結果

問題 No.997 Jumping Kangaroo
コンテスト
ユーザー nebocco
提出日時 2021-03-05 07:32:30
言語 Rust
(1.83.0 + proconio)
結果
AC  
実行時間 1 ms / 2,000 ms
コード長 6,711 bytes
コンパイル時間 11,419 ms
コンパイル使用メモリ 391,136 KB
実行使用メモリ 5,248 KB
最終ジャッジ日時 2024-10-06 01:12:06
合計ジャッジ時間 12,688 ms
ジャッジサーバーID
（参考情報） 		judge4 / judge1
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ファイルパターン 結果
sample AC * 3
other AC * 25
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ソースコード

diff # 

fn main() {
	let mut io = IO::new();
    input!{ from io,
		n: usize, w: usize, k: i64,
		a: [usize; n]
    }
	const MOD: i64 = 1_000_000_007;
	let mut dp = vec![0; 2 * w + 1];
	dp[0] = 1;
	for i in 1..=2*w {
		for &x in &a {
			if i >= x {
				dp[i] += dp[i-x];
			}
		}
		dp[i] %= MOD;
	}
	let p = dp[w];
	let q = (dp[2*w] - dp[w].pow(2)).rem_euclid(MOD);
	let ans = kitamasa(&vec![1, dp[w]], &vec![q, p], k, MOD);
    io.println(ans);
}


// ------------ Kitamasa's algorithm start ------------

/// d_i = d[i] (0 <= i < k),
/// a_k = c_0 * a_0 + c_1 * a_1 + ... + c_{k-1} * a_{k-1}
/// calculate a_n
/// O(k^2 logk)
pub fn kitamasa(a: &[i64], c: &[i64], n: i64, modulo: i64) -> i64 {
	/// x = f(s): a_s = f(s) * a[0..k]
	/// calculate f(s+1) from f(s)
	/// O(k)
	fn plus_one(x: &[i64], c: &[i64], modulo: i64) -> Vec<i64> {
		let k = c.len();
		let mut res = vec![0; k];
		for i in 1..k {
			res[i] = (x[i-1] + x[k-1] * c[i]) % modulo;
		}
		res[0] = x[k-1] * c[0] % modulo;
		res
	}

	/// calculate f(s*2) from f(s), f(s+1), ..., f(s+k-1)
	/// O(k^2)
	fn mult_two(x: &[i64], c: &[i64], modulo: i64) -> Vec<i64> {
		let k = c.len();
		let mut res = vec![0; k];
		let mut v = x.to_owned();
		for i in 0..k {
			for j in 0..k {
				res[j] = (res[j] + x[i] * v[j]) % modulo;
			}
			v = plus_one(&v, c, modulo);
		}
		res
	}
	let k = a.len();
	if (n as usize) < k {
		return a[n as usize];
	}
	assert!(k > 1, "please use modpow().");
	let mut s = 0;
	let mut f = vec![0; k];
	f[0] = 1;
	for i in (0..64 - n.leading_zeros()).rev() {
		if s < k {
			for _ in 0..s {
				f = plus_one(&f, c, modulo);
			}
		} else {
			f = mult_two(&f, c, modulo)
		}
		s <<= 1;
		if n >> i & 1 == 1{
			f = plus_one(&f, c, modulo);
			s |= 1;
		}
	}
	let mut res = 0;
	for i in 0..k {
		res = (res + f[i] * a[i]) % modulo;
	}
	res
}

// ------------ Kitamasa's algorithm end ------------


// ------------ io module start ------------
use std::io::{stdout, BufWriter, Read, StdoutLock, Write};

pub struct IO {
	iter: std::str::SplitAsciiWhitespace<'static>,
	buf: BufWriter<StdoutLock<'static>>,
}

impl IO {
	pub fn new() -> Self {
		let mut input = String::new();
		std::io::stdin().read_to_string(&mut input).unwrap();
		let input = Box::leak(input.into_boxed_str());
		let out = Box::new(stdout());
		IO {
			iter: input.split_ascii_whitespace(),
			buf: BufWriter::new(Box::leak(out).lock()),
		}
	}
	fn scan_str(&mut self) -> &'static str {
		self.iter.next().unwrap()
	}
	pub fn scan<T: Scan>(&mut self) -> <T as Scan>::Output {
		<T as Scan>::scan(self)
	}
	pub fn scan_vec<T: Scan>(&mut self, n: usize) -> Vec<<T as Scan>::Output> {
		(0..n).map(|_| self.scan::<T>()).collect()
	}
	pub fn print<T: Print>(&mut self, x: T) {
		<T as Print>::print(self, x);
	}
	pub fn println<T: Print>(&mut self, x: T) {
		self.print(x);
		self.print("\n");
	}
	pub fn iterln<T: Print, I: Iterator<Item = T>>(&mut self, mut iter: I, delim: &str) {
		if let Some(v) = iter.next() {
			self.print(v);
			for v in iter {
				self.print(delim);
				self.print(v);
			}
		}
		self.print("\n");
	}
	pub fn flush(&mut self) {
		self.buf.flush().unwrap();
	}
}

