結果

問題 No.1474 かさまＪ
ユーザー akakimidoriakakimidori
提出日時 2021-04-09 22:05:06
言語 Rust
(1.77.0)
結果
AC  
実行時間 173 ms / 2,500 ms
コード長 9,411 bytes
コンパイル時間 2,938 ms
コンパイル使用メモリ 147,136 KB
実行使用メモリ 5,752 KB
最終ジャッジ日時 2023-09-07 11:23:37
合計ジャッジ時間 4,176 ms
ジャッジサーバーID
（参考情報） 		judge13 / judge12
このコードへのチャレンジ
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テストケース

テストケース表示
入力 結果 実行時間
実行使用メモリ
testcase_00 AC 2 ms
4,384 KB
testcase_01 AC 2 ms
4,380 KB
testcase_02 AC 14 ms
4,380 KB
testcase_03 AC 3 ms
4,376 KB
testcase_04 AC 4 ms
4,380 KB
testcase_05 AC 75 ms
4,576 KB
testcase_06 AC 82 ms
4,568 KB
testcase_07 AC 66 ms
4,544 KB
testcase_08 AC 135 ms
5,332 KB
testcase_09 AC 140 ms
5,368 KB
testcase_10 AC 10 ms
4,380 KB
testcase_11 AC 2 ms
4,376 KB
testcase_12 AC 3 ms
4,380 KB
testcase_13 AC 122 ms
5,076 KB
testcase_14 AC 153 ms
5,336 KB
testcase_15 AC 139 ms
5,376 KB
testcase_16 AC 6 ms
4,380 KB
testcase_17 AC 44 ms
4,380 KB
testcase_18 AC 144 ms
5,496 KB
testcase_19 AC 165 ms
5,596 KB
testcase_20 AC 173 ms
5,752 KB
権限があれば一括ダウンロードができます

ソースコード

diff # 

// ---------- begin ModInt ----------
mod modint {

    #[allow(dead_code)]
    pub struct Mod;
    impl ConstantModulo for Mod {
        const MOD: u32 = 1_000_000_007;
    }

    #[allow(dead_code)]
    pub struct StaticMod;
    static mut STATIC_MOD: u32 = 0;
    impl Modulo for StaticMod {
        fn modulo() -> u32 {
            unsafe { STATIC_MOD }
        }
    }

    #[allow(dead_code)]
    impl StaticMod {
        pub fn set_modulo(p: u32) {
            unsafe {
                STATIC_MOD = p;
            }
        }
    }

    use std::marker::*;
    use std::ops::*;

    pub trait Modulo {
        fn modulo() -> u32;
    }

    pub trait ConstantModulo {
        const MOD: u32;
    }

    impl<T> Modulo for T
    where
        T: ConstantModulo,
    {
        fn modulo() -> u32 {
            T::MOD
        }
    }

    pub struct ModInt<T>(pub u32, PhantomData<T>);

    impl<T> Clone for ModInt<T> {
        fn clone(&self) -> Self {
            ModInt::new_unchecked(self.0)
        }
    }

    impl<T> Copy for ModInt<T> {}

    impl<T: Modulo> Add for ModInt<T> {
        type Output = ModInt<T>;
        fn add(self, rhs: Self) -> Self::Output {
            let mut d = self.0 + rhs.0;
            if d >= T::modulo() {
                d -= T::modulo();
            }
            ModInt::new_unchecked(d)
        }
    }

    impl<T: Modulo> AddAssign for ModInt<T> {
        fn add_assign(&mut self, rhs: Self) {
            *self = *self + rhs;
        }
    }

    impl<T: Modulo> Sub for ModInt<T> {
        type Output = ModInt<T>;
        fn sub(self, rhs: Self) -> Self::Output {
            let mut d = T::modulo() + self.0 - rhs.0;
            if d >= T::modulo() {
                d -= T::modulo();
            }
            ModInt::new_unchecked(d)
        }
    }

    impl<T: Modulo> SubAssign for ModInt<T> {
        fn sub_assign(&mut self, rhs: Self) {
            *self = *self - rhs;
        }
    }

    impl<T: Modulo> Mul for ModInt<T> {
        type Output = ModInt<T>;
        fn mul(self, rhs: Self) -> Self::Output {
            let v = self.0 as u64 * rhs.0 as u64 % T::modulo() as u64;
            ModInt::new_unchecked(v as u32)
        }
    }

    impl<T: Modulo> MulAssign for ModInt<T> {
        fn mul_assign(&mut self, rhs: Self) {
            *self = *self * rhs;
        }
    }

    impl<T: Modulo> Neg for ModInt<T> {
        type Output = ModInt<T>;
        fn neg(self) -> Self::Output {
            if self.0 == 0 {
                Self::zero()
            } else {
                Self::new_unchecked(T::modulo() - self.0)
            }
        }
    }

    impl<T> std::fmt::Display for ModInt<T> {
        fn fmt<'a>(&self, f: &mut std::fmt::Formatter<'a>) -> std::fmt::Result {
            write!(f, "{}", self.0)
        }
    }

    impl<T> std::fmt::Debug for ModInt<T> {
        fn fmt<'a>(&self, f: &mut std::fmt::Formatter<'a>) -> std::fmt::Result {
            write!(f, "{}", self.0)
        }
    }

    impl<T: Modulo> std::str::FromStr for ModInt<T> {
        type Err = std::num::ParseIntError;
        fn from_str(s: &str) -> Result<Self, Self::Err> {
            let val = s.parse::<u32>()?;
            Ok(ModInt::new(val))
        }
    }

    impl<T: Modulo> From<usize> for ModInt<T> {
        fn from(val: usize) -> ModInt<T> {
            ModInt::new_unchecked((val % T::modulo() as usize) as u32)
        }
    }

    impl<T: Modulo> From<u64> for ModInt<T> {
        fn from(val: u64) -> ModInt<T> {
            ModInt::new_unchecked((val % T::modulo() as u64) as u32)
        }
    }

    impl<T: Modulo> From<i64> for ModInt<T> {
        fn from(val: i64) -> ModInt<T> {
            let m = T::modulo() as i64;
            ModInt::new((val % m + m) as u32)
        }
    }

