結果
| 問題 | No.980 Fibonacci Convolution Hard |
| ユーザー |
 akiradeveloper
|
| 提出日時 | 2020-03-01 20:17:12 |
| 言語 | Rust (1.77.0 + proconio) |
| 結果 |
TLE
|
| 実行時間 | - |
| コード長 | 11,430 bytes |
| コンパイル時間 | 25,143 ms |
| コンパイル使用メモリ | 378,916 KB |
| 実行使用メモリ | 130,020 KB |
| 最終ジャッジ日時 | 2024-10-13 20:49:33 |
| 合計ジャッジ時間 | 23,046 ms |
|
ジャッジサーバーID （参考情報） |
judge5 / judge3 |
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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 | TLE | - |
| testcase_01 | -- | - |
| testcase_02 | -- | - |
| testcase_03 | -- | - |
| testcase_04 | -- | - |
| testcase_05 | -- | - |
| testcase_06 | -- | - |
| testcase_07 | -- | - |
| testcase_08 | -- | - |
| testcase_09 | -- | - |
| testcase_10 | -- | - |
| testcase_11 | -- | - |
| testcase_12 | -- | - |
| testcase_13 | -- | - |
| testcase_14 | -- | - |
| testcase_15 | -- | - |
| testcase_16 | -- | - |
コンパイルメッセージ
warning: method `pow` is never used
--> src/main.rs:183:12
|
169 | impl Polynomial {
| --------------- method in this implementation
...
183 | pub fn pow(&self, k: i64) -> Self {
| ^^^
|
= note: `#[warn(dead_code)]` on by default
warning: variable `Q` should have a snake case name
--> src/main.rs:114:9
|
114 | Q:usize,
| ^ help: convert the identifier to snake case: `q`
|
= note: `#[warn(non_snake_case)]` on by default
warning: variable `NMAX` should have a snake case name
--> src/main.rs:117:9
|
117 | let NMAX = 2000000;
| ^^^^ help: convert the identifier to snake case: `nmax`
warning: unused `Result` that must be used
--> src/main.rs:131:9
|
131 | writeln!(out,"{}",p2.coeff[qi]);
| ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
|
= note: this `Result` may be an `Err` variant, which should be handled
= note: `#[warn(unused_must_use)]` on by default
= note: this warning originates in the macro `writeln` (in Nightly builds, run with -Z macro-backtrace for more info)
warning: variable `L` should have a snake case name
--> src/main.rs:340:9
|
340 | let L = x.len();
| ^ help: convert the identifier to snake case: `l`
ソースコード
#[doc = " https://github.com/hatoo/competitive-rust-snippets"]
#[allow(unused_imports)]
use std::cmp::{max, min, Ordering};
#[allow(unused_imports)]
use std::collections::{BTreeMap, BTreeSet, BinaryHeap, HashMap, HashSet, VecDeque};
#[allow(unused_imports)]
use std::iter::FromIterator;
#[macro_export]
macro_rules ! chmax { ( $ x : expr , $ ( $ v : expr ) ,+ ) => { $ ( $ x = std :: cmp :: max ( $ x ,$ v ) ; ) + } ; }
#[macro_export]
macro_rules ! chmin { ( $ x : expr , $ ( $ v : expr ) ,+ ) => { $ ( $ x = std :: cmp :: min ( $ x ,$ v ) ; ) + } ; }
#[macro_export]
