#586684 (Rust) No.1300 Sum of Inversions

• 問題: No.1300 Sum of Inversions
• ユーザー: nebocco
• 提出日時: 2020-11-28 20:42:52
• 言語: Rust (1.77.0 + proconio)
• 結果: AC
• 実行時間: 104 ms / 2,000 ms
• コード長: 16,909 bytes
• コンパイル時間: 14,345 ms
• コンパイル使用メモリ: 400,696 KB
• 実行使用メモリ: 13,204 KB
• 最終ジャッジ日時: 2024-09-13 01:37:30
• 合計ジャッジ時間: 18,600 ms
• ジャッジサーバーID （参考情報）: judge2 / judge5

入力	結果	実行時間; 実行使用メモリ
testcase_00	AC	1 ms; 6,816 KB
testcase_01	AC	1 ms; 6,816 KB
testcase_02	AC	1 ms; 6,816 KB
testcase_03	AC	80 ms; 11,448 KB
testcase_04	AC	78 ms; 11,200 KB
testcase_05	AC	65 ms; 10,396 KB
testcase_06	AC	92 ms; 12,128 KB
testcase_07	AC	89 ms; 11,804 KB
testcase_08	AC	102 ms; 12,360 KB
testcase_09	AC	97 ms; 12,340 KB
testcase_10	AC	49 ms; 7,672 KB
testcase_11	AC	52 ms; 7,832 KB
testcase_12	AC	78 ms; 11,320 KB
testcase_13	AC	76 ms; 11,092 KB
testcase_14	AC	104 ms; 12,980 KB
testcase_15	AC	97 ms; 12,172 KB
testcase_16	AC	79 ms; 11,532 KB
testcase_17	AC	47 ms; 7,464 KB
testcase_18	AC	57 ms; 8,340 KB
testcase_19	AC	70 ms; 10,768 KB
testcase_20	AC	71 ms; 10,836 KB
testcase_21	AC	69 ms; 10,824 KB
testcase_22	AC	65 ms; 10,400 KB
testcase_23	AC	94 ms; 12,116 KB
testcase_24	AC	68 ms; 10,476 KB
testcase_25	AC	53 ms; 8,112 KB
testcase_26	AC	51 ms; 8,068 KB
testcase_27	AC	59 ms; 10,300 KB
testcase_28	AC	98 ms; 12,468 KB
testcase_29	AC	68 ms; 10,788 KB
testcase_30	AC	100 ms; 12,196 KB
testcase_31	AC	64 ms; 10,428 KB
testcase_32	AC	68 ms; 10,520 KB
testcase_33	AC	19 ms; 7,168 KB
testcase_34	AC	24 ms; 8,704 KB
testcase_35	AC	65 ms; 12,516 KB
testcase_36	AC	67 ms; 13,204 KB

ソースコード

fn main() {
    type Fp = F998244353;
    let mut io = IO::new();
	let n = io.scan();
    let a: Vec<i64> = io.scan_vec(n);
    let (m, _, _, res) = compress(&a);
    let mut bitfv = FenwickTree::<Fp>::new(m);
    let mut bitbv = FenwickTree::<Fp>::new(m);
    let mut bitf = FenwickTree::<i64>::new(m);
    let mut bitb = FenwickTree::<i64>::new(m);
    let a = a.into_iter().map(Fp::new).collect::<Vec<Fp>>();
    for (&x, &y) in res.iter().zip(a.iter()) {
        bitb.add(x, 1);
        bitbv.add(x, y);
    }
    let mut ans = Fp::zero();
    for i in 0..n {
        bitb.add(res[i], -1);
        bitbv.add(res[i], -a[i]);
        let bkc = Fp::new(bitb.sum(..res[i]));
        let frc = Fp::new(bitf.sum(res[i]+1..));
        let bkv = bitbv.sum(..res[i]);
        let frv = bitfv.sum(res[i]+1..);
        ans += a[i] * bkc * frc + bkc * frv + frc * bkv;
        bitf.add(res[i], 1);
        bitfv.add(res[i], a[i]);
    }
    io.println(ans);
}

