#662661 (C++17) No.1526 Sum of Mex 2

提出ソース

結果

問題	No.1526 Sum of Mex 2
ユーザー	hitonanode
提出日時	2021-06-03 00:28:27
言語	C++17 (gcc 12.3.0 + boost 1.83.0)
結果	AC
実行時間	265 ms / 3,000 ms
コード長	10,187 bytes
コンパイル時間	1,906 ms
コンパイル使用メモリ	101,664 KB
実行使用メモリ	31,396 KB
最終ジャッジ日時	2024-11-15 20:15:12
合計ジャッジ時間	4,866 ms
ジャッジサーバーID （参考情報）	judge3 / judge4

このコードへのチャレンジ
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テストケース

テストケース表示

入力	結果	実行時間実行使用メモリ
testcase_00	AC	2 ms 6,816 KB
testcase_01	AC	2 ms 6,816 KB
testcase_02	AC	2 ms 6,820 KB
testcase_03	AC	2 ms 6,820 KB
testcase_04	AC	2 ms 6,816 KB
testcase_05	AC	2 ms 6,820 KB
testcase_06	AC	2 ms 6,816 KB
testcase_07	AC	2 ms 6,820 KB
testcase_08	AC	2 ms 6,820 KB
testcase_09	AC	2 ms 6,820 KB
testcase_10	AC	2 ms 6,816 KB
testcase_11	AC	2 ms 6,816 KB
testcase_12	AC	2 ms 6,816 KB
testcase_13	AC	8 ms 6,832 KB
testcase_14	AC	10 ms 9,172 KB
testcase_15	AC	12 ms 9,740 KB
testcase_16	AC	42 ms 29,992 KB
testcase_17	AC	34 ms 27,600 KB
testcase_18	AC	6 ms 6,816 KB
testcase_19	AC	5 ms 6,816 KB
testcase_20	AC	20 ms 16,000 KB
testcase_21	AC	42 ms 30,868 KB
testcase_22	AC	24 ms 17,496 KB
testcase_23	AC	42 ms 30,168 KB
testcase_24	AC	43 ms 31,396 KB
testcase_25	AC	41 ms 30,272 KB
testcase_26	AC	43 ms 29,992 KB
testcase_27	AC	42 ms 30,420 KB
testcase_28	AC	42 ms 30,560 KB
testcase_29	AC	42 ms 30,716 KB
testcase_30	AC	44 ms 30,416 KB
testcase_31	AC	44 ms 30,804 KB
testcase_32	AC	43 ms 30,604 KB
testcase_33	AC	265 ms 30,228 KB
evil_largest	AC	906 ms 101,100 KB

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ソースコード

raw source code

#include <iostream>
#include <utility>
#include <vector>
using namespace std;

#ifndef ATCODER_INTERNAL_BITOP_HPP
#define ATCODER_INTERNAL_BITOP_HPP 1

#ifdef _MSC_VER
#include <intrin.h>
#endif

namespace atcoder {

namespace internal {

// @param n `0 <= n`
// @return minimum non-negative `x` s.t. `n <= 2**x`
int ceil_pow2(int n) {
    int x = 0;
    while ((1U << x) < (unsigned int)(n)) x++;
    return x;
}

// @param n `1 <= n`
// @return minimum non-negative `x` s.t. `(n & (1 << x)) != 0`
int bsf(unsigned int n) {
#ifdef _MSC_VER
    unsigned long index;
    _BitScanForward(&index, n);
    return index;
#else
    return __builtin_ctz(n);
#endif
}

} // namespace internal

} // namespace atcoder

#endif // ATCODER_INTERNAL_BITOP_HPP
#ifndef ATCODER_LAZYSEGTREE_HPP
#define ATCODER_LAZYSEGTREE_HPP 1

#include <algorithm>
#include <cassert>
#include <iostream>
#include <vector>

// #include "atcoder/internal_bit"

namespace atcoder {

template <class S, S (*op)(S, S), S (*e)(), class F, S (*mapping)(F, S), F (*composition)(F, F), F (*id)()>
struct lazy_segtree {
public:
    lazy_segtree() : lazy_segtree(0) {}
    explicit lazy_segtree(int n) : lazy_segtree(std::vector<S>(n, e())) {}
    explicit lazy_segtree(const std::vector<S>& v) : _n(int(v.size())) {
        log = internal::ceil_pow2(_n);
        size = 1 << log;
        d = std::vector<S>(2 * size, e());
        lz = std::vector<F>(size, id());
        for (int i = 0; i < _n; i++) d[size + i] = v[i];
        for (int i = size - 1; i >= 1; i--) { update(i); }
    }

    void set(int p, S x) {
        assert(0 <= p && p < _n);
        p += size;
        for (int i = log; i >= 1; i--) push(p >> i);
        d[p] = x;
        for (int i = 1; i <= log; i++) update(p >> i);
    }

    S get(int p) const {
        assert(0 <= p && p < _n);
        p += size;
        for (int i = log; i >= 1; i--) push(p >> i);
        return d[p];
    }

