結果

問題 No.215 素数サイコロと合成数サイコロ (3-Hard)
ユーザー koba-e964
提出日時 2023-03-31 11:15:31
言語 Rust
(1.83.0 + proconio)
結果
TLE  
実行時間 -
コード長 9,659 bytes
コンパイル時間 15,731 ms
コンパイル使用メモリ 387,172 KB
実行使用メモリ 17,824 KB
最終ジャッジ日時 2024-09-22 16:25:15
合計ジャッジ時間 23,041 ms
ジャッジサーバーID
（参考情報） 		judge4 / judge5
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ファイルパターン 結果
other TLE * 1 -- * 1
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ソースコード

diff #
プレゼンテーションモードにする

use std::io::Read;
fn get_word() -> String {
    let stdin = std::io::stdin();
    let mut stdin=stdin.lock();
    let mut u8b: [u8; 1] = [0];
    loop {
        let mut buf: Vec<u8> = Vec::with_capacity(16);
        loop {
            let res = stdin.read(&mut u8b);
            if res.unwrap_or(0) == 0 || u8b[0] <= b' ' {
                break;
            } else {
                buf.push(u8b[0]);
            }
        }
        if buf.len() >= 1 {
            let ret = String::from_utf8(buf).unwrap();
            return ret;
        }
    }
}
fn get<T: std::str::FromStr>() -> T { get_word().parse().ok().unwrap() }
/// 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)]
        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>;
// Verified by: yukicoder No.1112
// https://yukicoder.me/submissions/510746
// https://en.wikipedia.org/wiki/Berlekamp%E2%80%93Massey_algorithm
// Complexity: O(n^2)
// Depends on MInt.rs
fn berlekamp_massey<P: mod_int::Mod + PartialEq>(
    n: usize,
    s: &[mod_int::ModInt<P>],
) -> Vec<mod_int::ModInt<P>>{
    type ModInt<P> = mod_int::ModInt<P>;
    let mut b = ModInt::new(1);
    let mut cp = vec![ModInt::new(0); n + 1];
    let mut bp = vec![mod_int::ModInt::new(0); n];
    cp[0] = mod_int::ModInt::new(1);
    bp[0] = mod_int::ModInt::new(1);
    let mut m = 1;
    let mut l = 0;
    for i in 0..2 * n + 1 {
        assert!(i >= l);
        assert!(l <= n);
        if i == 2 * n { break; }
        let mut d = s[i];
        for j in 1..l + 1 {
            d += cp[j] * s[i - j];
        }
        if d == ModInt::new(0) {
            m += 1;
            continue;
        }
        if 2 * l > i {
            // cp -= d/b * x^m * bp
            let factor = d * b.inv();
            for j in 0..n + 1 - m {
                cp[m + j] -= factor * bp[j];
            }
            m += 1;
            continue;
        }
        let factor = d * b.inv();
        let tp = cp.clone();
        for j in 0..n + 1 - m {
            cp[m + j] -= factor * bp[j];
        }
        bp = tp;
        b = d;
        l = i + 1 - l;
        m = 1;
    }
    cp[0..l + 1].to_vec()
}
fn polymul(a: &[MInt], b: &[MInt], mo: &[MInt]) -> Vec<MInt> {
    let n = a.len();
    debug_assert_eq!(b.len(), n);
    debug_assert_eq!(mo.len(), n + 1);
    debug_assert_eq!(mo[n], 1.into());
    let mut ret = vec![MInt::new(0); 2 * n - 1];
    for i in 0..n {
        for j in 0..n {
            ret[i + j] += a[i] * b[j];
        }
    }
    for i in (n..2 * n - 1).rev() {
        let val = ret[i];
        for j in 0..n {
            ret[i - n + j] -= val * mo[j];
        }
    }
    ret[..n].to_vec()
}
    