    #[allow(dead_code)]
    impl<T> ModInt<T> {
        pub fn new_unchecked(d: u32) -> Self {
            ModInt(d, PhantomData)
        }
        pub fn zero() -> Self {
            ModInt::new_unchecked(0)
        }
        pub fn one() -> Self {
            ModInt::new_unchecked(1)
        }
        pub fn is_zero(&self) -> bool {
            self.0 == 0
        }
    }

    #[allow(dead_code)]
    impl<T: Modulo> ModInt<T> {
        pub fn new(d: u32) -> Self {
            ModInt::new_unchecked(d % T::modulo())
        }
        pub fn pow(&self, mut n: u64) -> Self {
            let mut t = Self::one();
            let mut s = *self;
            while n > 0 {
                if n & 1 == 1 {
                    t *= s;
                }
                s *= s;
                n >>= 1;
            }
            t
        }
        pub fn inv(&self) -> Self {
            assert!(self.0 != 0);
            self.pow(T::modulo() as u64 - 2)
        }
    }
}
// ---------- end ModInt ----------
// ---------- begin Precalc ----------
mod precalc {
    use super::modint::*;
    #[allow(dead_code)]
    pub struct Precalc<T> {
        inv: Vec<ModInt<T>>,
        fact: Vec<ModInt<T>>,
        ifact: Vec<ModInt<T>>,
    }
    #[allow(dead_code)]
    impl<T: Modulo> Precalc<T> {
        pub fn new(n: usize) -> Precalc<T> {
            let mut inv = vec![ModInt::one(); n + 1];
            let mut fact = vec![ModInt::one(); n + 1];
            let mut ifact = vec![ModInt::one(); n + 1];
            for i in 2..(n + 1) {
                fact[i] = fact[i - 1] * ModInt::new_unchecked(i as u32);
            }
            ifact[n] = fact[n].inv();
            if n > 0 {
                inv[n] = ifact[n] * fact[n - 1];
            }
            for i in (1..n).rev() {
                ifact[i] = ifact[i + 1] * ModInt::new_unchecked((i + 1) as u32);
                inv[i] = ifact[i] * fact[i - 1];
            }
            Precalc {
                inv: inv,
                fact: fact,
                ifact: ifact,
            }
        }
        pub fn inv(&self, n: usize) -> ModInt<T> {
            assert!(n > 0);
            self.inv[n]
        }
        pub fn fact(&self, n: usize) -> ModInt<T> {
            self.fact[n]
        }
        pub fn ifact(&self, n: usize) -> ModInt<T> {
            self.ifact[n]
        }
        pub fn perm(&self, n: usize, k: usize) -> ModInt<T> {
            if k > n {
                return ModInt::zero();
            }
            self.fact[n] * self.ifact[n - k]
        }
        pub fn comb(&self, n: usize, k: usize) -> ModInt<T> {
            if k > n {
                return ModInt::zero();
            }
            self.fact[n] * self.ifact[k] * self.ifact[n - k]
        }
    }
}
// ---------- end Precalc ----------
// ---------- begin input macro ----------
// reference: 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 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, bytes) => {
        read_value!($iter, String).bytes().collect::<Vec<u8>>()
    };
    ($iter:expr, usize1) => {
        read_value!($iter, usize) - 1
    };
    ($iter:expr, $t:ty) => {
        $iter.next().unwrap().parse::<$t>().expect("Parse error")
    };
}
// ---------- end input macro ----------

// S_i, L の条件
// 愚直なDP?
// dp[i][a][b]: i 以降を p = a, q = b 残ってる状態で正しく埋める方法の数
// q=0 ならp=0, 1, ....
// 1 <= q <= s_i なら p = l - q, ...

use modint::*;
type M = ModInt<Mod>;

fn run() {
    input! {
        n: usize,
        p: usize,
        q: usize,
        l: usize,
        s: [usize; n],
    }
    let w = 20000;
    let pc = precalc::Precalc::new(2 * w + 1000);
    if q == 0 {
        let ans = pc.comb(p + n - 1, n - 1);
        println!("{}", ans);
        return;
    }
    let mut dp = vec![vec![M::zero(); w + 1]; n + 1];
    dp[0][0] = M::one();
    for &s in s.iter() {
        for i in (1..=n).rev() {
            let mut imos = vec![M::zero(); w + 1];
            for j in 0..w {
                let v = dp[i - 1][j];
                imos[j + 1] += v;
                if j + s + 1 <= w {
                    imos[j + s + 1] -= v;
                }
            }
            for j in 1..=w {
                imos[j] = imos[j] + imos[j - 1];
                dp[i][j] += imos[j];
            }
        }
    }
    let mut ans = M::zero();
    for (i, dp) in dp.iter().enumerate() {
        for (q, &dp) in dp.iter().enumerate().take(q + 1) {
            if i * l <= p + q {
                let rem = p - (i * l - q);
                ans += dp * pc.comb(rem + n - 1, n - 1);
            }
        }
    }
    println!("{}", ans);
}

fn main() {
    run();
}
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