// ------------ traits start ------------

impl<T: Mod> Scan for Fp<T> {
    fn scan(s: &mut IO) -> Self {
        Self::new(i64::scan(s))
    }
}

impl<T: Mod> Print for Fp<T> {
    fn print(w: &mut IO, x: Self) {
        w.print(x.into_inner());
    }
}

// ------------ traits end ------------

// ------------ libraries start ------------

use std::collections::HashMap;

pub fn compress<T: Clone + Ord + Hash>(l: &[T])-> (usize, HashMap<T, usize>, Vec<T>, Vec<usize>) {
    let mut f = l.to_owned();
    f.sort();
    f.dedup();
    let dict: HashMap<T, usize> = f.iter().cloned().zip(0..f.len()).collect();
    let res: Vec<usize> = l.iter().map(|x| *dict.get(x).unwrap()).collect();
    (f.len(), dict, f, res)
}

// ------------ FenwickTree with generics start ------------

#[derive(Clone, Debug)]
pub struct FenwickTree<T>(Vec<T>);

impl<T: Monoid> FenwickTree<T> {
    #[inline]
    fn lsb(x: usize) -> usize {
        x & x.wrapping_neg()
    }

    pub fn new(n: usize) -> Self {
        Self(vec![T::zero(); n+1])
    }

    pub fn prefix_sum(&self, i: usize) -> T {
        std::iter::successors(Some(i), |&i| Some(i - Self::lsb(i)))
        .take_while(|&i| i != 0)
        .map(|i| self.0[i].clone())
        .fold(T::zero(), |sum, x| sum + x)
    }

    pub fn add(&mut self, i: usize, x: T) {
        let n = self.0.len();
        std::iter::successors(Some(i + 1), |&i| Some(i + Self::lsb(i)))
        .take_while(|&i| i < n)
        .for_each(|i| self.0[i] = self.0[i].clone() + x.clone());
    }

    pub fn partition(&self, pred: impl Fn(usize, &T) -> bool) -> (usize, T) {
        assert!(pred(0, &self.0[0]), "need to be pred(0, 0)");
        let mut j = 0;
        let mut current = self.0[0].clone();
        let n = self.0.len();
        for d in std::iter::successors(Some(n.next_power_of_two() >> 1), |&d| { Some(d >> 1)})
            .take_while(|&d| d != 0)
        {
            if j + d < n {
                let next = current.clone() + self.0[j + d].clone();
                if pred(j + d, &next) {
                    current = next;
                    j += d;
                }
            }
        }
        (j, current)
    }
}

impl<T: Monoid> From<Vec<T>> for FenwickTree<T> {
    fn from(src: Vec<T>) -> Self {
        let mut table = std::iter::once(T::zero())
            .chain(src.into_iter())
            .collect::<Vec<T>>();
        let n = table.len();
        (1..n)
            .map(|i| (i, i + Self::lsb(i)))
            .filter(|&(_, j)| j < n)
            .for_each(|(i, j)| {
                table[j] = table[j].clone() + table[i].clone();
            });
        Self(table)
    }
}

impl<T: Group> FenwickTree<T> {
    pub fn sum<R: RangeBounds<usize>>(&self, rng: R) -> T {
        let Range { start, end } = bounds_within(rng, self.0.len() - 1);
        self.prefix_sum(end) + -self.prefix_sum(start)
    }
}

use std::ops::Bound::{Excluded, Included, Unbounded};
use std::ops::{Range, RangeBounds};

/// 区間を配列サイズに収まるように丸める。
///
/// 与えられた区間 `r` と `0..len` の共通部分を、有界な半開区間として返す。
///
/// # Examples
/// ```
/// use bibliotheca::utils::bounds::bounds_within;
///
/// assert_eq!(bounds_within(.., 7), 0..7);
/// assert_eq!(bounds_within(..=4, 7), 0..5);
/// ```
pub fn bounds_within<R: RangeBounds<usize>>(r: R, len: usize) -> Range<usize> {
    let e_ex = match r.end_bound() {
        Included(&e) => e + 1,
        Excluded(&e) => e,
        Unbounded => len,
    }
    .min(len);
    let s_in = match r.start_bound() {
        Included(&s) => s,
        Excluded(&s) => s + 1,
        Unbounded => 0,
    }
    .min(e_ex);
    s_in..e_ex
}

