test/src/datastructure/fenwick_tree/fenwick_tree_2d/random_is.test.cpp

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• Last update: 2024-01-30 22:04:45+09:00
• Problem: https://atcoder.jp/contests/arc108/tasks/arc108_e

Depends on

• Fenwick Tree 2d (library/datastructure/fenwick_tree/fenwick_tree_2d.hpp)
• セグメント木 (library/datastructure/segment_tree/segment_tree.hpp)
• 逆元テーブル (library/math/inv_mods.hpp)
• Type Traits (library/type_traits/type_traits.hpp)
• Update Proxy Object (library/util/update_proxy_object.hpp)

Code

#define PROBLEM "https://atcoder.jp/contests/arc108/tasks/arc108_e"

#include <iostream>
#include <atcoder/modint>

#include "library/math/inv_mods.hpp"
#include "library/datastructure/segment_tree/segment_tree.hpp"
#include "library/datastructure/fenwick_tree/fenwick_tree_2d.hpp"

using namespace suisen;
using mint = atcoder::modint1000000007;

mint op(mint x, mint y) {
    return x + y;
}
mint e() {
    return 0;
}

int main() {
    std::ios::sync_with_stdio(false);
    std::cin.tie(nullptr);

    int n;
    std::cin >> n;
    std::vector<int> a(n);

    inv_mods<mint> invs(n);

    for (int &e : a) std::cin >> e;
    a.insert(a.begin(), 0);
    a.insert(a.end(), n + 1);

    std::vector dp_segs(n + 2, SegmentTree<mint, op, e>(n + 2));
    std::vector pd_segs(n + 2, SegmentTree<mint, op, e>(n + 2));

    FenwickTree2D<int> ft_point(n + 2, n + 2);
    for (int i = 1; i <= n; ++i) ++ft_point[{i, a[i]}];

    mint ans = 0;
    for (int w = 1; w <= n; ++w) {
        for (int l = 1, r = w; r <= n; ++l, ++r) {
            int vl = a[l - 1], vr = a[r + 1];
            if (vl > vr) continue;
            int k = ft_point(l, r + 1, vl, vr);
            if (k == 0) continue;
            mint val = 1 + ((dp_segs[l](vl, vr) + pd_segs[r](vl, vr)) * invs[k]).val();
            dp_segs[l][a[r + 1]] += val;
            pd_segs[r][a[l - 1]] += val;
            if (w == n) ans = val;
        }
    }
    std::cout << ans.val() << std::endl;
    return 0;
}

#line 1 "test/src/datastructure/fenwick_tree/fenwick_tree_2d/random_is.test.cpp"
#define PROBLEM "https://atcoder.jp/contests/arc108/tasks/arc108_e"

#include <iostream>
#include <atcoder/modint>

#line 1 "library/math/inv_mods.hpp"



#include <vector>

namespace suisen {
    template <typename mint>
    class inv_mods {
    public:
        inv_mods() = default;
        inv_mods(int n) { ensure(n); }
        const mint& operator[](int i) const {
            ensure(i);
            return invs[i];
        }
        static void ensure(int n) {
            int sz = invs.size();
            if (sz < 2) invs = { 0, 1 }, sz = 2;
            if (sz < n + 1) {
                invs.resize(n + 1);
                for (int i = sz; i <= n; ++i) invs[i] = mint(mod - mod / i) * invs[mod % i];
            }
        }
    private:
        static std::vector<mint> invs;
        static constexpr int mod = mint::mod();
    };
    template <typename mint>
    std::vector<mint> inv_mods<mint>::invs{};

    template <typename mint>
    std::vector<mint> get_invs(const std::vector<mint>& vs) {
        const int n = vs.size();

        mint p = 1;
        for (auto& e : vs) {
            p *= e;
            assert(e != 0);
        }
        mint ip = p.inv();

        std::vector<mint> rp(n + 1);
        rp[n] = 1;
        for (int i = n - 1; i >= 0; --i) {
            rp[i] = rp[i + 1] * vs[i];
        }
        std::vector<mint> res(n);
        for (int i = 0; i < n; ++i) {
            res[i] = ip * rp[i + 1];
            ip *= vs[i];
        }
        return res;
    }
}


