Submission #1362458

#TimeUsernameProblemLanguageResultExecution timeMemory
1362458kawhietFancy Fence (CEOI20_fancyfence)C++20
30 / 100
1095 ms3048 KiB
#include <bits/stdc++.h>
using namespace std;

#ifdef LOCAL
#include "debug.h"
#else
#define dbg(...) 47
#endif

template <typename T>
T inverse(T a, T m) {
    T u = 0, v = 1;
    while (a != 0) {
        T t = m / a;
        m -= t * a; swap(a, m);
        u -= t * v; swap(u, v);
    }
    assert(m == 1);
    return u;
}

template <typename T>
class Modular {
public:
    using Type = typename decay<decltype(T::value)>::type;

    constexpr Modular() : value() {}
    template <typename U>
    Modular(const U& x) {
        value = normalize(x);
    }

    template <typename U>
    static Type normalize(const U& x) {
        Type v;
        if (-mod() <= x && x < mod()) v = static_cast<Type>(x);
        else v = static_cast<Type>(x % mod());
        if (v < 0) v += mod();
        return v;
    }

    const Type& operator()() const { return value; }
    template <typename U>
    explicit operator U() const { return static_cast<U>(value); }
    constexpr static Type mod() { return T::value; }

    Modular& operator+=(const Modular& other) {
        value += other.value;
        value -= (value >= mod()) * mod();
        return *this;
    }

    Modular& operator-=(const Modular& other) {
        value -= other.value;
        value += (value < 0) * mod();
        return *this;
    }

    template <typename U> Modular& operator+=(const U& other) { return *this += Modular(other); }
    template <typename U> Modular& operator-=(const U& other) { return *this -= Modular(other); }

    Modular& operator++() { return *this += 1; }
    Modular& operator--() { return *this -= 1; }
    Modular operator++(int) { Modular result(*this); *this += 1; return result; }
    Modular operator--(int) { Modular result(*this); *this -= 1; return result; }
    Modular operator-() const { return Modular(-value); }

    template <typename U = T>
    typename enable_if<is_same<typename Modular<U>::Type, int>::value, Modular>::type&
    operator*=(const Modular& rhs) {
        value = normalize(static_cast<int64_t>(value) * static_cast<int64_t>(rhs.value));
        return *this;
    }

    template <typename U = T>
    typename enable_if<is_same<typename Modular<U>::Type, int64_t>::value, Modular>::type&
    operator*=(const Modular& rhs) {
        int64_t q = int64_t(static_cast<long double>(value) * rhs.value / mod());
        value = normalize(value * rhs.value - q * mod());
        return *this;
    }

    template <typename U = T>
    typename enable_if<!is_integral<typename Modular<U>::Type>::value, Modular>::type&
    operator*=(const Modular& rhs) {
        value = normalize(value * rhs.value);
        return *this;
    }

    Modular& operator/=(const Modular& other) { return *this *= Modular(inverse(other.value, mod())); }

    friend const Type& abs(const Modular& x) { return x.value; }

    template <typename U>
    friend bool operator==(const Modular<U>& lhs, const Modular<U>& rhs);

    template <typename U>
    friend bool operator<(const Modular<U>& lhs, const Modular<U>& rhs);

    template <typename V, typename U>
    friend V& operator>>(V& stream, Modular<U>& number);

private:
    Type value;
};

template <typename T> bool operator==(const Modular<T>& lhs, const Modular<T>& rhs) { return lhs.value == rhs.value; }
template <typename T, typename U> bool operator==(const Modular<T>& lhs, U rhs) { return lhs == Modular<T>(rhs); }
template <typename T, typename U> bool operator==(U lhs, const Modular<T>& rhs) { return Modular<T>(lhs) == rhs; }

template <typename T> bool operator!=(const Modular<T>& lhs, const Modular<T>& rhs) { return !(lhs == rhs); }
template <typename T, typename U> bool operator!=(const Modular<T>& lhs, U rhs) { return !(lhs == rhs); }
template <typename T, typename U> bool operator!=(U lhs, const Modular<T>& rhs) { return !(lhs == rhs); }

template <typename T> bool operator<(const Modular<T>& lhs, const Modular<T>& rhs) { return lhs.value < rhs.value; }

template <typename T> Modular<T> operator+(const Modular<T>& lhs, const Modular<T>& rhs) { return Modular<T>(lhs) += rhs; }
template <typename T, typename U> Modular<T> operator+(const Modular<T>& lhs, U rhs) { return Modular<T>(lhs) += rhs; }
template <typename T, typename U> Modular<T> operator+(U lhs, const Modular<T>& rhs) { return Modular<T>(lhs) += rhs; }

