結果

問題 No.119 旅行のツアーの問題
ユーザー nebocconebocco
提出日時 2021-03-17 19:02:15
言語 Rust
(1.77.0 + proconio)
結果
WA  
実行時間 -
コード長 8,805 bytes
コンパイル時間 14,465 ms
コンパイル使用メモリ 382,736 KB
実行使用メモリ 6,824 KB
最終ジャッジ日時 2024-11-15 12:47:38
合計ジャッジ時間 15,548 ms
ジャッジサーバーID
（参考情報） 		judge1 / judge5
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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 WA -
testcase_01 WA -
testcase_02 WA -
testcase_03 WA -
testcase_04 WA -
testcase_05 WA -
testcase_06 WA -
testcase_07 WA -
testcase_08 WA -
testcase_09 WA -
testcase_10 WA -
testcase_11 WA -
testcase_12 WA -
testcase_13 WA -
testcase_14 WA -
testcase_15 WA -
testcase_16 WA -
testcase_17 WA -
testcase_18 WA -
testcase_19 WA -
testcase_20 WA -
testcase_21 WA -
testcase_22 WA -
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ソースコード

diff # 

fn main() {
	let mut io = IO::new();
    input!{ from io,
		n: usize,
		c: [i64; n]
    }
	let m = c.iter().sum::<i64>();
	let invm = Fact::modinv(m, MOD);
	let fact = Fact::new(m as usize, MOD);
	let mut x = m;
	for &y in &c {
		x = gcd(x, y);
	}
	let factors = factorize(x);
	let divisors = divisor(x);
	let mut h = std::collections::HashMap::new();
	let mut ans = 0;
	for &q in &divisors {
		let d = c.iter().map(|&y| (y / q) as usize).collect::<Vec<_>>();
		h.insert(q, fact.multi(&d));
	}
	for &(p, _) in &factors {
		for &q in &divisors {
			if x % (q * p) == 0 {
				let v = *h.get(&(p*q)).unwrap();
				*h.get_mut(&q).unwrap() -= v;
			}
		}
	}
	for &q in &divisors {
		ans = (ans + *h.get(&q).unwrap() * invm % MOD * q).rem_euclid(MOD);
	}
    io.println(ans);
}

const MOD: i64 = 1_000_000_007;

pub fn gcd(mut a: i64, mut b: i64) -> i64 {
    while b != 0 {
        a %= b;
        std::mem::swap(&mut a, &mut b);
    }
    a
}

pub fn divisor(x: i64) -> Vec<i64> {
    let mut res = Vec::new();
    for i in 1..x+1 {
        if i * i > x { break; }
        if x % i == 0 {
            res.push(i);
            if i * i < x {
                res.push(x / i);
            }
        }
    }
	res.sort();
    res
}

pub fn factorize(x: i64) -> Vec<(i64, usize)> {
    let mut y = x;
    let mut res = Vec::new();
    for i in 2..x+1 {
        if i * i > x { break; }
        if y % i == 0 {
            let mut cnt = 0;
            while y % i == 0 {
                y /= i;
                cnt += 1;
            }
            res.push((i, cnt));
        }
    }
    if y > 1 { res.push((y, 1)); }
    res
}

// ------------ struct Fact start ------------

pub struct Fact {
    modulo: i64,
    fact: Vec<i64>,
    inv_fact: Vec<i64>
}

impl Fact {
    pub fn new(size: usize, modulo: i64) -> Self {
        let mut fact = vec![1; size + 1];
        let mut inv_fact = vec![1; size + 1];
        for i in 1..size+1 {
            fact[i] = fact[i-1] * i as i64 % modulo;
        }
        inv_fact[size] = Self::modinv(fact[size], modulo);
        for i in (1..size+1).rev() {
            inv_fact[i-1] = inv_fact[i] * i as i64 % modulo;
        }
        Fact {
            modulo, fact, inv_fact
        }
    }

    pub fn extgcd(a: i64, b: i64) -> (i64, i64) {
        let mut x1 = 1;
        let mut y1 = 0;
        let mut m = a;
        let mut x2 = 0;
        let mut y2 = 1;
        let mut n = b;
        while m % n != 0 {
            let q = m / n;
            x1 -= q * x2;
            y1 -= q * y2;
            m -= q * n;
            std::mem::swap(&mut x1, &mut x2);
            std::mem::swap(&mut y1, &mut y2);
            std::mem::swap(&mut m, &mut n);
        }
        (x2, y2)
    }

    pub fn modinv(mut x: i64, modulo: i64) -> i64 {
        x = x.rem_euclid(modulo);
        Self::extgcd(x, modulo).0.rem_euclid(modulo)
    }

    pub fn permutation(&self, n:usize, r:usize) -> i64 {
        assert!(r > n || n < self.fact.len(),
        "index out of range: length is {}, but given {}", self.fact.len(), n);
        if n < r { return 0 };
        self.fact[n] * self.inv_fact[n-r] % self.modulo
    }

    pub fn combination(&self, n:usize, r:usize) -> i64 {
        assert!(r > n || n < self.fact.len(),
        "index out of range: length is {}, but given {}", self.fact.len(), n);
        if n < r { return 0 };
        self.fact[n] * self.inv_fact[r] % self.modulo * self.inv_fact[n-r] % self.modulo
    }

    pub fn multi(&self, l: &[usize]) -> i64 {
        let n = l.iter().sum::<usize>();
        assert!(n < self.fact.len(),
        "index out of range: length is {}, but given {}", self.fact.len(), n);
        let mut ans = self.fact[n];
        for &x in l {
            ans = ans * self.inv_fact[x] % self.modulo;
        }
        ans
    }
}

// ------------ struct Fact 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);

impl Scan for char {
	type Output = char;
	fn scan(s: &mut IO) -> Self::Output {
		s.scan_str().chars().next().unwrap()
	}
}

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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