#690542 (Rust) No.1649 Manhattan Square

• 問題: No.1649 Manhattan Square
• ユーザー: koba-e964
• 提出日時: 2021-08-17 17:57:34
• 言語: Rust (1.83.0 + proconio)
• 結果: AC
• 実行時間: 848 ms / 3,000 ms
• コード長: 7,296 bytes
• コンパイル時間: 13,978 ms
• コンパイル使用メモリ: 378,432 KB
• 実行使用メモリ: 26,864 KB
• 最終ジャッジ日時: 2024-10-10 16:26:29
• 合計ジャッジ時間: 43,233 ms
• ジャッジサーバーID （参考情報）: judge1 / judge2

ファイルパターン	結果
sample	AC * 2
other	AC * 43

ソースコード

// https://qiita.com/tanakh/items/0ba42c7ca36cd29d0ac8
macro_rules! input {
    ($($r:tt)*) => {
        let stdin = std::io::stdin();
        let mut bytes = std::io::Read::bytes(std::io::BufReader::new(stdin.lock()));
        let mut next = move || -> String{
            bytes.by_ref().map(|r|r.unwrap() as char)
                .skip_while(|c|c.is_whitespace())
                .take_while(|c|!c.is_whitespace())
                .collect()
        };
        input_inner!{next, $($r)*}
    };
}

macro_rules! input_inner {
    ($next:expr) => {};
    ($next:expr,) => {};
    ($next:expr, $var:ident : $t:tt $($r:tt)*) => {
        let $var = read_value!($next, $t);
        input_inner!{$next $($r)*}
    };
}

macro_rules! read_value {
    ($next:expr, ( $($t:tt),* )) => { ($(read_value!($next, $t)),*) };
    ($next:expr, [ $t:tt ; $len:expr ]) => {
        (0..$len).map(|_| read_value!($next, $t)).collect::<Vec<_>>()
    };
    ($next:expr, $t:ty) => ($next().parse::<$t>().expect("Parse error"));
}

/// Verified by https://atcoder.jp/contests/abc198/submissions/21774342
mod mod_int {
    use std::ops::*;
    pub trait Mod: Copy { fn m() -> i64; }
    #[derive(Copy, Clone, Hash, PartialEq, Eq, PartialOrd, Ord)]
    pub struct ModInt<M> { pub x: i64, phantom: ::std::marker::PhantomData<M> }
    impl<M: Mod> ModInt<M> {
        // x >= 0
        pub fn new(x: i64) -> Self { ModInt::new_internal(x % M::m()) }
        fn new_internal(x: i64) -> Self {
            ModInt { x: x, phantom: ::std::marker::PhantomData }
        }
        pub fn pow(self, mut e: i64) -> Self {
            debug_assert!(e >= 0);
            let mut sum = ModInt::new_internal(1);
            let mut cur = self;
            while e > 0 {
                if e % 2 != 0 { sum *= cur; }
                cur *= cur;
                e /= 2;
            }
            sum
        }
        #[allow(dead_code)]
        pub fn inv(self) -> Self { self.pow(M::m() - 2) }
    }
    impl<M: Mod, T: Into<ModInt<M>>> Add<T> for ModInt<M> {
        type Output = Self;
        fn add(self, other: T) -> Self {
            let other = other.into();
            let mut sum = self.x + other.x;
            if sum >= M::m() { sum -= M::m(); }
            ModInt::new_internal(sum)
        }
    }
    impl<M: Mod, T: Into<ModInt<M>>> Sub<T> for ModInt<M> {
        type Output = Self;
        fn sub(self, other: T) -> Self {
            let other = other.into();
            let mut sum = self.x - other.x;
            if sum < 0 { sum += M::m(); }
            ModInt::new_internal(sum)
        }
    }
    impl<M: Mod, T: Into<ModInt<M>>> Mul<T> for ModInt<M> {
        type Output = Self;
        fn mul(self, other: T) -> Self { ModInt::new(self.x * other.into().x % M::m()) }
    }
    impl<M: Mod, T: Into<ModInt<M>>> AddAssign<T> for ModInt<M> {
        fn add_assign(&mut self, other: T) { *self = *self + other; }
    }
    impl<M: Mod, T: Into<ModInt<M>>> SubAssign<T> for ModInt<M> {
        fn sub_assign(&mut self, other: T) { *self = *self - other; }
    }
    impl<M: Mod, T: Into<ModInt<M>>> MulAssign<T> for ModInt<M> {
        fn mul_assign(&mut self, other: T) { *self = *self * other; }
    }
    impl<M: Mod> Neg for ModInt<M> {
        type Output = Self;
        fn neg(self) -> Self { ModInt::new(0) - self }
    }
    impl<M> ::std::fmt::Display for ModInt<M> {
        fn fmt(&self, f: &mut ::std::fmt::Formatter) -> ::std::fmt::Result {
            self.x.fmt(f)
        }
    }
    impl<M: Mod> From<i64> for ModInt<M> {
        fn from(x: i64) -> Self { Self::new(x) }
    }
} // mod mod_int

macro_rules! define_mod {
    ($struct_name: ident, $modulo: expr) => {
        #[derive(Copy, Clone, PartialEq, Eq, PartialOrd, Ord, Hash)]
        struct $struct_name {}
        impl mod_int::Mod for $struct_name { fn m() -> i64 { $modulo } }
    }
}
const MOD: i64 = 998_244_353;
define_mod!(P, MOD);
type MInt = mod_int::ModInt<P>;