// ------------ FenwickTree with generics end ------------


// ------------ libraries end ------------

// ------------ traits start ------------
use std::{
    fmt::{Debug, Display},
    hash::Hash,
    iter,
    marker::PhantomData,
    ops,
};
crate::define_fp!(pub F998244353, Mod998244353, 998244353);
crate::define_fp!(pub F1000000007, Mod1000000007, 1000000007);

#[derive(Clone, PartialEq, Copy, Eq, Hash)]
pub struct Fp<T>(i64, PhantomData<T>);
pub trait Mod: Debug + Clone + PartialEq + Copy + Eq + Hash {
    const MOD: i64;
}
impl<T: Mod> Fp<T> {
    pub fn new(mut x: i64) -> Self {
        x %= T::MOD;
        Self::unchecked(if x < 0 { x + T::MOD } else { x })
    }
    pub fn into_inner(self) -> i64 {
        self.0
    }
    pub fn r#mod() -> i64 {
        T::MOD
    }
    pub fn inv(self) -> Self {
        assert_ne!(self.0, 0, "Zero division");
        let (sign, x) = if self.0 * 2 < T::MOD {
            (1, self.0)
        } else {
            (-1, T::MOD - self.0)
        };
        let (g, _a, b) = ext_gcd(T::MOD, x);
        let ans = sign * b;
        assert_eq!(g, 1);
        Self::unchecked(if ans < 0 { ans + T::MOD } else { ans })
    }
    pub fn frac(x: i64, y: i64) -> Self {
        Fp::new(x) / Fp::new(y)
    }
    pub fn pow(mut self, mut p: u64) -> Self {
        let mut ans = Fp::new(1);
        while p != 0 {
            if p & 1 == 1 {
                ans *= self;
            }
            self *= self;
            p >>= 1;
        }
        ans
    }
    fn unchecked(x: i64) -> Self {
        Self(x, PhantomData)
    }
}
impl<T: Mod> iter::Sum<Fp<T>> for Fp<T> {
    fn sum<I>(iter: I) -> Self
    where
        I: iter::Iterator<Item = Fp<T>>,
    {
        iter.fold(Fp::new(0), ops::Add::add)
    }
}

impl<'a, T: 'a + Mod> iter::Sum<&'a Fp<T>> for Fp<T> {
    fn sum<I>(iter: I) -> Self
    where
        I: iter::Iterator<Item = &'a Fp<T>>,
    {
        iter.fold(Fp::new(0), ops::Add::add)
    }
}

impl<T: Mod> iter::Product<Fp<T>> for Fp<T> {
    fn product<I>(iter: I) -> Self
    where
        I: iter::Iterator<Item = Fp<T>>,
    {
        iter.fold(Self::new(1), ops::Mul::mul)
    }
}

impl<'a, T: 'a + Mod> iter::Product<&'a Fp<T>> for Fp<T> {
    fn product<I>(iter: I) -> Self
    where
        I: iter::Iterator<Item = &'a Fp<T>>,
    {
        iter.fold(Self::new(1), ops::Mul::mul)
    }
}
impl<T: Mod> Debug for Fp<T> {
    fn fmt(&self, f: &mut std::fmt::Formatter<'_>) -> Result<(), std::fmt::Error> {
        write!(f, "{}", self.0)
    }
}
impl<T: Mod> Display for Fp<T> {
    fn fmt(&self, f: &mut std::fmt::Formatter<'_>) -> Result<(), std::fmt::Error> {
        write!(f, "{}", self.0)
    }
}