fn polypow(a: &[MInt], mut e: i64, mo: &[MInt]) -> Vec<MInt> {
    let n = a.len();
    debug_assert_eq!(mo.len(), n + 1);
    let mut prod = vec![MInt::new(0); n];
    prod[0] += 1;
    let mut cur = a.to_vec();
    while e > 0 {
        if e % 2 == 1 {
            prod = polymul(&prod, &cur, mo);
        }
        cur = polymul(&cur, &cur, mo);
        e /= 2;
    }
    prod
}
// Finds u a^e v^T by using Berlekamp-massey algorithm.
// The linear map a is given as a closure.
// Complexity: O(n^2 log e + nT(n)) where n = |u| and T(n) = complexity of a.
// Ref: https://yukicoder.me/wiki/black_box_linear_algebra
fn eval_matpow<F: FnMut(&[MInt]) -> Vec<MInt>>(mut a: F, e: i64, u: &[MInt], v: &[MInt]) -> MInt {
    let k = u.len();
    // Find first 2k terms
    let mut terms = vec![MInt::new(0); 2 * k];
    let mut cur = u.to_vec();
    for pos in 0..2 * k {
        for i in 0..k {
            terms[pos] += cur[i] * v[i];
        }
        cur = a(&cur);
    }
    let mut poly = berlekamp_massey(k, &terms);
    poly.reverse();
    if poly.len() == 2 {
        let r = -poly[0];
        return terms[0] * r.pow(e);
    }
    let mut base = vec![MInt::new(0); poly.len() - 1];
    base[1] += 1;
    let powpoly = polypow(&base, e, &poly);
    let mut ans = MInt::new(0);
    for i in 0..poly.len() - 1 {
        ans += powpoly[i] * terms[i];
    }
    ans
}
fn get_trans(a: [usize; 6], c: usize) -> Vec<MInt> {
    let len = a[5] * c + 1;
    let mut dp = vec![vec![MInt::new(0); len]; c + 1];
    dp[0][0] += 1;
    for &v in &a {
        // *= (1-x^{v{p+1}}y^{p+1}) / (1 - x^vy)
        for j in 0..c {
            for i in 0..len - v {
                dp[j + 1][i + v] = dp[j + 1][i + v] + dp[j][i];
            }
        }
    }
    dp[c].to_vec()
}
// https://yukicoder.me/problems/no/215 (6)
// 行列累乗でやろうとすると 7500^3 回の計算を要するため、kitamasa 法を使う。数列のゼロ化多項式がわかれば、最初の 7500 項程度を計算することで Bostan
    -Mori が使えて O(7500^2 log N)。
// 数列のゼロ化多項式は Berlekamp-Massey で O(7500^2) 程度で計算できるはずなので、これで計算できる。
fn main() {
    let n: i64 = get();
    let p: usize = get();
    let c: usize = get();
    let len = p * 13 + c * 12 + 1;
    let mut trans = vec![MInt::new(0); len];
    trans[0] += 1;
    let ps = [2, 3, 5, 7, 11, 13];
    let cs = [4, 6, 8, 9, 10, 12];
    let ptrans = get_trans(ps, p);
    let ctrans = get_trans(cs, c);
    for i in 0..ptrans.len() {
        for j in 0..ctrans.len() {
            trans[i + j] += ptrans[i] * ctrans[j];
        }
    }
    let a = |u: &[MInt]| {
        let mut v = vec![MInt::new(0); len - 1];
        for i in 0..len - 2 {
            v[i + 1] = u[i];
        }
        for i in 0..len - 1 {
            v[0] += u[i] * trans[i + 1];
        }
        v
    };
    let mut start = vec![MInt::new(0); len - 1];
    start[0] += 1;
    let mut rec = vec![MInt::new(0); len - 1];
    for i in (0..len - 1).rev() {
        rec[i] = trans[i + 1];
        if i + 1 < len - 1 {
            rec[i] = rec[i + 1] + rec[i];
        }
    }
    let val = eval_matpow(a, n - 1, &start, &rec);
    println!("{}", val);
}
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