結果
| 問題 |
No.1300 Sum of Inversions
|
| ユーザー |
 urectanc
|
| 提出日時 | 2025-09-04 19:48:19 |
| 言語 | Rust (1.83.0 + proconio) |
| 結果 |
AC
|
| 実行時間 | 213 ms / 2,000 ms |
| コード長 | 10,125 bytes |
| コンパイル時間 | 14,308 ms |
| コンパイル使用メモリ | 389,132 KB |
| 実行使用メモリ | 32,384 KB |
| 最終ジャッジ日時 | 2025-09-04 19:48:42 |
| 合計ジャッジ時間 | 20,066 ms |
|
ジャッジサーバーID （参考情報） |
judge3 / judge5 |
（要ログイン）
| ファイルパターン | 結果 |
|---|---|
| sample | AC * 3 |
| other | AC * 34 |
ソースコード
use std::collections::BTreeMap;
use bit::BinaryIndexedTree;
use modint::ModInt998244353;
use proconio::input;
type Mint = ModInt998244353;
fn main() {
input! {
n: usize,
a: [i64; n],
}
let mut by_value = BTreeMap::new();
let mut bit_small_cnt = BinaryIndexedTree::new(n, 0);
let mut bit_small_sum = BinaryIndexedTree::new(n, 0);
let mut bit_large_cnt = BinaryIndexedTree::new(n, 0);
let mut bit_large_sum = BinaryIndexedTree::new(n, 0);
for (i, &a) in a.iter().enumerate() {
by_value.entry(a).or_insert(vec![]).push(i);
bit_large_cnt.add(i, 1);
bit_large_sum.add(i, a);
}
let mut ans = Mint::new(0);
for (&a, v) in &by_value {
for &i in v {
bit_large_cnt.add(i, -1);
bit_large_sum.add(i, -a);
}
for &i in v {
let small_cnt = bit_small_cnt.sum(i, n);
let small_sum = bit_small_sum.sum(i, n);
let large_cnt = bit_large_cnt.sum(0, i);
let large_sum = bit_large_sum.sum(0, i);
ans += Mint::new(small_sum as u64) * large_cnt;
ans += Mint::new(large_sum as u64) * small_cnt;
ans += Mint::new(a as u64) * small_cnt * large_cnt;
}
for &i in v {
bit_small_cnt.add(i, 1);
bit_small_sum.add(i, a);
}
}
println!("{ans}");
}
#[allow(dead_code)]
mod bit {
pub struct BinaryIndexedTree<T> {
n: usize,
array: Vec<T>,
e: T,
}
impl<T> BinaryIndexedTree<T>
where
T: Clone + std::ops::AddAssign + std::ops::Sub<Output = T> + std::cmp::PartialOrd,
{
pub fn new(n: usize, e: T) -> Self {
Self {
n,
array: vec![e.clone(); n + 1],
e,
}
}
pub fn add(&mut self, i: usize, x: T) {
let mut i = i + 1;
while i <= self.n {
self.array[i] += x.clone();
i += i & i.wrapping_neg();
}
}
pub fn cum(&self, mut i: usize) -> T {
let mut cum = self.e.clone();
while i > 0 {
cum += self.array[i].clone();
i -= i & i.wrapping_neg();
}
cum
}
pub fn sum(&self, l: usize, r: usize) -> T {
self.cum(r) - self.cum(l)
}
pub fn lower_bound(&self, mut x: T) -> usize {
let mut i = 0;
let mut k = 1 << (self.n.next_power_of_two().trailing_zeros());
while k > 0 {
if i + k <= self.n && self.array[i + k] < x {
x = x - self.array[i + k].clone();
i += k;
}
k >>= 1;
}
i
}
}
}
#[allow(dead_code)]
mod modint {
use std::ops::{Add, AddAssign, Div, DivAssign, Mul, MulAssign, Neg, Sub, SubAssign};
pub type ModInt998244353 = ModInt<998244353>;
pub type ModInt1000000007 = ModInt<1000000007>;
type ModIntInner = u64;
#[derive(Clone, Copy, PartialEq, Eq)]
pub struct ModInt<const M: ModIntInner> {
val: ModIntInner,
}
impl<const M: ModIntInner> ModInt<M> {
const IS_PRIME: bool = is_prime(M as u32);
pub const fn modulus() -> ModIntInner {
M
}
pub const fn new(val: ModIntInner) -> Self {
assert!(M < (1 << 31));
Self {
val: val.rem_euclid(M),
}
}
pub const fn new_unchecked(val: ModIntInner) -> Self {
Self { val }
}
pub const fn val(&self) -> ModIntInner {
self.val
}
pub fn pow(self, mut exp: u64) -> Self {
let mut result = Self::new(1);
let mut base = self;
while exp > 0 {
if exp & 1 == 1 {
result *= base;
}
base *= base;
exp >>= 1;
}
result
}
pub fn inv(self) -> Self {
assert!(Self::IS_PRIME);
self.pow(M as u64 - 2).into()
}
}
impl<const M: ModIntInner> std::fmt::Display for ModInt<M> {
fn fmt(&self, f: &mut std::fmt::Formatter<'_>) -> std::fmt::Result {
write!(f, "{}", self.val)
}
}
impl<const M: ModIntInner> std::fmt::Debug for ModInt<M> {
fn fmt(&self, f: &mut std::fmt::Formatter<'_>) -> std::fmt::Result {
write!(f, "{}", self.val)
}
}
impl<const M: ModIntInner> std::str::FromStr for ModInt<M> {
type Err = std::num::ParseIntError;
