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 (1.77.0 + 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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ソースコード
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);
}