#723512 (Rust) No.1548 [Cherry 2nd Tune B] 貴方と私とサイクルとモーメント

• 問題: No.1548 [Cherry 2nd Tune B] 貴方と私とサイクルとモーメント
• ユーザー: koba-e964
• 提出日時: 2021-12-11 14:13:49
• 言語: Rust (1.77.0 + proconio)
• 結果: AC
• 実行時間: 806 ms / 4,500 ms
• コード長: 12,851 bytes
• コンパイル時間: 27,688 ms
• コンパイル使用メモリ: 377,732 KB
• 実行使用メモリ: 52,736 KB
• 最終ジャッジ日時: 2024-07-19 19:09:06
• 合計ジャッジ時間: 42,409 ms
• ジャッジサーバーID （参考情報）: judge5 / judge1

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	2 ms; 6,816 KB
testcase_02	AC	464 ms; 27,348 KB
testcase_03	AC	161 ms; 14,592 KB
testcase_04	AC	513 ms; 52,264 KB
testcase_05	AC	33 ms; 6,940 KB
testcase_06	AC	315 ms; 27,020 KB
testcase_07	AC	573 ms; 52,648 KB
testcase_08	AC	455 ms; 27,320 KB
testcase_09	AC	311 ms; 14,848 KB
testcase_10	AC	431 ms; 52,276 KB
testcase_11	AC	511 ms; 52,224 KB
testcase_12	AC	172 ms; 8,320 KB
testcase_13	AC	376 ms; 52,224 KB
testcase_14	AC	269 ms; 14,464 KB
testcase_15	AC	475 ms; 52,608 KB
testcase_16	AC	445 ms; 27,392 KB
testcase_17	AC	526 ms; 52,180 KB
testcase_18	AC	557 ms; 52,520 KB
testcase_19	AC	161 ms; 14,592 KB
testcase_20	AC	460 ms; 52,608 KB
testcase_21	AC	319 ms; 27,136 KB
testcase_22	AC	691 ms; 52,736 KB
testcase_23	AC	689 ms; 52,736 KB
testcase_24	AC	702 ms; 52,676 KB
testcase_25	AC	718 ms; 52,600 KB
testcase_26	AC	703 ms; 52,680 KB
testcase_27	AC	701 ms; 52,608 KB
testcase_28	AC	721 ms; 52,564 KB
testcase_29	AC	701 ms; 52,580 KB
testcase_30	AC	726 ms; 52,596 KB
testcase_31	AC	721 ms; 52,696 KB
testcase_32	AC	576 ms; 52,736 KB
testcase_33	AC	806 ms; 52,640 KB
testcase_34	AC	645 ms; 52,676 KB
testcase_35	AC	721 ms; 52,696 KB
testcase_36	AC	693 ms; 52,664 KB
testcase_37	AC	718 ms; 52,660 KB
testcase_38	AC	569 ms; 52,684 KB
testcase_39	AC	732 ms; 52,736 KB
testcase_40	AC	617 ms; 52,608 KB
testcase_41	AC	679 ms; 52,736 KB

ソースコード

#[allow(unused_imports)]
use std::cmp::*;
#[allow(unused_imports)]
use std::collections::*;
use std::io::Read;

#[allow(dead_code)]
fn getline() -> String {
    let mut ret = String::new();
    std::io::stdin().read_line(&mut ret).ok().unwrap();
    ret
}

fn get_word() -> String {
    let stdin = std::io::stdin();
    let mut stdin=stdin.lock();
    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.unwrap_or(0) == 0 || u8b[0] <= b' ' {
                break;
            } else {
                buf.push(u8b[0]);
            }
        }
        if buf.len() >= 1 {
            let ret = String::from_utf8(buf).unwrap();
            return ret;
        }
    }
}

/// 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> Default for ModInt<M> {
        fn default() -> Self { Self::new_internal(0) }
    }
    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 = 998_244_353;
define_mod!(P, MOD);
type MInt = mod_int::ModInt<P>;