macro_rules ! max { ( $ x : expr ) => ( $ x ) ; ( $ x : expr , $ ( $ xs : expr ) ,+ ) => { std :: cmp :: max ( $ x , max ! ( $ ( $ xs ) ,+ ) ) } ; }
#[macro_export]
macro_rules ! min { ( $ x : expr ) => ( $ x ) ; ( $ x : expr , $ ( $ xs : expr ) ,+ ) => { std :: cmp :: min ( $ x , min ! ( $ ( $ xs ) ,+ ) ) } ; }
#[macro_export]
macro_rules ! dvec { ( $ t : expr ; $ len : expr ) => { vec ! [ $ t ; $ len ] } ; ( $ t : expr ; $ len : expr , $ ( $ rest : expr ) ,* ) => { vec ! [ dvec ! ( $ t ; $ ( $ rest ) ,* ) ; $ len ] } ; }
#[doc = " main"]
#[allow(unused_imports)]
use std::io::{stdin, stdout, BufWriter, Write};
#[macro_export]
macro_rules ! input { ( source = $ s : expr , $ ( $ r : tt ) * ) => { let mut parser = Parser :: from_str ( $ s ) ; input_inner ! { parser , $ ( $ r ) * } } ; ( parser = $ parser : ident , $ ( $ r : tt ) * ) => { input_inner ! { $ parser , $ ( $ r ) * } } ; ( new_stdin_parser = $ parser : ident , $ ( $ r : tt ) * ) => { let stdin = std :: io :: stdin ( ) ; let reader = std :: io :: BufReader :: new ( stdin . lock ( ) ) ; let mut $ parser = Parser :: new ( reader ) ; input_inner ! { $ parser , $ ( $ r ) * } } ; ( $ ( $ r : tt ) * ) => { input ! { new_stdin_parser = parser , $ ( $ r ) * } } ; }
#[macro_export]
macro_rules ! input_inner { ( $ parser : ident ) => { } ; ( $ parser : ident , ) => { } ; ( $ parser : ident , $ var : ident : $ t : tt $ ( $ r : tt ) * ) => { let $ var = read_value ! ( $ parser , $ t ) ; input_inner ! { $ parser $ ( $ r ) * } } ; }
#[macro_export]
macro_rules ! read_value { ( $ parser : ident , ( $ ( $ t : tt ) ,* ) ) => { ( $ ( read_value ! ( $ parser , $ t ) ) ,* ) } ; ( $ parser : ident , [ $ t : tt ; $ len : expr ] ) => { ( 0 ..$ len ) . map ( | _ | read_value ! ( $ parser , $ t ) ) . collect ::< Vec < _ >> ( ) } ; ( $ parser : ident , chars ) => { read_value ! ( $ parser , String ) . chars ( ) . collect ::< Vec < char >> ( ) } ; ( $ parser : ident , usize1 ) => { read_value ! ( $ parser , usize ) - 1 } ; ( $ parser : ident , $ t : ty ) => { $ parser . next ::<$ t > ( ) . expect ( "Parse error" ) } ; }
use std::io;
use std::io::BufRead;
use std::str;
pub struct Parser<R> {
reader: R,
buf: Vec<u8>,
pos: usize,
}
impl Parser<io::Empty> {
pub fn from_str(s: &str) -> Parser<io::Empty> {
Parser {
reader: io::empty(),
buf: s.as_bytes().to_vec(),
pos: 0,
}
}
}
impl<R: BufRead> Parser<R> {
pub fn new(reader: R) -> Parser<R> {
Parser {
reader: reader,
buf: vec![],
pos: 0,
}
}
pub fn update_buf(&mut self) {
self.buf.clear();
self.pos = 0;
loop {
let (len, complete) = {
let buf2 = self.reader.fill_buf().unwrap();
self.buf.extend_from_slice(buf2);
let len = buf2.len();
if len == 0 {
break;
}
(len, buf2[len - 1] <= 0x20)
};