#line 1 "library/datastructure/segment_tree/segment_tree.hpp"



#include <cassert>
#line 6 "library/datastructure/segment_tree/segment_tree.hpp"

#line 1 "library/util/update_proxy_object.hpp"



#line 1 "library/type_traits/type_traits.hpp"



#include <limits>
#line 6 "library/type_traits/type_traits.hpp"
#include <type_traits>

namespace suisen {
    template <typename ...Constraints> using constraints_t = std::enable_if_t<std::conjunction_v<Constraints...>, std::nullptr_t>;

    template <typename T, typename = std::nullptr_t> struct bitnum { static constexpr int value = 0; };
    template <typename T> struct bitnum<T, constraints_t<std::is_integral<T>>> { static constexpr int value = std::numeric_limits<std::make_unsigned_t<T>>::digits; };
    template <typename T> static constexpr int bitnum_v = bitnum<T>::value;
    template <typename T, size_t n> struct is_nbit { static constexpr bool value = bitnum_v<T> == n; };
    template <typename T, size_t n> static constexpr bool is_nbit_v = is_nbit<T, n>::value;

    template <typename T, typename = std::nullptr_t> struct safely_multipliable { using type = T; };
    template <typename T> struct safely_multipliable<T, constraints_t<std::is_signed<T>, is_nbit<T, 32>>> { using type = long long; };
    template <typename T> struct safely_multipliable<T, constraints_t<std::is_signed<T>, is_nbit<T, 64>>> { using type = __int128_t; };
    template <typename T> struct safely_multipliable<T, constraints_t<std::is_unsigned<T>, is_nbit<T, 32>>> { using type = unsigned long long; };
    template <typename T> struct safely_multipliable<T, constraints_t<std::is_unsigned<T>, is_nbit<T, 64>>> { using type = __uint128_t; };
    template <typename T> using safely_multipliable_t = typename safely_multipliable<T>::type;

    template <typename T, typename = void> struct rec_value_type { using type = T; };
    template <typename T> struct rec_value_type<T, std::void_t<typename T::value_type>> {
        using type = typename rec_value_type<typename T::value_type>::type;
    };
    template <typename T> using rec_value_type_t = typename rec_value_type<T>::type;

    template <typename T> class is_iterable {
        template <typename T_> static auto test(T_ e) -> decltype(e.begin(), e.end(), std::true_type{});
        static std::false_type test(...);
    public:
        static constexpr bool value = decltype(test(std::declval<T>()))::value;
    };
    template <typename T> static constexpr bool is_iterable_v = is_iterable<T>::value;
    template <typename T> class is_writable {
        template <typename T_> static auto test(T_ e) -> decltype(std::declval<std::ostream&>() << e, std::true_type{});
        static std::false_type test(...);
    public:
        static constexpr bool value = decltype(test(std::declval<T>()))::value;
    };
    template <typename T> static constexpr bool is_writable_v = is_writable<T>::value;
    template <typename T> class is_readable {
        template <typename T_> static auto test(T_ e) -> decltype(std::declval<std::istream&>() >> e, std::true_type{});
        static std::false_type test(...);
    public:
        static constexpr bool value = decltype(test(std::declval<T>()))::value;
    };
    template <typename T> static constexpr bool is_readable_v = is_readable<T>::value;
} // namespace suisen

#line 5 "library/util/update_proxy_object.hpp"