impl Default for IO {
	fn default() -> Self {
		Self::new()
	}
}

pub trait Scan {
	type Output;
	fn scan(io: &mut IO) -> Self::Output;
}

macro_rules! impl_scan {
	($($t:tt),*) => {
		$(
			impl Scan for $t {
				type Output = Self;
				fn scan(s: &mut IO) -> Self::Output {
					s.scan_str().parse().unwrap()
				}
			}
		)*
	};
}

impl_scan!(i16, i32, i64, isize, u16, u32, u64, usize, String, f32, f64);

pub enum Bytes {}
impl Scan for Bytes {
	type Output = &'static [u8];
	fn scan(s: &mut IO) -> Self::Output {
		s.scan_str().as_bytes()
	}
}

pub enum Chars {}
impl Scan for Chars {
	type Output = Vec<char>;
	fn scan(s: &mut IO) -> Self::Output {
		s.scan_str().chars().collect()
	}
}

pub enum Usize1 {}
impl Scan for Usize1 {
	type Output = usize;
	fn scan(s: &mut IO) -> Self::Output {
		s.scan::<usize>().wrapping_sub(1)
	}
}

impl<T: Scan, U: Scan> Scan for (T, U) {
	type Output = (T::Output, U::Output);
	fn scan(s: &mut IO) -> Self::Output {
		(T::scan(s), U::scan(s))
	}
}

impl<T: Scan, U: Scan, V: Scan> Scan for (T, U, V) {
	type Output = (T::Output, U::Output, V::Output);
	fn scan(s: &mut IO) -> Self::Output {
		(T::scan(s), U::scan(s), V::scan(s))
	}
}

impl<T: Scan, U: Scan, V: Scan, W: Scan> Scan for (T, U, V, W) {
	type Output = (T::Output, U::Output, V::Output, W::Output);
	fn scan(s: &mut IO) -> Self::Output {
		(T::scan(s), U::scan(s), V::scan(s), W::scan(s))
	}
}

pub trait Print {
	fn print(w: &mut IO, x: Self);
}

macro_rules! impl_print_int {
	($($t:ty),*) => {
		$(
			impl Print for $t {
				fn print(w: &mut IO, x: Self) {
					w.buf.write_all(x.to_string().as_bytes()).unwrap();
				}
			}
		)*
	};
}

impl_print_int!(i16, i32, i64, isize, u16, u32, u64, usize, f32, f64);

impl Print for u8 {
	fn print(w: &mut IO, x: Self) {
		w.buf.write_all(&[x]).unwrap();
	}
}

impl Print for &[u8] {
	fn print(w: &mut IO, x: Self) {
		w.buf.write_all(x).unwrap();
	}
}

impl Print for &str {
	fn print(w: &mut IO, x: Self) {
		w.print(x.as_bytes());
	}
}

impl Print for String {
	fn print(w: &mut IO, x: Self) {
		w.print(x.as_bytes());
	}
}

impl<T: Print, U: Print> Print for (T, U) {
	fn print(w: &mut IO, (x, y): Self) {
		w.print(x);
		w.print(" ");
		w.print(y);
	}
}

impl<T: Print, U: Print, V: Print> Print for (T, U, V) {
	fn print(w: &mut IO, (x, y, z): Self) {
		w.print(x);
		w.print(" ");
		w.print(y);
		w.print(" ");
		w.print(z);
	}
}

mod neboccoio_macro {
	#[macro_export]
	macro_rules! input {
		(@start $io:tt @read @rest) => {};

		(@start $io:tt @read @rest, $($rest: tt)*) => {
			input!(@start $io @read @rest $($rest)*)
		};

		(@start $io:tt @read @rest mut $($rest:tt)*) => {
			input!(@start $io @read @mut [mut] @rest $($rest)*)
		};

		(@start $io:tt @read @rest $($rest:tt)*) => {
			input!(@start $io @read @mut [] @rest $($rest)*)
		};

		(@start $io:tt @read @mut [$($mut:tt)?] @rest $var:tt: [[$kind:tt; $len1:expr]; $len2:expr] $($rest:tt)*) => {
			let $($mut)* $var = (0..$len2).map(|_| $io.scan_vec::<$kind>($len1)).collect::<Vec<Vec<$kind>>>();
			input!(@start $io @read @rest $($rest)*)
		};

		(@start $io:tt @read @mut [$($mut:tt)?] @rest $var:tt: [$kind:tt; $len:expr] $($rest:tt)*) => {
			let $($mut)* $var = $io.scan_vec::<$kind>($len);
			input!(@start $io @read @rest $($rest)*)
		};

		(@start $io:tt @read @mut [$($mut:tt)?] @rest $var:tt: $kind:tt $($rest:tt)*) => {
			let $($mut)* $var = $io.scan::<$kind>();
			input!(@start $io @read @rest $($rest)*)
		};

		(from $io:tt $($rest:tt)*) => {
			input!(@start $io @read @rest $($rest)*)
		};
	}
}

// ------------ io module end ------------
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