self.reader.consume(len);
if complete {
break;
}
}
}
pub fn next<T: str::FromStr>(&mut self) -> Result<T, T::Err> {
loop {
let mut begin = self.pos;
while begin < self.buf.len() && (self.buf[begin] <= 0x20) {
begin += 1;
}
let mut end = begin;
while end < self.buf.len() && (self.buf[end] > 0x20) {
end += 1;
}
if begin != self.buf.len() {
self.pos = end;
return str::from_utf8(&self.buf[begin..end]).unwrap().parse::<T>();
} else {
self.update_buf();
}
}
}
}
#[allow(unused_macros)]
macro_rules ! debug { ( $ ( $ a : expr ) ,* ) => { eprintln ! ( concat ! ( $ ( stringify ! ( $ a ) , " = {:?}, " ) ,* ) , $ ( $ a ) ,* ) ; } }
#[doc = " https://github.com/hatoo/competitive-rust-snippets"]
const BIG_STACK_SIZE: bool = true;
#[allow(dead_code)]
fn main() {
use std::thread;
if BIG_STACK_SIZE {
thread::Builder::new()
.stack_size(32 * 1024 * 1024)
.name("solve".into())
.spawn(solve)
.unwrap()
.join()
.unwrap();
} else {
solve();
}
}
fn solve() {
let out = stdout();
let mut out = BufWriter::new(out.lock());
input!{
p:i64,
Q:usize,
q:[usize;Q]
}
let NMAX = 2000000;
let mo = 1_000_000_007;
let mut a = vec![0;NMAX+1];
a[1] = 0;
a[2] = 1;
for i in 3..=NMAX {
a[i] = p * a[i-1];
a[i] %= mo;
a[i] += a[i-2];
a[i] %= mo;
}
let p1 = Polynomial::new(a, mo);
let p2 = p1.multiply(&p1);
for qi in q {
writeln!(out,"{}",p2.coeff[qi]);
}
}
#[doc = "ax+by=gcd(a,b) returns (gcd, x, y)"]
#[allow(dead_code)]
pub fn extgcd(a: i64, b: i64) -> (i64, i64, i64) {
if b == 0 {
(a, 1, 0)
} else {
let (gcd, x, y) = extgcd(b, a % b);
(gcd, y, x - (a / b) * y)
}
}
#[doc = "ay=1 (mod m) -> y=a^{-1}"]
pub fn modinv(a: i64, m: i64) -> i64 {
let (_, x, _) = extgcd(a, m);
(m + x % m) % m
}
#[allow(dead_code)]
#[doc = " x ^ n % m"]
pub fn modpow(x: i64, n: i64, m: i64) -> i64 {
let mut res = 1;
let mut x = x % m;
let mut n = n;
while n > 0 {
if n & 1 == 1 {
res = (res * x) % m;
}
x = (x * x) % m;
n >>= 1;
}
res
}
#[derive(Debug)]
struct Polynomial {
coeff: Vec<i64>,
mo: i64,
}
impl Polynomial {
pub fn new(coeff: Vec<i64>, mo: i64) -> Polynomial {
Polynomial {
coeff: coeff,
mo: mo,
}
}
pub fn multiply(&self, other: &Self) -> Self {
assert!(self.mo == other.mo);
Polynomial {
coeff: ntt_multiply(&self.coeff, &other.coeff, self.mo),
mo: self.mo,
}
}
pub fn pow(&self, k: i64) -> Self {
let mut res = Polynomial {
coeff: vec![1],
mo: self.mo,
};
let mut x = Polynomial {
coeff: self.coeff.clone(),
mo: self.mo,
};
let mut k = k;
while k > 0 {
if k & 1 == 1 {
res = res.multiply(&x);
}
x = x.multiply(&x);
k >>= 1;
}
res
}
}
struct NTT {
pub mo: i64,
}
impl NTT {
pub fn new(mo: i64) -> NTT {
NTT { mo: mo }
}
fn _ntt(&self, a: &mut [i64], n: usize, inverse: bool) {
let g = 3;