// ax + by = gcd(x, y) なる、互いに素な (a, b) を一組探して、(g, a, b) を返します。
//
// | 0  -x |   | y  -x | | x  0 |
// | 1   b | = | a   b | | y  1 |
fn ext_gcd(x: i64, y: i64) -> (i64, i64, i64) {
    let (b, g) = {
        let mut x = x;
        let mut y = y;
        let mut u = 0;
        let mut v = 1;
        while x != 0 {
            let q = y / x;
            y -= q * x;
            v -= q * u;
            std::mem::swap(&mut x, &mut y);
            std::mem::swap(&mut u, &mut v);
        }
        (v, y)
    };
    assert_eq!((g - b * y) % x, 0);
    let a = (g - b * y) / x;
    (g, a, b)
}

#[macro_export]
macro_rules! define_fp {
    ($vis:vis $fp:ident, $t:ident, $mod:expr) => {
        #[derive(Debug, Clone, PartialEq, Copy, Eq, Hash)]
        $vis struct $t;
        // NOTE: `$crate::` があるとうまく展開できません。
        impl Mod for $t {
            const MOD: i64 = $mod;
        }
        // NOTE: `$crate::` があるとうまく展開できません。
        $vis type $fp = Fp<$t>;
    }
}

use std::ops::*;

impl<T: Mod> Associative for Fp<T> {}

impl<T: Mod> Zero for Fp<T> {
    fn zero() -> Self { Self::unchecked(0) }
    fn is_zero(&self) -> bool { self.0 == 0 }
}

impl<T: Mod> One for Fp<T> {
    fn one() -> Self { Self::unchecked(1) }
    fn is_one(&self) -> bool { self.0 == 1 }
}

impl<T: Mod> Add for Fp<T> {
    type Output = Self;
    fn add(self, rhs: Self) -> Self {
        let res = self.0 + rhs.0;
        Self::unchecked(if T::MOD <= res { res - T::MOD } else { res })
    }
}

impl<T: Mod> Sub for Fp<T> {
    type Output = Self;
    fn sub(self, rhs: Self) -> Self {
        let res = self.0 - rhs.0;
        Self::unchecked(if res < 0 { res + T::MOD } else { res })
    }
}

impl<T: Mod> Mul for Fp<T> {
    type Output = Self;
    fn mul(self, rhs: Self) -> Self {
        Self::new(self.0 * rhs.0)
    }
}

#[allow(clippy::suspicious_arithmetic_impl)]
impl<T: Mod> Div for Fp<T> {
    type Output = Self;
    fn div(self, rhs: Self) -> Self {
        self * rhs.inv()
    }
}

impl<M: Mod> Neg for Fp<M> {
    type Output = Self;
    fn neg(self) -> Self {
        if self.0 == 0 {
            Self::unchecked(0)
        } else {
            Self::unchecked(M::MOD - self.0)
        }
    }
}

impl<M: Mod> Neg for &Fp<M> {
    type Output = Fp<M>;
    fn neg(self) -> Self::Output {
        if self.0 == 0 {
            Fp::unchecked(0)
        } else {
            Fp::unchecked(M::MOD - self.0)
        }
    }
}

macro_rules! forward_assign_biop {
    ($(impl $trait:ident, $fn_assign:ident, $fn:ident)*) => {
        $(
            impl<M: Mod> $trait for Fp<M> {
                fn $fn_assign(&mut self, rhs: Self) {
                    *self = self.$fn(rhs);
                }
            }
        )*
    };
}

forward_assign_biop! {
    impl AddAssign, add_assign, add
    impl SubAssign, sub_assign, sub
    impl MulAssign, mul_assign, mul
    impl DivAssign, div_assign, div
}

macro_rules! forward_ref_binop {
    ($(impl $imp:ident, $method:ident)*) => {
        $(
            impl<'a, T: Mod> $imp<Fp<T>> for &'a Fp<T> {
                type Output = Fp<T>;
                fn $method(self, other: Fp<T>) -> Self::Output {
                    $imp::$method(*self, other)
                }
            }

            impl<'a, T: Mod> $imp<&'a Fp<T>> for Fp<T> {
                type Output = Fp<T>;
                fn $method(self, other: &Fp<T>) -> Self::Output {
                    $imp::$method(self, *other)
                }
            }

            impl<'a, T: Mod> $imp<&'a Fp<T>> for &'a Fp<T> {
                type Output = Fp<T>;
                fn $method(self, other: &Fp<T>) -> Self::Output {
                    $imp::$method(*self, *other)
                }
            }
        )*
    };
}

forward_ref_binop! {
    impl Add, add
    impl Sub, sub
    impl Mul, mul
    impl Div, div
}

use std::marker::Sized;
/// 元
pub trait Element: Sized + Clone + PartialEq {}
impl<T: Sized + Clone + PartialEq> Element for T {}