    S prod(int l, int r) const {
        assert(0 <= l && l <= r && r <= _n);
        if (l == r) return e();

        l += size;
        r += size;

        for (int i = log; i >= 1; i--) {
            if (((l >> i) << i) != l) push(l >> i);
            if (((r >> i) << i) != r) push((r - 1) >> i);
        }

        S sml = e(), smr = e();
        while (l < r) {
            if (l & 1) sml = op(sml, d[l++]);
            if (r & 1) smr = op(d[--r], smr);
            l >>= 1;
            r >>= 1;
        }

        return op(sml, smr);
    }

    S all_prod() const { return d[1]; }

    void apply(int p, F f) {
        assert(0 <= p && p < _n);
        p += size;
        for (int i = log; i >= 1; i--) push(p >> i);
        d[p] = mapping(f, d[p]);
        for (int i = 1; i <= log; i++) update(p >> i);
    }
    void apply(int l, int r, F f) {
        assert(0 <= l && l <= r && r <= _n);
        if (l == r) return;

        l += size;
        r += size;

        for (int i = log; i >= 1; i--) {
            if (((l >> i) << i) != l) push(l >> i);
            if (((r >> i) << i) != r) push((r - 1) >> i);
        }

        {
            int l2 = l, r2 = r;
            while (l < r) {
                if (l & 1) all_apply(l++, f);
                if (r & 1) all_apply(--r, f);
                l >>= 1;
                r >>= 1;
            }
            l = l2;
            r = r2;
        }

        for (int i = 1; i <= log; i++) {
            if (((l >> i) << i) != l) update(l >> i);
            if (((r >> i) << i) != r) update((r - 1) >> i);
        }
    }

    template <bool (*g)(S)> int max_right(int l) const {
        return max_right(l, [](S x) { return g(x); });
    }
    template <class G> int max_right(int l, G g) const {
        assert(0 <= l && l <= _n);
        assert(g(e()));
        if (l == _n) return _n;
        l += size;
        for (int i = log; i >= 1; i--) push(l >> i);
        S sm = e();
        do {
            while (l % 2 == 0) l >>= 1;
            if (!g(op(sm, d[l]))) {
                while (l < size) {
                    push(l);
                    l = (2 * l);
                    if (g(op(sm, d[l]))) {
                        sm = op(sm, d[l]);
                        l++;
                    }
                }
                return l - size;
            }
            sm = op(sm, d[l]);
            l++;
        } while ((l & -l) != l);
        return _n;
    }

    template <bool (*g)(S)> int min_left(int r) const {
        return min_left(r, [](S x) { return g(x); });
    }
    template <class G> int min_left(int r, G g) const {
        assert(0 <= r && r <= _n);
        assert(g(e()));
        if (r == 0) return 0;
        r += size;
        for (int i = log; i >= 1; i--) push((r - 1) >> i);
        S sm = e();
        do {
            r--;
            while (r > 1 && (r % 2)) r >>= 1;
            if (!g(op(d[r], sm))) {
                while (r < size) {
                    push(r);
                    r = (2 * r + 1);
                    if (g(op(d[r], sm))) {
                        sm = op(d[r], sm);
                        r--;
                    }
                }
                return r + 1 - size;
            }
            sm = op(d[r], sm);
        } while ((r & -r) != r);
        return 0;
    }

protected:
    int _n, size, log;
    mutable std::vector<S> d;
    mutable std::vector<F> lz;

    void update(int k) const { d[k] = op(d[2 * k], d[2 * k + 1]); }
    virtual void all_apply(int k, F f) const {
        d[k] = mapping(f, d[k]);
        if (k < size) lz[k] = composition(f, lz[k]);
    }
    void push(int k) const {
        all_apply(2 * k, lz[k]);
        all_apply(2 * k + 1, lz[k]);
        lz[k] = id();
    }
};
} // namespace atcoder
#endif // ATCODER_LAZYSEGTREE_HPP

template <class S, S (*op)(S, S), S (*e)(), class F, S (*mapping)(F, S), F (*composition)(F, F), F (*id)()>
class segtree_beats : public atcoder::lazy_segtree<S, op, e, F, mapping, composition, id> {
    using Base = atcoder::lazy_segtree<S, op, e, F, mapping, composition, id>;
    using Base::lazy_segtree;
    void all_apply(int k, F f) const override {
        Base::d[k] = mapping(f, Base::d[k]);
        if (k < Base::size) {
            Base::lz[k] = composition(f, Base::lz[k]);
            if (Base::d[k].fail) Base::push(k), Base::update(k);
        }
    }
};

namespace RangeChMinMaxAddSum {
#include <algorithm>

template <typename Num> inline Num second_lowest(Num a, Num a2, Num c, Num c2) noexcept { // a < a2, c < c2
    return a == c ? std::min(a2, c2) : a2 <= c ? a2 : c2 <= a ? c2 : std::max(a, c);
}
template <typename Num> inline Num second_highest(Num a, Num a2, Num b, Num b2) noexcept { // a > a2, b > b2
    return a == b ? std::max(a2, b2) : a2 >= b ? a2 : b2 >= a ? b2 : std::min(a, b);
}