let mut h = modpow(g, (self.mo - 1) / n as i64, self.mo);
if inverse {
h = modinv(h, self.mo);
}
let mut i = 0;
for j in 1..n - 1 {
let mut k = n >> 1;
loop {
i ^= k;
if k > i {
k >>= 1;
} else {
break;
}
}
if j < i {
let tmp = a[i];
a[i] = a[j];
a[j] = tmp;
}
}
let mut m = 1;
loop {
if m < n {
let m2 = m * 2;
let base = modpow(h, (n / m2) as i64, self.mo);
let mut w = 1;
for x in 0..m {
let mut s = x;
loop {
if s < n {
let u = a[s];
let d = (a[s + m] * w) % self.mo;
a[s] = u + d;
if a[s] >= self.mo {
a[s] -= self.mo;
}
a[s + m] = u - d;
if a[s + m] < 0 {
a[s + m] += self.mo;
}
s += m2;
} else {
break;
}
}
w = (w * base) % self.mo;
}
m *= 2;
} else {
break;
}
}
for i in 0..n {
if a[i] < 0 {
a[i] += self.mo;
}
}
}
fn ntt(&self, a: &mut [i64], n: usize) {
self._ntt(a, n, false);
}
fn intt(&self, a: &mut [i64], n: usize) {
self._ntt(a, n, true);
let n_inv = modinv(a.len() as i64, self.mo);
for i in 0..n {
a[i] = (a[i] * n_inv) % self.mo;
}
}
pub fn convolve(&self, a: &[i64], b: &[i64]) -> Vec<i64> {
let mut a = a.to_vec();
let mut b = b.to_vec();
let mut n = 1;
while n < a.len() + b.len() {
n <<= 1;
}
a.resize(n, 0);
b.resize(n, 0);
self.ntt(&mut a, n);
self.ntt(&mut b, n);
let mut c = vec![0; n];
for i in 0..n {
c[i] = (a[i] * b[i]) % self.mo;
}
self.intt(&mut c, n);
c
}
}
#[doc = "compute minimum x from a list of x % m[i] = r[i]"]
pub fn garner(mr: Vec<(i64, i64)>, mo: i64) -> i64 {
let mut mr = mr;
mr.push((mo, 0));
let mut coef = vec![1; mr.len()];
let mut constants = vec![0; mr.len()];
for i in 0..mr.len() - 1 {
let v = (mr[i].1 + mr[i].0 - constants[i]) * modinv(coef[i], mr[i].0) % mr[i].0;
for j in i + 1..mr.len() {
constants[j] += coef[j] * v;
constants[j] %= mr[j].0;
coef[j] *= mr[i].0;
coef[j] %= mr[j].0;
}
}
constants[mr.len() - 1]
}
pub fn ntt_multiply(a: &[i64], b: &[i64], mo: i64) -> Vec<i64> {
let mut a = a.to_vec();
let mut b = b.to_vec();
let n = a.len();
let m = b.len();
for i in 0..n {
a[i] %= mo;
}
for i in 0..m {
b[i] %= mo;
}
let ntt1 = NTT::new(167772161);
let ntt2 = NTT::new(469762049);
let ntt3 = NTT::new(1224736769);
let x = ntt1.convolve(&a, &b);
let y = ntt2.convolve(&a, &b);
let z = ntt3.convolve(&a, &b);
let m1 = ntt1.mo;
let m2 = ntt2.mo;
let m3 = ntt3.mo;
let m1_inv_m2 = modinv(m1, m2);
let m12_inv_m3 = modinv(m1 * m2, m3);
let m12_mod = (m1 * m2) % mo;
let L = x.len();
let mut res = vec![0; L];
for i in 0..L {
let mut v1 = (y[i] - x[i]) * m1_inv_m2;
v1 %= m2;
if v1 < 0 {
v1 += m2;
}
let mut v2 = (z[i] - (x[i] + m1 * v1) % m3) * m12_inv_m3;
v2 %= m3;
if v2 < 0 {
v2 += m3;
}
let mut const3 = (x[i] + m1 * v1 + m12_mod * v2) % mo;
if const3 < 0 {
const3 += mo;
}
res[i] = const3;
}
res.truncate(n + m - 1);
res
}