namespace suisen {

template <typename T, typename UpdateFunc, constraints_t<std::is_invocable<UpdateFunc>> = nullptr>
struct UpdateProxyObject {
    public:
        UpdateProxyObject(T &v, UpdateFunc update) : v(v), update(update) {}
        operator T() const { return v; }
        auto& operator++() && { ++v, update(); return *this; }
        auto& operator--() && { --v, update(); return *this; }
        auto& operator+=(const T &val) && { v += val, update(); return *this; }
        auto& operator-=(const T &val) && { v -= val, update(); return *this; }
        auto& operator*=(const T &val) && { v *= val, update(); return *this; }
        auto& operator/=(const T &val) && { v /= val, update(); return *this; }
        auto& operator%=(const T &val) && { v %= val, update(); return *this; }
        auto& operator =(const T &val) && { v  = val, update(); return *this; }
        auto& operator<<=(const T &val) && { v <<= val, update(); return *this; }
        auto& operator>>=(const T &val) && { v >>= val, update(); return *this; }
        template <typename F, constraints_t<std::is_invocable_r<T, F, T>> = nullptr>
        auto& apply(F f) && { v = f(v), update(); return *this; }
    private:
        T &v;
        UpdateFunc update;
};

} // namespace suisen


#line 8 "library/datastructure/segment_tree/segment_tree.hpp"

namespace suisen {
template <typename T, T(*op)(T, T), T(*e)()>
class SegmentTree {
    public:
        SegmentTree() : SegmentTree(0) {}
        explicit SegmentTree(int n) : SegmentTree(std::vector<T>(n, e())) {}
        SegmentTree(const std::vector<T> &a) : n(a.size()), m(ceil_pow2(n)), data(2 * m, e()) {
            build(a);
        }

        void build(const std::vector<T> &a) {
            assert(int(a.size()) <= m);
            std::copy(a.begin(), a.end(), data.begin() + m);
            for (int k = m - 1; k > 0; --k) update(k);
        }
        const T& get(int i) const {
            assert(0 <= i and i < n);
            return data[i + m];
        }
        T operator()(int l, int r) const {
            T res_l = e(), res_r = e();
            for (l += m, r += m; l < r; l >>= 1, r >>= 1) {
                if (l & 1) res_l = op(res_l, data[l++]);
                if (r & 1) res_r = op(data[--r], res_r);
            }
            return op(res_l, res_r);
        }
        T prod(int l, int r) const { return (*this)(l, r); }
        T prefix_prod(int r) const { return (*this)(0, r); }
        T suffix_prod(int l) const { return (*this)(l, m); }
        T all_prod() const { return data[1]; }

        void set(int i, const T &val) {
            (*this)[i] = val;
        }
        auto operator[](int i) {
            assert(0 <= i and i < n);
            int k = i + m;
            return UpdateProxyObject { data[k], [this, k]{ update_from(k); } };
        }

        template <typename Pred, constraints_t<std::is_invocable_r<bool, Pred, T>> = nullptr>
        int max_right(int l, const Pred &f) const {
            assert(0 <= l and l <= n);
            assert(f(e));
            if (l == n) return n;
            l += m;
            T sum_l = e;
            do {
                while (l % 2 == 0) l >>= 1;
                if (not f(op(sum_l, data[l]))) {
                    while (l < m) {
                        l = 2 * l;
                        if (f(op(sum_l, data[l]))) sum_l = op(sum_l, data[l++]);
                    }
                    return l - m;
                }
                sum_l = op(sum_l, data[l]);
                l++;
            } while ((l & -l) != l);
            return n;
        }
        template <bool(*f)(T)>
        int max_right(int l) { return max_right(l, f); }

        template <typename Pred, constraints_t<std::is_invocable_r<bool, Pred, T>> = nullptr>
        int min_left(int r, const Pred &f) const {
            assert(0 <= r && r <= n);
            assert(f(e));
            if (r == 0) return 0;
            r += m;
            T sum_r = e;
            do {
                r--;
                while (r > 1 && (r % 2)) r >>= 1;
                if (not f(op(data[r], sum_r))) {
                    while (r < m) {
                        r = 2 * r + 1;
                        if (f(op(data[r], sum_r))) sum_r = op(data[r--], sum_r);
                    }
                    return r + 1 - m;
                }
                sum_r = op(data[r], sum_r);
            } while ((r & -r) != r);
            return 0;
        }
        template <bool(*f)(T)>
        int min_left(int l) { return min_left(l, f); }

    private:
        int n, m;
        std::vector<T> data;

        static constexpr int ceil_pow2(int n) {
            int m = 1;
            while (m < n) m <<= 1;
            return m;
        }
        void update_from(int k) {
            for (k >>= 1; k; k >>= 1) update(k);
        }
        void update(int k) {
            data[k] = op(data[k * 2], data[k * 2 + 1]);
        }
};
} // namespace suisen