template <typename T> Modular<T> operator-(const Modular<T>& lhs, const Modular<T>& rhs) { return Modular<T>(lhs) -= rhs; }
template <typename T, typename U> Modular<T> operator-(const Modular<T>& lhs, U rhs) { return Modular<T>(lhs) -= rhs; }
template <typename T, typename U> Modular<T> operator-(U lhs, const Modular<T>& rhs) { return Modular<T>(lhs) -= rhs; }

template <typename T> Modular<T> operator*(const Modular<T>& lhs, const Modular<T>& rhs) { return Modular<T>(lhs) *= rhs; }
template <typename T, typename U> Modular<T> operator*(const Modular<T>& lhs, U rhs) { return Modular<T>(lhs) *= rhs; }
template <typename T, typename U> Modular<T> operator*(U lhs, const Modular<T>& rhs) { return Modular<T>(lhs) *= rhs; }

template <typename T> Modular<T> operator/(const Modular<T>& lhs, const Modular<T>& rhs) { return Modular<T>(lhs) /= rhs; }
template <typename T, typename U> Modular<T> operator/(const Modular<T>& lhs, U rhs) { return Modular<T>(lhs) /= rhs; }
template <typename T, typename U> Modular<T> operator/(U lhs, const Modular<T>& rhs) { return Modular<T>(lhs) /= rhs; }

template<typename T, typename U>
Modular<T> power(const Modular<T>& a, const U& b) {
    assert(b >= 0);
    Modular<T> x = a, res = 1;
    U p = b;
    while (p > 0) {
        if (p & 1) res *= x;
        x *= x;
        p >>= 1;
    }
    return res;
}

template <typename T>
bool IsZero(const Modular<T>& number) {
    return number() == 0;
}

template <typename T>
string to_string(const Modular<T>& number) {
    return to_string(number());
}

template <typename U, typename T>
U& operator<<(U& stream, const Modular<T>& number) {
    return stream << number();
}

template <typename U, typename T>
U& operator>>(U& stream, Modular<T>& number) {
    typename common_type<typename Modular<T>::Type, int64_t>::type x;
    stream >> x;
    number.value = Modular<T>::normalize(x);
    return stream;
}

// using ModType = int;
// struct VarMod { static ModType value; };
// ModType VarMod::value;
// ModType& md = VarMod::value;
// using Mint = Modular<VarMod>;

constexpr int md = 1e9 + 7;
using Mint = Modular<std::integral_constant<decay<decltype(md)>::type, md>>;

// vector<Mint> fact(1, 1);
// vector<Mint> inv_fact(1, 1);

// Mint C(int n, int k) {
//     if (k < 0 || k > n) {
//         return 0;
//     }
//     while ((int) fact.size() < n + 1) {
//         fact.push_back(fact.back() * (int) fact.size());
//         inv_fact.push_back(1 / fact.back());
//     }
//     return fact[n] * inv_fact[k] * inv_fact[n - k];
// }

Mint get(Mint h, Mint w) {
    return h * w * (h + 1) * (w + 1) / 4;
}

signed main() {
    ios::sync_with_stdio(false);
    cin.tie(nullptr);
    int n;
    cin >> n;
    vector<int> h(n), w(n);
    for (int i = 0; i < n; i++) {
        cin >> h[i];
    }
    for (int i = 0; i < n; i++) {
        cin >> w[i];
    }
    vector<Mint> p(n + 1);
    for (int i = 0; i < n; i++) {
        p[i + 1] = p[i] + w[i];
    }
    vector<int> l(n, -1), r(n, n), stk;
    for (int i = 0; i < n; i++) {
        while (!stk.empty() && h[stk.back()] >= h[i]) {
            stk.pop_back();
        }
        if (!stk.empty()) {
            l[i] = stk.back();
        }
        stk.push_back(i);
    }
    stk.clear();
    for (int i = n - 1; i >= 0; i--) {
        while (!stk.empty() && h[stk.back()] >= h[i]) {
            stk.pop_back();
        }
        if (!stk.empty()) {
            r[i] = stk.back();
        }
        stk.push_back(i);
    }
    vector<int> ord(n);
    iota(ord.begin(), ord.end(), 0);
    sort(ord.begin(), ord.end(), [&](int i, int j) {
        return h[i] < h[j];
    });
    for (int i = 0; i < n; i++) {
        l[i]++;
        r[i]--;
    }
    Mint ans = 0;
    vector<int> a(n);
    for (auto i : ord) {
        Mint x = p[r[i] + 1] - p[l[i]];
        ans += get(Mint(h[i]), x);
        ans -= get(Mint(a[i]), x);
        for (int j = l[i]; j <= r[i]; j++) {
            a[j] = h[i];
        }
    }
    cout << ans << '\n';
    return 0;
}
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