/// 結合性
pub trait Associative: Magma {}

/// マグマ
pub trait Magma: Element + Add<Output=Self> {}
impl<T: Element + Add<Output=Self>> Magma for T {}

/// 半群
pub trait SemiGroup: Magma + Associative {}
impl<T: Magma + Associative> SemiGroup for T {}

/// モノイド
pub trait Monoid: SemiGroup + Zero {}
impl<T: SemiGroup + Zero> Monoid for T {}

pub trait ComMonoid: Monoid + AddAssign {}
impl<T: Monoid + AddAssign> ComMonoid for T {}

/// 群
pub trait Group: Monoid + Neg<Output=Self> {}
impl<T: Monoid + Neg<Output=Self>> Group for T {}

pub trait ComGroup: Group + ComMonoid {}
impl<T: Group + ComMonoid> ComGroup for T {}

/// 半環
pub trait SemiRing: ComMonoid + Mul<Output=Self> + One {}
impl<T: ComMonoid + Mul<Output=Self> + One> SemiRing for T {}

/// 環
pub trait Ring: ComGroup + SemiRing {}
impl<T: ComGroup + SemiRing> Ring for T {}

pub trait ComRing: Ring + MulAssign {}
impl<T: Ring + MulAssign> ComRing for T {}

/// 体
pub trait Field: ComRing + Div<Output=Self> + DivAssign {}
impl<T: ComRing + Div<Output=Self> + DivAssign> Field for T {}

/// 加法単元
pub trait Zero: Element {
    fn zero() -> Self;
    fn is_zero(&self) -> bool;
}

/// 乗法単元
pub trait One: Element {
    fn one() -> Self;
    fn is_one(&self) -> bool;
}

macro_rules! impl_integer {
    ($($T:ty,)*) => {
        $(
            impl Associative for $T {}

            impl Zero for $T {
                fn zero() -> Self { 0 }
                fn is_zero(&self) -> bool { *self == 0 }
            }

            impl<'a> Zero for &'a $T {
                fn zero() -> Self { &0 }
                fn is_zero(&self) -> bool { *self == &0 }
            }

            impl One for $T {
                fn one() -> Self { 1 }
                fn is_one(&self) -> bool { *self == 1 }
            }
            impl<'a> One for &'a $T {
                fn one() -> Self { &1 }
                fn is_one(&self) -> bool { *self == &1 }
            }
        )*
    };
}
impl_integer! {
    i8, i16, i32, i64, i128, isize,
    u8, u16, u32, u64, u128, usize,
}

// ------------ traits 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()
	}
	fn scan_raw(&mut self) -> &'static [u8] {
		self.scan_str().as_bytes()
	}
	pub fn scan<T: Scan>(&mut self) -> T {
		T::scan(self)
	}
	pub fn scan_vec<T: Scan>(&mut self, n: usize) -> Vec<T> {
		(0..n).map(|_| self.scan()).collect()
	}
}

impl IO {
	pub fn print<T: Print>(&mut self, x: T) {
		T::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 {
	fn scan(io: &mut IO) -> Self;
}

macro_rules! impl_parse_int {
	($($t:tt),*) => {
		$(
			impl Scan for $t {
				fn scan(s: &mut IO) -> Self {
					let mut res = 0;
					let mut neg = false;
					for d in s.scan_raw() {
						if *d == b'-' {
							neg = true;
						} else {
							res *= 10;
							res += (*d - b'0') as $t;
						}
					}
					if neg { res = res.wrapping_neg(); }
					res
				}
			}
		)*
	};
}

impl_parse_int!(i16, i32, i64, isize, u16, u32, u64, usize);

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

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

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

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<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);
	}
}

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

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