#line 1 "library/datastructure/fenwick_tree/fenwick_tree_2d.hpp"



#line 5 "library/datastructure/fenwick_tree/fenwick_tree_2d.hpp"

namespace suisen {

    template <typename T>
    class FenwickTree2D {
    public:
        FenwickTree2D() = default;
        explicit FenwickTree2D(int n, int m) : n(n), m(m), data(n, std::vector<T>(m, T{})) {}
        void add(int i, int j, T v) {
            for (int x = i + 1; x <= n; x += (x & -x)) for (int y = j + 1; y <= m; y += (y & -y)) {
                data[x - 1][y - 1] += v;
            }
        }
        T sum(int xl, int xr, int yl, int yr) const {
            return sum(xr, yr) - sum(xl, yr) - sum(xr, yl) + sum(xl, yl);
        }
        auto operator[](std::pair<int, int> index) {
            auto [i, j] = index;
            struct {
                int i, j;
                FenwickTree2D& ft;
                operator T() const { return ft.sum(i, i + 1, j, j + 1); }
                auto& operator++() { return *this += 1; }
                auto& operator--() { return *this -= 1; }
                auto& operator+=(T val) { ft.add(i, j, val); return *this; }
                auto& operator-=(T val) { ft.add(i, j, -val); return *this; }
                auto& operator*=(T val) { T cur = *this; ft.add(i, j, cur * val - cur); return *this; }
                auto& operator/=(T val) { T cur = *this; ft.add(i, j, cur / val - cur); return *this; }
                auto& operator%=(T val) { T cur = *this; ft.add(i, j, cur % val - cur); return *this; }
                auto& operator =(T val) { T cur = *this; ft.add(i, j, val - cur); return *this; }
            } obj{ i, j, *this };
            return obj;
        }
        T operator()(int xl, int xr, int yl, int yr) const { return sum(xl, xr, yl, yr); }

    private:
        int n, m;
        std::vector<std::vector<T>> data;

        T sum(int xr, int yr) const {
            T s{};
            for (int x = xr; x; x -= x & -x) for (int y = yr; y; y -= y & -y) {
                s += data[x - 1][y - 1];
            }
            return s;
        }
    };

} // namespace suisen


#line 9 "test/src/datastructure/fenwick_tree/fenwick_tree_2d/random_is.test.cpp"

using namespace suisen;
using mint = atcoder::modint1000000007;

mint op(mint x, mint y) {
    return x + y;
}
mint e() {
    return 0;
}

int main() {
    std::ios::sync_with_stdio(false);
    std::cin.tie(nullptr);

    int n;
    std::cin >> n;
    std::vector<int> a(n);

    inv_mods<mint> invs(n);

    for (int &e : a) std::cin >> e;
    a.insert(a.begin(), 0);
    a.insert(a.end(), n + 1);

    std::vector dp_segs(n + 2, SegmentTree<mint, op, e>(n + 2));
    std::vector pd_segs(n + 2, SegmentTree<mint, op, e>(n + 2));

    FenwickTree2D<int> ft_point(n + 2, n + 2);
    for (int i = 1; i <= n; ++i) ++ft_point[{i, a[i]}];

    mint ans = 0;
    for (int w = 1; w <= n; ++w) {
        for (int l = 1, r = w; r <= n; ++l, ++r) {
            int vl = a[l - 1], vr = a[r + 1];
            if (vl > vr) continue;
            int k = ft_point(l, r + 1, vl, vr);
            if (k == 0) continue;
            mint val = 1 + ((dp_segs[l](vl, vr) + pd_segs[r](vl, vr)) * invs[k]).val();
            dp_segs[l][a[r + 1]] += val;
            pd_segs[r][a[l - 1]] += val;
            if (w == n) ans = val;
        }
    }
    std::cout << ans.val() << std::endl;
    return 0;
}

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