#573425 (Rust) No.1276 3枚のカード

• 問題: No.1276 3枚のカード
• ユーザー: koba-e964
• 提出日時: 2020-10-30 23:18:29
• 言語: Rust (1.83.0 + proconio)
• 結果: AC
• 実行時間: 421 ms / 2,000 ms
• コード長: 8,696 bytes
• コンパイル時間: 15,183 ms
• コンパイル使用メモリ: 379,600 KB
• 実行使用メモリ: 6,948 KB
• 最終ジャッジ日時: 2024-07-22 03:00:51
• 合計ジャッジ時間: 31,221 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
other	AC * 61

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, [graph1; $len:expr]) => {{
        let mut g = vec![vec![]; $len];
        let ab = read_value!($next, [(usize1, usize1)]);
        for (a, b) in ab {
            g[a].push(b);
            g[b].push(a);
        }
        g
    }};
    ($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, chars) => {
        read_value!($next, String).chars().collect::<Vec<char>>()
    };
    ($next:expr, usize1) => (read_value!($next, usize) - 1);
    ($next:expr, [ $t:tt ]) => {{
        let len = read_value!($next, usize);
        read_value!($next, [$t; len])
    }};
    ($next:expr, $t:ty) => ($next().parse::<$t>().expect("Parse error"));
}

#[allow(unused)]
macro_rules! debug {
    ($($format:tt)*) => (write!(std::io::stderr(), $($format)*).unwrap());
}
#[allow(unused)]
macro_rules! debugln {
    ($($format:tt)*) => (writeln!(std::io::stderr(), $($format)*).unwrap());
}

/// 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> ::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>;

fn sqrt(x: i64) -> i64 {
    if x <= 1 {
        return x;
    }
    let mut lo = 1;
    let mut hi = 1 << 30;
    while hi - lo > 1 {
        let mid = (hi + lo) / 2;
        if mid * mid <= x {
            lo = mid;
        } else {
            hi = mid;
        }
    }
    lo
}

fn solve() {
    let out = std::io::stdout();
    let mut out = BufWriter::new(out.lock());
    macro_rules! puts {
        ($($format:tt)*) => (let _ = write!(out,$($format)*););
    }
    #[allow(unused)]
    macro_rules! putvec {
        ($v:expr) => {
            for i in 0..$v.len() {
                puts!("{}{}", $v[i], if i + 1 == $v.len() {"\n"} else {" "});
            }
        }
    }
    input!(n: i64);
    let mut tot = MInt::new(0);
    let sq = sqrt(n);
    // B | C
    // B | A, C
    for k in 1..sq + 1 {
        let q = n / k;
        if q >= 1 {
            tot += MInt::new(q - 1) * (n - 2);
        }
        if q >= 2 {
            tot -= MInt::new(q - 1) * (q - 2);
        }
    }
    for k in 2..sq + 1 {
        let lo = max(sq, n / (k + 1));
        let hi = n / k;
        if lo < hi {
            tot += MInt::new(k - 1) * (n - 2) * (hi - lo);
            tot -= MInt::new(k - 1) * (k - 2) * (hi - lo);
        }
    }
    eprintln!("pre (A | B | C incl) = {}", tot);
    // A | B | C
    const W: usize = 50_000;
    // const W: usize = 2;
    let mut dps = vec![MInt::new(0); W];
    for i in 1..W {
        let mut tot = MInt::new(0);
        let s = sqrt(i as i64);
        for j in 1..s + 1 {
            tot += i as i64 / j - 1;
        }
        for j in 1..s + 1 {
            let lo = max(s, i as i64 / (j + 1));
            let hi = i as i64 / j;
            if lo < hi {
                tot += MInt::new(j - 1) * (hi - lo);
            }
        }
        dps[i] = tot;
    }
    let bc = n as usize / W;
    let mut dpb = vec![MInt::new(0); bc + 1];
    for i in 1..bc + 1 {
        let mut tot = MInt::new(0);
        let x = n / i as i64;
        let s = sqrt(x);
        for j in 1..s + 1 {
            tot += x as i64 / j - 1;
        }
        for j in 1..s + 1 {
            let lo = max(s, x as i64 / (j + 1));
            let hi = x as i64 / j;
            if lo < hi {
                tot += MInt::new(j - 1) * (hi - lo);
            }
        }
        dpb[i] = tot;
    }
    eprintln!("dps = {:?}", &dps[..min(dps.len(), 20)]);
    eprintln!("dpb = {:?}", &dpb[..min(dpb.len(), 20)]);
    // TODO opt
    for i in 2..bc + 1 {
        tot -= dpb[i];
    }
    for i in 1..min(W as i64, n + 1) {
        let lo = max(max(1, bc) as i64, n / (i as i64 + 1));
        let hi = n / i as i64;
        if lo < hi {
            tot -= dps[i as usize] * (hi - lo);
        }
    }
    puts!("{}\n", tot);
}

fn main() {
    // In order to avoid potential stack overflow, spawn a new thread.
    let stack_size = 104_857_600; // 100 MB
    let thd = std::thread::Builder::new().stack_size(stack_size);
    thd.spawn(|| solve()).unwrap().join().unwrap();
}