#706855 (Rust) No.1144 Triangles

• 問題: No.1144 Triangles
• ユーザー: koba-e964
• 提出日時: 2021-10-12 00:30:20
• 言語: Rust (1.77.0)
• 結果: AC
• 実行時間: 687 ms / 3,000 ms
• コード長: 7,117 bytes
• コンパイル時間: 1,985 ms
• コンパイル使用メモリ: 167,320 KB
• 実行使用メモリ: 4,372 KB
• 最終ジャッジ日時: 2023-10-14 11:28:58
• 合計ジャッジ時間: 12,676 ms
• ジャッジサーバーID （参考情報）: judge11 / judge15

入力	結果	実行時間; 実行使用メモリ
testcase_00	AC	1 ms; 4,356 KB
testcase_01	AC	1 ms; 4,352 KB
testcase_02	AC	1 ms; 4,352 KB
testcase_03	AC	1 ms; 4,348 KB
testcase_04	AC	685 ms; 4,352 KB
testcase_05	AC	687 ms; 4,352 KB
testcase_06	AC	683 ms; 4,356 KB
testcase_07	AC	686 ms; 4,356 KB
testcase_08	AC	687 ms; 4,352 KB
testcase_09	AC	1 ms; 4,352 KB
testcase_10	AC	1 ms; 4,352 KB
testcase_11	AC	1 ms; 4,352 KB
testcase_12	AC	1 ms; 4,356 KB
testcase_13	AC	1 ms; 4,348 KB
testcase_14	AC	625 ms; 4,356 KB
testcase_15	AC	616 ms; 4,352 KB
testcase_16	AC	662 ms; 4,348 KB
testcase_17	AC	667 ms; 4,348 KB
testcase_18	AC	663 ms; 4,348 KB
testcase_19	AC	25 ms; 4,356 KB
testcase_20	AC	2 ms; 4,352 KB
testcase_21	AC	2 ms; 4,352 KB
testcase_22	AC	635 ms; 4,356 KB
testcase_23	AC	34 ms; 4,348 KB
testcase_24	AC	623 ms; 4,352 KB
testcase_25	AC	187 ms; 4,372 KB
testcase_26	AC	19 ms; 4,348 KB
testcase_27	AC	3 ms; 4,348 KB
testcase_28	AC	119 ms; 4,348 KB

コンパイルメッセージ

warning: unused import: `BufWriter`
 --> Main.rs:5:22
  |
5 | use std::io::{Write, BufWriter};
  |                      ^^^^^^^^^
  |
  = note: `#[warn(unused_imports)]` on by default

warning: unused import: `Write`
 --> Main.rs:5:15
  |
5 | use std::io::{Write, BufWriter};
  |               ^^^^^

warning: type alias `P` is never used
   --> Main.rs:150:6
    |
150 | type P = (Coord, Coord);
    |      ^
    |
    = note: `#[warn(dead_code)]` on by default

warning: function `inn` is never used
   --> Main.rs:152:4
    |
152 | fn inn((ax, ay): P, (bx, by): P) -> Coord {
    |    ^^^

warning: function `det` is never used
   --> Main.rs:156:4
    |
156 | fn det((ax, ay): P, (bx, by): P) -> Coord {
    |    ^^^

warning: function `sub` is never used
   --> Main.rs:160:4
    |
160 | fn sub((ax, ay): P, (bx, by): P) -> P {
    |    ^^^

warning: 6 warnings emitted

ソースコード

#[allow(unused_imports)]
use std::cmp::*;
#[allow(unused_imports)]
use std::collections::*;
use std::io::{Write, BufWriter};
// 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> ::std::fmt::Debug for ModInt<M> {
        fn fmt(&self, f: &mut ::std::fmt::Formatter) -> ::std::fmt::Result {
            let (mut a, mut b, _) = red(self.x, M::m());
            if b < 0 {
                a = -a;
                b = -b;
            }
            write!(f, "{}/{}", a, b)
        }
    }
    impl<M: Mod> From<i64> for ModInt<M> {
        fn from(x: i64) -> Self { Self::new(x) }
    }
    // Finds the simplest fraction x/y congruent to r mod p.
    // The return value (x, y, z) satisfies x = y * r + z * p.
    fn red(r: i64, p: i64) -> (i64, i64, i64) {
        if r.abs() <= 10000 {
            return (r, 1, 0);
        }
        let mut nxt_r = p % r;
        let mut q = p / r;
        if 2 * nxt_r >= r {
            nxt_r -= r;
            q += 1;
        }
        if 2 * nxt_r <= -r {
            nxt_r += r;
            q -= 1;
        }
        let (x, z, y) = red(nxt_r, r);
        (x, y - q * z, z)
    }
} // 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 = 1_000_000_007;
define_mod!(PP, MOD);
type MInt = mod_int::ModInt<PP>;

type Coord = i64; // the type of coordinates
type P = (Coord, Coord);

fn inn((ax, ay): P, (bx, by): P) -> Coord {
    ax * bx + ay * by
}

fn det((ax, ay): P, (bx, by): P) -> Coord {
    ax * by - ay * bx
}

fn sub((ax, ay): P, (bx, by): P) -> P {
    (ax - bx, ay - by)
}

trait Change { fn chmax(&mut self, x: Self); fn chmin(&mut self, x: Self); }
impl<T: PartialOrd> Change for T {
    fn chmax(&mut self, x: T) { if *self < x { *self = x; } }
    fn chmin(&mut self, x: T) { if *self > x { *self = x; } }
}

fn arg_sort(xy: &mut [(Coord, Coord, i32)]) {
    fn half((x, y, _): (Coord, Coord, i32)) -> i32 {
        assert_ne!((x, y), (0, 0));
        if y >= 0 {
            if x > 0 || y > 0 {
                1
            } else {
                2
            }
        } else {
            2
        }
    }
    xy.sort_unstable_by(|&a, &b| {
        half(a).cmp(&half(b)).then_with(
            || 0.cmp(&(a.0 * b.1 - a.1 * b.0))
                .then_with(|| a.2.cmp(&b.2)))
    });
}

fn calc(a: Vec<(i64, i64)>) -> MInt {
    let n = a.len();
    let mut b = vec![];
    for (x, y) in a {
        b.push((x, y, 0));
        b.push((-x, -y, 1));
    }
    arg_sort(&mut b);
    let mut acc_x = vec![MInt::new(0); 3 * n + 1];
    let mut acc_y = vec![MInt::new(0); 3 * n + 1];
    let mut tot = MInt::new(0);
    for i in 0..3 * n {
        let (x, y) = if b[i % (2 * n)].2 == 0 {
            (MOD + b[i % (2 * n)].0, MOD + b[i % (2 * n)].1)
        } else {
            (0, 0)
        };
        acc_x[i + 1] = acc_x[i] + x;
        acc_y[i + 1] = acc_y[i] + y;
    }
    for i in 0..2 * n {
        if b[i].2 != 0 { continue; }
        let p = acc_x[i + n] - acc_x[i];
        let q = acc_y[i + n] - acc_y[i];
        tot += q * (MOD + b[i].0) - p * (MOD + b[i].1);
    }
    tot
}

// Tags: counting, area-of-triangles, sort-by-argument
fn main() {
    input! {
        n: usize,
        xy: [(i64, i64); n],
    }
    let mut tot = MInt::new(0);
    for i in 0..n {
        let (x, y) = xy[i];
        let v: Vec<_> = xy[i + 1..].iter().map(|&(a, b)| (a - x, b - y))
            .filter(|&p| p != (0, 0)).collect();
        tot += calc(v);
    }
    println!("{}", tot);
}