#699966 (Rust) No.122 傾向と対策：門松列（その３）

• 問題: No.122 傾向と対策：門松列（その３）
• ユーザー: koba-e964
• 提出日時: 2021-09-16 19:21:39
• 言語: Rust (1.77.0)
• 結果: AC
• 実行時間: 26 ms / 5,000 ms
• コード長: 7,368 bytes
• コンパイル時間: 1,039 ms
• コンパイル使用メモリ: 153,460 KB
• 実行使用メモリ: 4,380 KB
• 最終ジャッジ日時: 2023-09-12 01:54:37
• 合計ジャッジ時間: 2,151 ms
• ジャッジサーバーID （参考情報）: judge12 / judge13

入力	結果	実行時間; 実行使用メモリ
testcase_00	AC	19 ms; 4,376 KB
testcase_01	AC	19 ms; 4,376 KB
testcase_02	AC	26 ms; 4,376 KB
testcase_03	AC	23 ms; 4,380 KB
testcase_04	AC	19 ms; 4,376 KB
testcase_05	AC	26 ms; 4,380 KB
testcase_06	AC	18 ms; 4,380 KB
testcase_07	AC	18 ms; 4,376 KB

ソースコード

use std::io::*;
fn get_word() -> String {
    let mut stdin = std::io::stdin();
    let mut u8b: [u8; 1] = [0];
    loop {
        let mut buf: Vec<u8> = Vec::with_capacity(16);
        loop {
            let res = stdin.read(&mut u8b);
            if res.is_err() || res.ok().unwrap() == 0 || u8b[0] <= ' ' as u8 {
                break;
            } else {
                buf.push(u8b[0]);
            }
        }
        if buf.len() >= 1 {
            let ret = std::string::String::from_utf8(buf).unwrap();
            return ret;
        }
    }
}
fn parse<T: std::str::FromStr>(s: &str) -> T { s.parse::<T>().ok().unwrap() }

#[allow(dead_code)]
fn get<T: std::str::FromStr>() -> T { parse(&get_word()) }

/// 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!(P, MOD);
type MInt = mod_int::ModInt<P>;

/**
 * Returns the least index of elements that are modified, wrapped with Some.
 * If the entire array is reversed, it returns None instead.
 * v's elements must be pairwise distinct.
 */
fn next_permutation<T: Ord>(v: &mut [T]) -> Option<usize> {
    let mut tail_dec: usize = 1;
    let n = v.len();
    while tail_dec < n {
        if v[n - tail_dec - 1] > v[n - tail_dec] {
            tail_dec += 1;
        } else {
            break;
        }
    }
    // v[n - tail_dec .. n] is strictly decreasing
    if tail_dec < n {
        let x = n - tail_dec - 1;
        let mut y = n;
        {
            let pivot = &v[x];
            for i in (n - tail_dec .. n).rev() {
                if v[i] > *pivot {
                    y = i;
                    break;
                }
            }
            assert!(y < n);
        }
        v.swap(x, y);
    }
    v[n - tail_dec .. n].reverse();
    if tail_dec < n {
        Some(n - tail_dec - 1)
    } else {
        None
    }
}

const W: usize = 20010;

// ret[v]: #ways to pick elements from a with max v
// picked elements should form an increasing sequence 
fn calc2(a: &[(usize, usize)]) -> Vec<MInt> {
    let mut dp = vec![MInt::new(1); W];
    for &(l, r) in a {
        let mut ep = vec![MInt::new(0); W];
        for i in l..r + 1 {
            ep[i] = ep[i - 1] + dp[i - 1];
        }
        for i in r + 1..W {
            ep[i] = ep[i - 1];
        }
        dp = ep;
    }
    for i in (0..W - 1).rev() {
        dp[i + 1] = dp[i + 1] - dp[i];
    }
    dp
}

// ret[v]: #ways to pick different elements from a with max v
fn calc1(a: &[(usize, usize)]) -> Vec<MInt> {
    let n = a.len();
    let mut p: Vec<_> = (0..n).collect();
    let mut ans = vec![MInt::new(0); W];
    loop {
        let mut b = vec![(0, 0); n];
        for i in 0..n {
            b[i] = a[p[i]];
        }
        let sub = calc2(&b);
        for i in 0..W {
            ans[i] += sub[i];
        }
        if let None = next_permutation(&mut p) {
            break;
        }
    }
    ans
}

fn solve(a: &[usize; 7], b: &[usize; 7]) -> MInt {
    let mut lo = [(0, 0); 4];
    let mut hi = [(0, 0); 3];
    for i in 0..4 {
        lo[i] = (a[2 * i], b[2 * i]);
    }
    for i in 0..3 {
        hi[i] = (W - b[2 * i + 1], W - a[2 * i + 1]);
    }
    let a = calc1(&lo);
    let b = calc1(&hi);
    let mut tot = MInt::new(0);
    let mut acc = MInt::new(0);
    for i in 0..W {
        acc += a[i];
        tot += acc * b[W - 1 - i];
    }
    tot
}

fn main() {
    let mut mi = [0usize; 7];
    let mut ma = [0usize; 7];
    for i in 0..7 {
        mi[i] = get();
        ma[i] = get();
    }
    let tot = solve(&mi, &ma);
    for i in 0..7 {
        let t1 = W - ma[i];
        let t2 = W - mi[i];
        mi[i] = t1;
        ma[i] = t2;
    }
    let tot = tot + solve(&mi, &ma);
    println!("{}", tot);
}