// Lazy Segment Tree. This data structure is useful for fast folding and updating on intervals of an array
// whose elements are elements of monoid T. Note that constructing this tree requires the identity
// element of T and the operation of T. This is monomorphised, because of efficiency. T := i64, biop = max, upop = (+)
// Reference: https://github.com/atcoder/ac-library/blob/master/atcoder/lazysegtree.hpp
// Verified by: https://judge.yosupo.jp/submission/68794
//              https://atcoder.jp/contests/joisc2021/submissions/27734236
pub trait ActionRing {
    type T: Clone + Copy; // data
    type U: Clone + Copy + PartialEq + Eq; // action
    fn biop(x: Self::T, y: Self::T) -> Self::T;
    fn update(x: Self::T, a: Self::U) -> Self::T;
    fn upop(fst: Self::U, snd: Self::U) -> Self::U;
    fn e() -> Self::T;
    fn upe() -> Self::U; // identity for upop
}
#[derive(Clone)]
pub struct LazySegTree<R: ActionRing + Clone> {
    n: usize,
    dep: usize,
    dat: Vec<R::T>,
    lazy: Vec<R::U>,
}
impl<R: ActionRing + Clone> LazySegTree<R> {
    pub fn new(n_: usize) -> Self {
        let mut n = 1;
        let mut dep = 0;
        while n < n_ { n *= 2; dep += 1; } // n is a power of 2
        LazySegTree {
            n: n,
            dep: dep,
            dat: vec![R::e(); 2 * n],
            lazy: vec![R::upe(); n],
        }
    }
    #[allow(unused)]
    pub fn with(a: &[R::T]) -> Self {
        let mut ret = Self::new(a.len());
        let n = ret.n;
        for i in 0..a.len() {
            ret.dat[n + i] = a[i];
        }
        for i in (1..n).rev() {
            ret.update_node(i);
        }
        ret
    }
    #[inline]
    pub fn set(&mut self, idx: usize, x: R::T) {
        debug_assert!(idx < self.n);
        self.apply_any(idx, |_t| x);
    }
    #[inline]
    pub fn apply(&mut self, idx: usize, f: R::U) {
        debug_assert!(idx < self.n);
        self.apply_any(idx, |t| R::update(t, f));
    }
    pub fn apply_any<F: Fn(R::T) -> R::T>(&mut self, idx: usize, f: F) {
        debug_assert!(idx < self.n);
        let idx = idx + self.n;
        for i in (1..self.dep + 1).rev() {
            self.push(idx >> i);
        }
        self.dat[idx] = f(self.dat[idx]);
        for i in 1..self.dep + 1 {
            self.update_node(idx >> i);
        }
    }
    pub fn get(&mut self, idx: usize) -> R::T {
        debug_assert!(idx < self.n);
        let idx = idx + self.n;
        for i in (1..self.dep + 1).rev() {
            self.push(idx >> i);
        }
        self.dat[idx]
    }
    /* [l, r) (note: half-inclusive) */
    #[inline]
    pub fn query(&mut self, l: usize, r: usize) -> R::T {
        debug_assert!(l <= r && r <= self.n);
        if l == r { return R::e(); }
        let mut l = l + self.n;
        let mut r = r + self.n;
        for i in (1..self.dep + 1).rev() {
            if ((l >> i) << i) != l { self.push(l >> i); }
            if ((r >> i) << i) != r { self.push((r - 1) >> i); }
        }
        let mut sml = R::e();
        let mut smr = R::e();
        while l < r {
            if (l & 1) != 0 {
                sml = R::biop(sml, self.dat[l]);
                l += 1;
            }
            if (r & 1) != 0 {
                r -= 1;
                smr = R::biop(self.dat[r], smr);
            }
            l >>= 1;
            r >>= 1;
        }
        R::biop(sml, smr)
    }
    /* ary[i] = upop(ary[i], v) for i in [l, r) (half-inclusive) */
    #[inline]
    pub fn update(&mut self, l: usize, r: usize, f: R::U)  {
        debug_assert!(l <= r && r <= self.n);
        if l == r { return; }
        let mut l = l + self.n;
        let mut r = r + self.n;
        for i in (1..self.dep + 1).rev() {
            if ((l >> i) << i) != l { self.push(l >> i); }
            if ((r >> i) << i) != r { self.push((r - 1) >> i); }
        }
        {
            let l2 = l;
            let r2 = r;
            while l < r {
                if (l & 1) != 0 {
                    self.all_apply(l, f);
                    l += 1;
                }
                if (r & 1) != 0 {
                    r -= 1;
                    self.all_apply(r, f);
                }
                l >>= 1;
                r >>= 1;
            }
            l = l2;
            r = r2;
        }
        for i in 1..self.dep + 1 {
            if ((l >> i) << i) != l { self.update_node(l >> i); }
            if ((r >> i) << i) != r { self.update_node((r - 1) >> i); }
        }
    }
    #[inline]
    fn update_node(&mut self, k: usize) {
        self.dat[k] = R::biop(self.dat[2 * k], self.dat[2 * k + 1]);
    }
    fn all_apply(&mut self, k: usize, f: R::U) {
        self.dat[k] = R::update(self.dat[k], f);
        if k < self.n {
            self.lazy[k] = R::upop(self.lazy[k], f);
        }
    }
    fn push(&mut self, k: usize) {
        let val = self.lazy[k];
        self.all_apply(2 * k, val);
        self.all_apply(2 * k + 1, val);
        self.lazy[k] = R::upe();
    }
}

