#717078 (Rust) No.907 Continuous Kadomatu

• 問題: No.907 Continuous Kadomatu
• ユーザー: koba-e964
• 提出日時: 2021-11-17 21:11:35
• 言語: Rust (1.77.0 + proconio)
• 結果: AC
• 実行時間: 87 ms / 2,000 ms
• コード長: 6,559 bytes
• コンパイル時間: 13,940 ms
• コンパイル使用メモリ: 385,696 KB
• 実行使用メモリ: 6,948 KB
• 最終ジャッジ日時: 2024-06-06 11:51:16
• 合計ジャッジ時間: 14,554 ms
• ジャッジサーバーID （参考情報）: judge4 / judge2

入力	結果	実行時間; 実行使用メモリ
testcase_00	AC	1 ms; 6,812 KB
testcase_01	AC	1 ms; 6,948 KB
testcase_02	AC	1 ms; 6,940 KB
testcase_03	AC	1 ms; 6,944 KB
testcase_04	AC	1 ms; 6,944 KB
testcase_05	AC	7 ms; 6,940 KB
testcase_06	AC	1 ms; 6,944 KB
testcase_07	AC	3 ms; 6,944 KB
testcase_08	AC	6 ms; 6,940 KB
testcase_09	AC	4 ms; 6,940 KB
testcase_10	AC	12 ms; 6,940 KB
testcase_11	AC	18 ms; 6,944 KB
testcase_12	AC	45 ms; 6,940 KB
testcase_13	AC	51 ms; 6,944 KB
testcase_14	AC	54 ms; 6,940 KB
testcase_15	AC	53 ms; 6,940 KB
testcase_16	AC	56 ms; 6,940 KB
testcase_17	AC	62 ms; 6,940 KB
testcase_18	AC	55 ms; 6,940 KB
testcase_19	AC	59 ms; 6,940 KB
testcase_20	AC	2 ms; 6,940 KB
testcase_21	AC	2 ms; 6,940 KB
testcase_22	AC	1 ms; 6,940 KB
testcase_23	AC	62 ms; 6,940 KB
testcase_24	AC	87 ms; 6,940 KB
testcase_25	AC	1 ms; 6,940 KB
testcase_26	AC	1 ms; 6,940 KB
testcase_27	AC	0 ms; 6,940 KB
testcase_28	AC	1 ms; 6,940 KB
testcase_29	AC	1 ms; 6,944 KB

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/arc093/submissions/3968098
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 = 1_000_000_007;
define_mod!(P, MOD);
type MInt = mod_int::ModInt<P>;

// https://yukicoder.me/problems/no/907 (4)
// 確率密度関数を不定積分。区間に分ける必要あり。
// Tags: real-numbers, continuous-probability-distribution
fn main() {
    input! {
        n: usize,
        ab: [(i64, i64); n],
    }
    let mut coo = vec![];
    for &(a, b) in &ab {
        coo.push(a);
        coo.push(b);
    }
    coo.sort(); coo.dedup();
    let m = coo.len();
    let mut dp = vec![vec![MInt::new(0)]; m - 1];
    {
        let (a, b) = ab[0];
        let inv = MInt::new(b - a).inv();
        let a = coo.binary_search(&a).unwrap();
        let b = coo.binary_search(&b).unwrap();
        for i in a..b {
            dp[i][0] = inv;
        }
    }
    let mut invtbl = vec![MInt::new(0); n + 1];
    for i in 1..n + 1 {
        invtbl[i] = MInt::new(i as i64).inv();
    }
    for i in 1..n {
        let (a, b) = ab[i];
        let inv = MInt::new(b - a).inv();
        let a = coo.binary_search(&a).unwrap();
        let b = coo.binary_search(&b).unwrap();
        let mut ep = vec![vec![MInt::new(0); i + 1]; m - 1];
        let mut tot = MInt::new(0);
        if i % 2 == 0 {
            // >=
            for j in (a..m - 1).rev() {
                let l = coo[j];
                let r = coo[j + 1];
                let mut cur = MInt::new(r - l) * inv;
                for k in 0..i {
                    tot += cur * invtbl[k + 1] * dp[j][k];
                    cur *= r - l;
                }
                if j < b {
                    for k in 0..i {
                        ep[j][k + 1] -= dp[j][k] * invtbl[k + 1] * inv;
                    }
                    ep[j][0] += tot;
                }
            }
        } else {
            // <=
            for j in 0..b {
                let l = coo[j];
                let r = coo[j + 1];
                if j >= a {
                    for k in 0..i {
                        ep[j][k + 1] += dp[j][k] * invtbl[k + 1] * inv;
                    }
                    ep[j][0] += tot;
                }
                let mut cur = MInt::new(r - l) * inv;
                for k in 0..i {
                    tot += cur * invtbl[k + 1] * dp[j][k];
                    cur *= r - l;
                }
            }
        }
        dp = ep;
    }
    let mut tot = MInt::new(0);
    for i in 0..m - 1 {
        let l = coo[i];
        let r = coo[i + 1];
        let mut cur = MInt::new(r - l);
        for j in 0..n {
            tot += cur * invtbl[j + 1] * dp[i][j];
            cur *= r - l;
        }
    }
    println!("{}", tot);
}