fn from_str(s: &str) -> Result<Self, Self::Err> {
let value = s.parse::<ModIntInner>()?;
Ok(ModInt::new(value))
}
}
impl<const M: ModIntInner> Neg for ModInt<M> {
type Output = Self;
fn neg(mut self) -> Self::Output {
if self.val > 0 {
self.val = M - self.val;
}
self
}
}
impl<const M: ModIntInner, T: Into<ModInt<M>>> AddAssign<T> for ModInt<M> {
fn add_assign(&mut self, rhs: T) {
self.val += rhs.into().val;
if self.val >= M {
self.val -= M;
}
}
}
impl<const M: ModIntInner, T: Into<ModInt<M>>> SubAssign<T> for ModInt<M> {
fn sub_assign(&mut self, rhs: T) {
self.val = self.val.wrapping_sub(rhs.into().val);
if self.val > M {
self.val = self.val.wrapping_add(M);
}
}
}
impl<const M: ModIntInner, T: Into<ModInt<M>>> MulAssign<T> for ModInt<M> {
fn mul_assign(&mut self, rhs: T) {
self.val = self.val * rhs.into().val % M;
}
}
impl<const M: ModIntInner, T: Into<ModInt<M>>> DivAssign<T> for ModInt<M> {
fn div_assign(&mut self, rhs: T) {
*self *= rhs.into().inv();
}
}
macro_rules! impl_binnary_operators {
($({ $op: ident, $op_assign: ident, $fn: ident, $fn_assign: ident}),*) => {$(
impl<const M: ModIntInner, T: Into<ModInt<M>>> $op<T> for ModInt<M> {
type Output = ModInt<M>;
fn $fn(mut self, rhs: T) -> ModInt<M> {
self.$fn_assign(rhs.into());
self
}
}
impl<const M: ModIntInner> $op<&ModInt<M>> for ModInt<M> {
type Output = ModInt<M>;
fn $fn(self, rhs: &ModInt<M>) -> ModInt<M> {
self.$fn(*rhs)
}
}
impl<const M: ModIntInner, T: Into<ModInt<M>>> $op<T> for &ModInt<M> {
type Output = ModInt<M>;
fn $fn(self, rhs: T) -> ModInt<M> {
(*self).$fn(rhs.into())
}
}
impl<const M: ModIntInner> $op<&ModInt<M>> for &ModInt<M> {
type Output = ModInt<M>;
fn $fn(self, rhs: &ModInt<M>) -> ModInt<M> {
(*self).$fn(*rhs)
}
}
impl<const M: ModIntInner> $op_assign<&ModInt<M>> for ModInt<M> {
fn $fn_assign(&mut self, rhs: &ModInt<M>) {
*self = self.$fn(*rhs);
}
}
)*};
}
impl_binnary_operators!(
{Add, AddAssign, add, add_assign},
{Sub, SubAssign, sub, sub_assign},
{Mul, MulAssign, mul, mul_assign},
{Div, DivAssign, div, div_assign}
);
impl<const M: ModIntInner> std::iter::Sum for ModInt<M> {
fn sum<I: Iterator<Item = Self>>(iter: I) -> Self {
iter.fold(Self::new(0), Add::add)
}
}
impl<'a, const M: ModIntInner> std::iter::Sum<&'a Self> for ModInt<M> {
fn sum<I: Iterator<Item = &'a Self>>(iter: I) -> Self {
iter.fold(Self::new(0), Add::add)
}
}
impl<const M: ModIntInner> std::iter::Product for ModInt<M> {
fn product<I: Iterator<Item = Self>>(iter: I) -> Self {
iter.fold(Self::new(1), Mul::mul)
}
}
impl<'a, const M: ModIntInner> std::iter::Product<&'a Self> for ModInt<M> {
fn product<I: Iterator<Item = &'a Self>>(iter: I) -> Self {
iter.fold(Self::new(1), Mul::mul)
}
}
macro_rules! impl_rem_euclid_signed {
($($ty:tt),*) => {
$(
impl<const M: ModIntInner> From<$ty> for ModInt<M> {
fn from(value: $ty) -> ModInt<M> {
Self::new_unchecked((value as i64).rem_euclid(M as i64) as ModIntInner)
}
}
)*
};
}
impl_rem_euclid_signed!(i8, i16, i32, i64, isize);
macro_rules! impl_rem_euclid_unsigned {
($($ty:tt),*) => {
$(
impl<const M: ModIntInner> From<$ty> for ModInt<M> {
fn from(value: $ty) -> ModInt<M> {
Self::new_unchecked((value as u64).rem_euclid(M as u64) as ModIntInner)
}
}
)*
};
}
impl_rem_euclid_unsigned!(u8, u16, u32, u64, usize);
const fn is_prime(n: u32) -> bool {
const fn miller_rabin(n: u32, witness: u32) -> bool {
let (n, witness) = (n as u64, witness as u64);
let mut d = n >> (n - 1).trailing_zeros();
let mut y = {
let (mut res, mut pow, mut e) = (1, witness, d);
while e > 0 {
if e & 1 == 1 {
res = res * pow % n;
}
pow = pow * pow % n;
e >>= 1;
}
res
};
while d != n - 1 && y != 1 && y != n - 1 {
y = y * y % n;
d <<= 1;
}
y == n - 1 || d & 1 == 1
}
const WITNESS: [u32; 3] = [2, 7, 61];
if n == 1 || n % 2 == 0 {
return n == 2;
}
let mut i = 0;
while i < WITNESS.len() {
if !miller_rabin(n, WITNESS[i]) {
return false;
}
i += 1;
}
true
}
}