#908713 (Rust) No.1526 Sum of Mex 2

• 問題: No.1526 Sum of Mex 2
• ユーザー: koba-e964
• 提出日時: 2023-08-28 13:51:40
• 言語: Rust (1.77.0 + proconio)
• 結果: AC
• 実行時間: 220 ms / 3,000 ms
• コード長: 8,544 bytes
• コンパイル時間: 18,610 ms
• コンパイル使用メモリ: 377,556 KB
• 実行使用メモリ: 10,240 KB
• 最終ジャッジ日時: 2024-06-09 09:06:28
• 合計ジャッジ時間: 21,765 ms
• ジャッジサーバーID （参考情報）: judge1 / judge3

入力	結果	実行時間; 実行使用メモリ
testcase_00	AC	1 ms; 5,248 KB
testcase_01	AC	1 ms; 5,248 KB
testcase_02	AC	1 ms; 5,248 KB
testcase_03	AC	1 ms; 5,248 KB
testcase_04	AC	1 ms; 5,376 KB
testcase_05	AC	1 ms; 5,376 KB
testcase_06	AC	1 ms; 5,376 KB
testcase_07	AC	1 ms; 5,376 KB
testcase_08	AC	1 ms; 5,376 KB
testcase_09	AC	1 ms; 5,376 KB
testcase_10	AC	1 ms; 5,376 KB
testcase_11	AC	1 ms; 5,376 KB
testcase_12	AC	1 ms; 5,376 KB
testcase_13	AC	8 ms; 5,376 KB
testcase_14	AC	10 ms; 5,376 KB
testcase_15	AC	12 ms; 5,376 KB
testcase_16	AC	58 ms; 9,856 KB
testcase_17	AC	42 ms; 8,064 KB
testcase_18	AC	6 ms; 5,376 KB
testcase_19	AC	4 ms; 5,376 KB
testcase_20	AC	25 ms; 5,632 KB
testcase_21	AC	58 ms; 9,600 KB
testcase_22	AC	34 ms; 6,400 KB
testcase_23	AC	60 ms; 9,728 KB
testcase_24	AC	61 ms; 9,984 KB
testcase_25	AC	60 ms; 9,728 KB
testcase_26	AC	63 ms; 9,856 KB
testcase_27	AC	63 ms; 10,112 KB
testcase_28	AC	64 ms; 10,240 KB
testcase_29	AC	60 ms; 9,856 KB
testcase_30	AC	64 ms; 10,240 KB
testcase_31	AC	59 ms; 10,240 KB
testcase_32	AC	58 ms; 9,856 KB
testcase_33	AC	220 ms; 10,112 KB
evil_largest	AC	822 ms; 29,052 KB

ソースコード

use std::cmp::*;
// 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 ; $len:expr ]) => {
        (0..$len).map(|_| read_value!($next, $t)).collect::<Vec<_>>()
    };
    ($next:expr, usize1) => (read_value!($next, usize) - 1);
    ($next:expr, $t:ty) => ($next().parse::<$t>().expect("Parse error"));
}

// 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
}
pub struct LazySegTree<R: ActionRing> {
    n: usize,
    dep: usize,
    dat: Vec<R::T>,
    lazy: Vec<R::U>,
}
impl<R: ActionRing> 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, rng: std::ops::Range<usize>) -> R::T {
        let (l, r) = (rng.start, rng.end);
        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, rng: std::ops::Range<usize>, f: R::U)  {
        let (l, r) = (rng.start, rng.end);
        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();
    }
}

enum Affine {}

type AffineInt = i64; // 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())
    }
}

// https://yukicoder.me/problems/no/1526 (3.5)
// c[i][j] = (A[i+1] 以降で初めて j+1 が出てくる場所) - 1, ただし存在しなければ N
// d[i][j] = max(c[i][0], ..., c[i][j]) とする。(0 <= j <= N)
// A[i+1] から始まる部分配列について、それらの mex の総和は
// N-i + \sum_{j=1}^N (d[i][j] - d[i][j-1])j
// = N^2+N-i - \sum_{j=0}^{N-1}d[i][j] である。
// これを計算すれば良いが、これは d[i] を遅延セグメント木で管理することでできる。
// c[i] と c[i-1] の差分は 1 要素であることに着目すると、はじめに右から c の変化の履歴を計算しておき、
// そのあと左から d を計算すればよい.
// Similar problems: https://yukicoder.me/problems/no/1349
fn main() {
    input! {
        n: usize,
        x: [usize1; n],
    }
    let nn = n as i64;
    let mut ev = vec![];
    let mut a = vec![n; n + 1];
    for i in (0..n).rev() {
        ev.push((x[i], a[x[i]]));
        a[x[i]] = i;
    }
    ev.reverse();
    let mut ans = 0i64;
    let mut st = LazySegTree::<Affine>::new(n);
    let mut ma = 0;
    for i in 0..n {
        ma = max(ma, a[i]);
        st.set(i, (ma as i64, 1));
    }
    for i in 0..n {
        let sum = st.query(0..n).0;
        ans += nn * (nn + 1) - i as i64 - sum;
        let (idx, to) = ev[i];
        if st.get(idx).0 < to as i64 {
            let mut pass = idx;
            let mut fail = n;
            while fail - pass > 1 {
                let mid = (fail + pass) / 2;
                if st.get(mid).0 < to as i64 {
                    pass = mid;
                } else {
                    fail = mid;
                }
            }
            st.update(idx..pass + 1, (0, to as i64));
        }
    }
    println!("{}", ans);
}