIndexedTree<T> {
    tree: Vec<T>,
}

impl<T: Default + Clone + Copy + std::ops::AddAssign + std::ops::Sub<Output = T>>
    BinaryIndexedTree<T>
{
    /// self = [0; size]
    pub fn new(size: usize) -> Self {
        return Self {
            tree: vec![T::default(); size + 1],
        };
    }

    /// self[i] <- self[i] + w
    pub fn add(&mut self, i: usize, w: T) {
        self._inner_add(i + 1, w);
    }

    /// return Σ_{j ∈ [0, i]} self[j]
    pub fn prefix_sum(&self, i: usize) -> T {
        self._inner_sum(i + 1)
    }

    /// return Σ_{j ∈ range} self[j]
    pub fn sum<R: std::ops::RangeBounds<usize>>(&self, range: R) -> T {
        let left = match range.start_bound() {
            std::ops::Bound::Included(&l) => l,
            std::ops::Bound::Excluded(&l) => l + 1,
            std::ops::Bound::Unbounded => 0,
        };

        let right = match range.end_bound() {
            std::ops::Bound::Included(&r) => r,
            std::ops::Bound::Excluded(&r) => r - 1,
            std::ops::Bound::Unbounded => self.tree.len() - 2,
        };

        if left == 0 {
            return self.prefix_sum(right);
        } else {
            return self.prefix_sum(right) - self.prefix_sum(left - 1);
        }
    }

    fn _inner_add(&mut self, mut i: usize, w: T) {
        while i < self.tree.len() {
            self.tree[i] += w;
            i += i & i.wrapping_neg();
        }
    }

    fn _inner_sum(&self, mut i: usize) -> T {
        let mut ret = T::default();
        while i > 0 {
            ret += self.tree[i];
            i -= i & i.wrapping_neg();
        }
        return ret;
    }
}

pub type MInt998244353 = ModInt<998244353>;

#[derive(Clone, Copy, Eq, PartialEq, Debug)]
pub struct ModInt<const P: u32> {
    value: u32,
}

impl<const P: u32> ModInt<P> {
    pub fn value(&self) -> u32 {
        assert!(self.value < P);
        return self.value;
    }

    pub fn new() -> Self {
        return Self { value: 0 };
    }

    pub fn from_raw(x: u32) -> Self {
        return Self { value: x };
    }

    pub fn inv(&self) -> Self {
        pub fn ext_gcd(a: isize, b: isize) -> (isize, isize) {
            let mut a_k = a;
            let mut b_k = b;

            let mut q_k = a_k / b_k;
            let mut r_k = a_k % b_k;

            let mut x_k = 0;
            let mut y_k = 1;
            let mut z_k = 1;
            let mut w_k = -q_k;

            a_k = b_k;
            b_k = r_k;

            while r_k != 0 {
                q_k = a_k / b_k;
                r_k = a_k % b_k;

                a_k = b_k;
                b_k = r_k;

                let nx = z_k;
                let ny = w_k;
                let nz = x_k - q_k * z_k;
                let nw = y_k - q_k * w_k;

                x_k = nx;
                y_k = ny;
                z_k = nz;
                w_k = nw;
            }

            (x_k, y_k)
        }

        let val = self.value() as isize;

        let ret = ext_gcd(val, P as isize).0;

        return Self::from(ret);
    }

    pub fn pow(&self, mut x: u64) -> Self {
        let mut ret = ModInt::from_raw(1);
        let mut a = self.clone();

        while x > 0 {
            if (x & 1) == 1 {
                ret = ret * a;
            }

            a *= a;
            x >>= 1;
        }

        return ret;
    }
}

impl<const P: u32> std::ops::Add for ModInt<P> {
    type Output = Self;
    fn add(self, rhs: Self) -> Self::Output {
        let mut ret = self.value() + rhs.value();

        if ret >= P {
            ret -= P;
        }

        return Self::from_raw(ret);
    }
}

impl<const P: u32> std::ops::AddAssign for ModInt<P> {
    fn add_assign(&mut self, rhs: Self) {
        self.value = (self.clone() + rhs).value();
    }
}

impl<const P: u32> std::ops::Sub for ModInt<P> {
    type Output = Self;
    fn sub(self, rhs: Self) -> Self::Output {
        if self.value() >= rhs.value() {
            return Self::from_raw(self.value() - rhs.value());
        } else {
            return Self::from_raw(P + self.value() - rhs.value());
        }
    }
}

impl<const P: u32> std::ops::SubAssign for ModInt<P> {
    fn sub_assign(&mut self, rhs: Self) {
        self.value = (self.clone() - rhs).value();
    }
}

impl<const P: u32> std::ops::Mul for ModInt<P> {
    type Output = Self;
    fn mul(self, rhs: Self) -> Self::Output {
        let ret = self.value() as usize * rhs.value() as usize;
        return Self::from(ret);
    }
}

impl<const P: u32> std::ops::MulAssign for ModInt<P> {
    fn mul_assign(&mut self, rhs: Self) {
        self.value = (self.clone() * rhs).value();
    }
}

impl<const P: u32> std::ops::Div for ModInt<P> {
    type Output = Self;
    fn div(self, rhs: Self) -> Self::Output {
        self * rhs.inv()
    }
}

impl<const P: u32> std::ops::DivAssign for ModInt<P> {
    fn div_assign(&mut self, rhs: Self) {
        self.value = (self.clone() / rhs).value();
    }
}

impl<const P: u32> std::ops::Neg for ModInt<P> {
    type Output = Self;
    fn neg(self) -> Self::Output {
        let value = self.value();
        return Self { value: P - value };
    }
}

macro_rules! int_from_impl {
    ($($t: ty), *) => {
        $(
            #[allow(unused_comparisons)]
            impl<const P: u32> From<$t> for ModInt<P> {
                fn from(value: $t) -> Self {
                    if value >= 0 {
                        Self {
                            value: (value % P as $t) as u32,
                        }
                    } else {
                        let rem = P as $t + value % P as $t;
                        Self { value: rem as u32 }
                    }
                }
            }
        ) *
    };
}

int_from_impl!(usize, isize, u64, i64, u32, i32, u128, i128);

impl<const P: u32> Default for ModInt<P> {
    fn default() -> Self {
        Self { value: 0 }
    }
}

impl<const P: u32> std::fmt::Display for ModInt<P> {
    fn fmt(&self, f: &mut std::fmt::Formatter<'_>) -> std::fmt::Result {
        write!(f, "{}", self.value)
    }
}

struct Scanner<R> {
    reader: R,
    buf_str: Vec<u8>,
    buf_iter: str::SplitWhitespace<'static>,
}
impl<R: BufRead> Scanner<R> {
    fn new(reader: R) -> Self {
        Self {
            reader,
            buf_str: vec![],
            buf_iter: "".split_whitespace(),
        }
    }
    fn token<T: str::FromStr>(&mut self) -> T {
        loop {
            if let Some(token) = self.buf_iter.next() {
                return token.parse().ok().expect("Failed parse");
            }
            self.buf_str.clear();
            self.reader
                .read_until(b'\n', &mut self.buf_str)
                .expect("Failed read");
            self.buf_iter = unsafe {
                let slice = str::from_utf8_unchecked(&self.buf_str);
                std::mem::transmute(slice.split_whitespace())
            }
        }
    }
}