/**
 * Segment Tree. This data structure is useful for fast folding on intervals of an array
 * whose elements are elements of monoid I. Note that constructing this tree requires the identity
 * element of I and the operation of I.
 * Verified by: yukicoder No. 259 (http://yukicoder.me/submissions/100581)
 *              AGC015-E (http://agc015.contest.atcoder.jp/submissions/1461001)
 */
struct SegTree<I, BiOp> {
    n: usize,
    dat: Vec<I>,
    op: BiOp,
    e: I,
}

impl<I, BiOp> SegTree<I, BiOp>
    where BiOp: Fn(I, I) -> I,
          I: Copy {
    pub fn new(n_: usize, op: BiOp, e: I) -> Self {
        let mut n = 1;
        while n < n_ { n *= 2; } // n is a power of 2
        SegTree {n: n, dat: vec![e; 2 * n - 1], op: op, e: e}
    }
    /* ary[k] <- v */
    pub fn update(&mut self, idx: usize, v: I) {
        let mut k = idx + self.n - 1;
        self.dat[k] = v;
        while k > 0 {
            k = (k - 1) / 2;
            self.dat[k] = (self.op)(self.dat[2 * k + 1], self.dat[2 * k + 2]);
        }
    }
    /* [a, b) (note: half-inclusive)
     * http://proc-cpuinfo.fixstars.com/2017/07/optimize-segment-tree/ */
    pub fn query(&self, mut a: usize, mut b: usize) -> I {
        let mut left = self.e;
        let mut right = self.e;
        a += self.n - 1;
        b += self.n - 1;
        while a < b {
            if (a & 1) == 0 {
                left = (self.op)(left, self.dat[a]);
            }
            if (b & 1) == 0 {
                right = (self.op)(self.dat[b - 1], right);
            }
            a = a / 2;
            b = (b - 1) / 2;
        }
        (self.op)(left, right)
    }
}

fn calc_1d(x: &[i64]) -> MInt {
    let n = x.len();
    let mut tot = MInt::new(0);
    let mut s = MInt::new(0);
    for &x in x {
        s += x;
        tot += MInt::new(x) * x * n as i64;
    }
    tot - s * s
}

fn calc_ru(xy: &[(i64, i64)]) -> MInt {
    let mut coord: Vec<i64> = xy.iter().map(|a| a.1).collect();
    coord.sort(); coord.dedup();
    let m = coord.len();
    let mut st_cnt = SegTree::new(m, |x, y| x + y, MInt::new(0));
    let mut st_x = SegTree::new(m, |x, y| x + y, MInt::new(0));
    let mut st_y = SegTree::new(m, |x, y| x + y, MInt::new(0));
    let mut st_val = SegTree::new(m, |x, y| x + y, MInt::new(0));
    let mut tot = MInt::new(0);
    for &(x, y) in xy.iter().rev() {
        let yidx = coord.binary_search(&y).unwrap();
        let val = st_val.query(yidx + 1, m);
        let xsum = st_x.query(yidx + 1, m);
        let ysum = st_y.query(yidx + 1, m);
        let cnt = st_cnt.query(yidx + 1, m);
        tot += val - xsum * y - ysum * x + cnt * x * y;
        st_cnt.update(yidx, st_cnt.query(yidx, yidx + 1) + 1);
        st_x.update(yidx, st_x.query(yidx, yidx + 1) + x);
        st_y.update(yidx, st_y.query(yidx, yidx + 1) + y);
        st_val.update(yidx, st_val.query(yidx, yidx + 1) + x * y);
    }
    tot * 2
}

fn main() {
    input! {
        n: usize,
        xy: [(i64, i64); n],
    }
    let mut x = vec![0; n];
    let mut y = vec![0; n];
    for i in 0..n {
        let (a, b) = xy[i];
        x[i] = a;
        y[i] = b;
    }
    let mut tot = calc_1d(&x) + calc_1d(&y);
    let mut xy = xy;
    xy.sort();
    tot += calc_ru(&xy);
    for i in 0..n {
        xy[i].1 = 1_000_000_000 - xy[i].1;
    }
    tot += calc_ru(&xy);
    println!("{}", tot);
}