AtCoder Beginner Contest 298 E

https://atcoder.jp/contests/abc298/tasks/abc298_e

単なるDPですが、Dを法とした逆数を求めなければなりません。拡張ユークリッド互除法ですね。一度書けば終わりですが。

// Unfair Sugoroku
#![allow(non_snake_case)]

use std::cmp::min;


//////////////////// constants ////////////////////

const D: usize = 998244353;


//////////////////// library ////////////////////

fn read<T: std::str::FromStr>() -> T {
    let mut line = String::new();
    std::io::stdin().read_line(&mut line).ok();
    line.trim().parse().ok().unwrap()
}

fn read_vec<T: std::str::FromStr>() -> Vec<T> {
    read::<String>().split_whitespace()
            .map(|e| e.parse().ok().unwrap()).collect()
}

// ax = by + 1 (a, b > 0)
fn linear_diophantine(a: i64, b: i64) -> Option<(i64, i64)> {
    if a == 1 {
        return Some((1, 0))
    }
    
    let q = b / a;
    let r = b % a;
    if r == 0 {
        return None
    }
    let (x1, y1) = linear_diophantine(r, a)?;
    Some((-q * x1 - y1, -x1))
}

fn inverse(a: i64, d: i64) -> i64 {
    let (x, _y) = linear_diophantine(a, d).unwrap();
    if x >= 0 {
        x % d
    }
    else {
        x % d + d
    }
}


//////////////////// process ////////////////////

fn read_input() -> (usize, usize, usize, usize, usize) {
    let v = read_vec();
    (v[0], v[1], v[2], v[3], v[4])
}

fn f(N: usize, A: usize, B: usize, P: usize, Q: usize) -> usize {
    let inv_P = inverse(P as i64, D as i64) as usize;
    let inv_Q = inverse(Q as i64, D as i64) as usize;
    
    let mut dp1: Vec<Vec<usize>>
                = (0..N+1).map(|_| (0..N+1).map(|_| 0).collect()).collect();
    let mut dp2 = dp1.to_vec();
    dp2[A][B] = 1;
    let mut win: usize = 0;
    for x in A..N {
        for y in B..N {
            for i in 1..P+1 {
                let x1 = min(x + i, N);
                let p = dp2[x][y] * inv_P % D;
                dp1[x1][y] = (dp1[x1][y] + p) % D;
                if x1 == N {
                    win += p
                }
            }
            for i in 1..Q+1 {
                let y1 = min(y + i, N);
                let p = dp1[x][y] * inv_Q % D;
                dp2[x][y1] = (dp2[x][y1] + p) % D;
            }
        }
    }
    win % D
}

fn main() {
    let (N, A, B, P, Q) = read_input();
    println!("{}", f(N, A, B, P, Q))
}