#[derive(Clone)]
enum Affine {}

type AffineInt = MInt; // Change here to change type
impl ActionRing for Affine {
    type T = (AffineInt, AffineInt); // data, size
    type U = (AffineInt, AffineInt); // action, (a, b) |-> x |-> ax + b
    fn biop((x, s): Self::T, (y, t): Self::T) -> Self::T {
        (x + y, s + t)
    }
    fn update((x, s): Self::T, (a, b): Self::U) -> Self::T {
        (x * a + b * s, s)
    }
    fn upop(fst: Self::U, snd: Self::U) -> Self::U {
        let (a, b) = fst;
        let (c, d) = snd;
        (a * c, b * c + d)
    }
    fn e() -> Self::T {
        (0.into(), 0.into())
    }
    fn upe() -> Self::U { // identity for upop
        (1.into(), 0.into())
    }
}

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

fn upd(n: usize, st: &mut LazySegTree<Affine>, l: usize, r: usize, x: MInt) {
    if l <= r {
        st.update(l, r + 1, (0.into(), x));
    } else {
        st.update(l, n, (0.into(), x));
        st.update(0, r + 1, (0.into(), x));
    }
}

fn que(n: usize, st: &mut LazySegTree<Affine>, l: usize, r: usize) -> MInt {
    if l <= r {
        st.query(l, r + 1).0
    } else {
        let a = st.query(l, n).0;
        let b = st.query(0, r + 1).0;
        a + b
    }
}

fn solve() {
    let n: usize = get();
    let a: Vec<i64> = (0..n).map(|_| get()).collect();
    let q: usize = get();
    let mut st = vec![LazySegTree::<Affine>::new(n); 4];
    for i in 0..n {
        let b = MInt::new(a[i]);
        let mut c = b;
        for j in 0..4 {
            st[j].set(i, (c, 1.into()));
            c *= b;
        }
    }
    let comb = vec![
        vec![1],
        vec![1, 1],
        vec![1, 2, 1],
        vec![1, 3, 3, 1],
        vec![1, 4, 6, 4, 1],
    ];
    for _ in 0..q {
        let ty: usize = get();
        let u = get::<usize>() - 1;
        let v = get::<usize>() - 1;
        let w = get::<usize>() - 1;
        let (u, v) = if u > v { (v, u) } else { (u, v) };
        let (l, r) = if u < w && w < v {
            (u, v)
        } else {
            (v, u)
        };
        if ty == 0 {
            let b: i64 = get();
            let b = MInt::new(b);
            let mut c = b;
            for i in 0..4 {
                upd(n, &mut st[i], l, r, c);
                c *= b;
            }
        } else {
            let len = (r + n - l) % n + 1;
            let len = len as i64;
            let leninv = MInt::new(len).inv();
            let mut ans = MInt::new(0);
            let avg = -que(n, &mut st[0], l, r) * leninv;
            let mut c = MInt::new(1);
            for i in (0..ty + 1).rev() {
                let tmp = if i == 0 {
                    MInt::new(len)
                } else {
                    que(n, &mut st[i - 1], l, r)
                } * comb[ty][i] * c;
                ans += tmp;
                c *= avg;
            }
            println!("{}", ans * leninv);
        }
    }
}

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();
}