using BNum = long long;
constexpr BNum BINF = 1LL << 61;

struct S {
    BNum lo, hi, lo2, hi2, sum;
    unsigned sz, nlo, nhi;
    bool fail;
    S() : lo(BINF), hi(-BINF), lo2(BINF), hi2(-BINF), sum(0), sz(0), nlo(0), nhi(0), fail(0) {}
    S(BNum x, unsigned sz_ = 1)
        : lo(x), hi(x), lo2(BINF), hi2(-BINF), sum(x * sz_), sz(sz_), nlo(sz_), nhi(sz_), fail(0) {}
    friend std::ostream &operator<<(std::ostream &os, const S s) {
        return os << "[(" << s.lo << "x" << s.nlo << ", " << s.lo2 << ", " << s.hi2 << ", " << s.hi << "x" << s.nhi << "), sz=" << s.sz << ", sum=" << s.sum << "]";
    }
};

S e() { return S(); }
S op(S l, S r) {
    if (l.lo > l.hi) return r;
    if (r.lo > r.hi) return l;
    S ret;
    ret.lo = std::min(l.lo, r.lo), ret.hi = std::max(l.hi, r.hi);
    ret.lo2 = second_lowest(l.lo, l.lo2, r.lo, r.lo2), ret.hi2 = second_highest(l.hi, l.hi2, r.hi, r.hi2);
    ret.sum = l.sum + r.sum, ret.sz = l.sz + r.sz;
    ret.nlo = l.nlo * (l.lo <= r.lo) + r.nlo * (r.lo <= l.lo);
    ret.nhi = l.nhi * (l.hi >= r.hi) + r.nhi * (r.hi >= l.hi);
    return ret;
}
struct F {
    BNum lb, ub, bias;
    F() : lb(-BINF), ub(BINF), bias(0) {}
    F(BNum chmax_, BNum chmin_, BNum add) : lb(chmax_), ub(chmin_), bias(add) {}
    static F chmin(BNum x) noexcept { return F(-BINF, x, BNum(0)); }
    static F chmax(BNum x) noexcept { return F(x, BINF, BNum(0)); }
    static F add(BNum x) noexcept { return F(-BINF, BINF, x); };
};

F composition(F fnew, F fold) {
    F ret;
    ret.lb = std::max(std::min(fold.lb + fold.bias, fnew.ub), fnew.lb) - fold.bias;
    ret.ub = std::min(std::max(fold.ub + fold.bias, fnew.lb), fnew.ub) - fold.bias;
    ret.bias = fold.bias + fnew.bias;
    return ret;
}
F id() { return F(); }
S mapping(F f, S x) {
    if (x.sz == 0) return e();
    if (x.lo == x.hi or f.lb == f.ub or f.lb >= x.hi or f.ub < x.lo)
        return S(std::min(std::max(x.lo, f.lb), f.ub) + f.bias, x.sz);
    if (x.lo2 == x.hi) {
        x.lo = x.hi2 = std::max(x.lo, f.lb) + f.bias, x.hi = x.lo2 = std::min(x.hi, f.ub) + f.bias;
        x.sum = x.lo * x.nlo + x.hi * x.nhi;
        return x;
    }
    if (f.lb < x.lo2 and f.ub > x.hi2) {
        BNum nxt_lo = std::max(x.lo, f.lb), nxt_hi = std::min(x.hi, f.ub);
        x.sum += (nxt_lo - x.lo) * x.nlo - (x.hi - nxt_hi) * x.nhi + f.bias * x.sz;
        x.lo = nxt_lo + f.bias, x.hi = nxt_hi + f.bias, x.lo2 += f.bias, x.hi2 += f.bias;
        return x;
    }
    x.fail = 1;
    return x;
}
using segtree = segtree_beats<S, op, e, F, mapping, composition, id>;
} // namespace RangeChMinMaxAddSum


int main() {
    ios::sync_with_stdio(false), cin.tie(nullptr);
    int N;
    cin >> N;
    vector<vector<int>> v2is(N);
    for (int i = 0; i < N; i++) {
        int a;
        cin >> a;
        v2is[a - 1].push_back(i);
    }
    vector<pair<int, int>> ranges{{0, N}};
    long long ret = 0;

    vector<RangeChMinMaxAddSum::S> init;
    for (int i = 0; i < N; i++) init.emplace_back(i);
    RangeChMinMaxAddSum::segtree tree(init);

    for (auto is : v2is) {
        if (ranges.empty()) break;
        int l = 0;
        for (auto i : is) {
            tree.apply(l, i + 1, RangeChMinMaxAddSum::F::chmax(i));
            l = i + 1;
        }
        tree.apply(l, N, RangeChMinMaxAddSum::F::chmax(N));
        auto tmp = (long long)N * N - tree.all_prod().sum;
        ret += tmp;
        if (!tmp) break;
    }
    cout << ret + (long long)N * (N + 1) / 2 << '\n';
}

yukicoder

結果

テストケース

ソースコード