#625143 (Rust) No.194 フィボナッチ数列の理解(1)

提出ソース

結果

問題	No.194 フィボナッチ数列の理解(1)
ユーザー	nebocco
提出日時	2021-03-05 07:30:25
言語	Rust (1.77.0 + proconio)
結果	AC
実行時間	8 ms / 5,000 ms
コード長	6,343 bytes
コンパイル時間	15,862 ms
コンパイル使用メモリ	378,448 KB
実行使用メモリ	5,248 KB
最終ジャッジ日時	2024-10-06 01:08:11
合計ジャッジ時間	14,104 ms
ジャッジサーバーID （参考情報）	judge2 / judge5

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	1 ms 5,248 KB
testcase_01	AC	1 ms 5,248 KB
testcase_02	AC	6 ms 5,248 KB
testcase_03	AC	1 ms 5,248 KB
testcase_04	AC	3 ms 5,248 KB
testcase_05	AC	3 ms 5,248 KB
testcase_06	AC	3 ms 5,248 KB
testcase_07	AC	4 ms 5,248 KB
testcase_08	AC	1 ms 5,248 KB
testcase_09	AC	3 ms 5,248 KB
testcase_10	AC	2 ms 5,248 KB
testcase_11	AC	2 ms 5,248 KB
testcase_12	AC	3 ms 5,248 KB
testcase_13	AC	2 ms 5,248 KB
testcase_14	AC	1 ms 5,248 KB
testcase_15	AC	5 ms 5,248 KB
testcase_16	AC	4 ms 5,248 KB
testcase_17	AC	2 ms 5,248 KB
testcase_18	AC	4 ms 5,248 KB
testcase_19	AC	6 ms 5,248 KB
testcase_20	AC	8 ms 5,248 KB
testcase_21	AC	8 ms 5,248 KB
testcase_22	AC	8 ms 5,248 KB
testcase_23	AC	1 ms 5,248 KB
testcase_24	AC	5 ms 5,248 KB
testcase_25	AC	4 ms 5,248 KB
testcase_26	AC	4 ms 5,248 KB
testcase_27	AC	5 ms 5,248 KB
testcase_28	AC	2 ms 5,248 KB
testcase_29	AC	7 ms 5,248 KB
testcase_30	AC	6 ms 5,248 KB
testcase_31	AC	1 ms 5,248 KB
testcase_32	AC	2 ms 5,248 KB
testcase_33	AC	3 ms 5,248 KB
testcase_34	AC	2 ms 5,248 KB
testcase_35	AC	3 ms 5,248 KB
testcase_36	AC	4 ms 5,248 KB
testcase_37	AC	1 ms 5,248 KB
testcase_38	AC	5 ms 5,248 KB
testcase_39	AC	3 ms 5,248 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

raw source code

fn main() {
	let mut io = IO::new();
    input!{ from io,
		n: usize, k: i64,
		a: [i64; n]
    }
	let ans = if k < 2_000_000 {
		solve_brute(n, k, a)
	} else {
		solve_fast(n, k, a)
	};
    io.println(ans);
}

fn solve_brute(n: usize, k: i64, a: Vec<i64>) -> (i64, i64) {
	let mut s = a.iter().sum::<i64>() % MOD;
	let mut ss = s * 2;
	let mut q = std::collections::VecDeque::new();
	q.extend(a);
	for _ in n as i64 + 1..k {
		q.push_back(s);
		s = (s * 2 - q.pop_front().unwrap()).rem_euclid(MOD);
		ss = (ss + s) % MOD
	}
	(s, ss)
}

fn solve_fast(n: usize, k: i64, mut a: Vec<i64>) -> (i64, i64) {
	let mut r = vec![vec![0; n+1]; n+1];
	r[n] = vec![1; n+1];
	r[n-1] = vec![1; n+1];
	r[n-1][n] = 0;
	for i in 0..n-1 {
		r[i][i+1] = 1;
	}
	let mut ret = vec![vec![0; n+1]; n+1];
	for i in 0..=n {
		ret[i][i] = 1;
	}
	let mut c = k - n as i64;
	while c != 0 {
		if c & 1 == 1 {
			ret = mat_mult(&r, &ret, MOD);
		}
		r = mat_mult(&r, &r, MOD);
		c >>= 1;
	}
	a.push(a.iter().sum::<i64>() % MOD);
	let mut s = 0;
	let mut f = 0;
	for i in 0..=n {
		s = (s + ret[n][i] * a[i]) % MOD;
		f = (f + ret[n-1][i] * a[i]) % MOD;
	}
	(f, s)
}

pub fn mat_mult(a: &[Vec<i64>], b: &[Vec<i64>], modulo: i64) -> Vec<Vec<i64>> {
	let n = a.len();
	let m = a[0].len();
	assert_eq!(b.len(), m);
	let o = b[0].len();
	let mut res = vec![vec![0; o]; n];
	for i in 0..n {
		for j in 0..m {
			for k in 0..o {
				res[i][k] = (res[i][k] + a[i][j] * b[j][k]) % modulo;
			}
		}
	}
	res
}


const MOD: i64 = 1_000_000_007;

// ------------ 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 ------------

yukicoder

結果

テストケース

ソースコード