Code : Rare Coins

Cubic : Without Template ↕

Submission

#include <bits/stdc++.h>
using namespace std;

// Template starts
#include <codeforces/modint.hpp>
// Template ends

constexpr int md = 998244353;
using mint = Modular<std::integral_constant<decay<decltype(md)>::type, md>>;

#define endl "\n"

int maxn = (int)1e6 + 1;
vector<mint> fac;

const mint p = mint(1) / 2;

void precompute_factorial() {
    fac.resize(maxn + 1);

    fac[0] = 1;
    for (int i = 1; i < maxn; i++) {
        fac[i] = i * fac[i - 1];
    }
}

mint comb(int n, int r) {
    if (r < 0 || r > n) {
        return 0;
    }
    return fac[n] / (fac[n - r] * fac[r]);
}

void solve() {
    int n, q;
    cin >> n >> q;
    vector<int> a(n), b(n);
    for (int i = 0; i < n; i++) {
        cin >> a[i];
    }
    for (int i = 0; i < n; i++) {
        cin >> b[i];
    }

    int ta = accumulate(a.begin(), a.end(), 0);
    int tb = accumulate(b.begin(), b.end(), 0);

    for (int zz = 0; zz < q; zz++) {
        int l, r;
        cin >> l >> r;
        l--, r--;
        int la = 0, lb = 0;
        for (int i = l; i <= r; i++) {
            la += a[i], lb += b[i];
        }
        int ra = ta - la;
        int rb = tb - lb;

        mint ans = 0;
        for (int x = 0; x <= lb; x++) {
            mint lhs = comb(lb, x) * power(p, lb);
            for (int y = 0; y < la - ra + x; y++) {
                mint rhs = comb(rb, y) * power(p, rb);
                ans += lhs * rhs;
            }
        }
        cout << ans << " ";
    }
    cout << endl;
}

int main() {
    precompute_factorial();
    solve();
    return 0;
}

Quadratic : Without Template ↕

Submission

#include <bits/stdc++.h>
using namespace std;

// Template starts
#include <codeforces/modint.hpp>
// Template ends

constexpr int md = 998244353;
using mint = Modular<std::integral_constant<decay<decltype(md)>::type, md>>;

#define endl "\n"

int maxn = (int)1e6 + 1;
vector<mint> fac;

const mint p = mint(1) / 2;

void precompute_factorial() {
    fac.resize(maxn + 1);

    fac[0] = 1;
    for (int i = 1; i < maxn; i++) {
        fac[i] = i * fac[i - 1];
    }
}

mint comb(int n, int r) {
    if (r < 0 || r > n) {
        return 0;
    }
    return fac[n] / (fac[n - r] * fac[r]);
}

void solve() {
    int n, q;
    cin >> n >> q;
    vector<int> a(n), b(n);
    for (int i = 0; i < n; i++) {
        cin >> a[i];
    }
    for (int i = 0; i < n; i++) {
        cin >> b[i];
    }

    int ta = accumulate(a.begin(), a.end(), 0);
    int tb = accumulate(b.begin(), b.end(), 0);

    for (int zz = 0; zz < q; zz++) {
        int l, r;
        cin >> l >> r;
        l--, r--;
        int la = 0, lb = 0;
        for (int i = l; i <= r; i++) {
            la += a[i], lb += b[i];
        }
        int ra = ta - la;
        int rb = tb - lb;

        // dp[i] is the number of ways to have value = i in the rb silver pile.
        vector<mint> dp(rb + 1);
        for (int i = 0; i <= rb; i++) {
            dp[i] = comb(rb, i) * power(p, rb) + (i ? dp[i - 1] : 0);
        }

        mint ans = 0;
        for (int x = 0; x <= lb; x++) {
            mint lhs = comb(lb, x) * power(p, lb);
            int lim = min(la - ra + x - 1, rb);
            if (lim < 0) {
                continue;
            }
            mint rhs = dp[lim];
            ans += lhs * rhs;
        }
        cout << ans << " ";
    }
    cout << endl;
}

int main() {
    precompute_factorial();
    solve();
    return 0;
}

Cubic : With Template ↕

Submission

#include <bits/stdc++.h>
using namespace std;

// Template starts
// ...
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) {
        if ((value += other.value) >= mod())
            value -= mod();
        return *this;
    }
    Modular &operator-=(const Modular &other) {
        if ((value -= other.value) < 0)
            value += 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, long long>::value,
                       Modular>::type &
    operator*=(const Modular &rhs) {
        long long q = static_cast<long long>(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());
}

// U == std::ostream? but done this way because of fastoutput
template <typename U, typename T>
U &operator<<(U &stream, const Modular<T> &number) {
    return stream << number();
}

// U == std::istream? but done this way because of fastinput
template <typename U, typename T> U &operator>>(U &stream, Modular<T> &number) {
    typename common_type<typename Modular<T>::Type, long long>::type x;
    stream >> x;
    number.value = Modular<T>::normalize(x);
    return stream;
}

// ...
// Template ends
constexpr int md = 998244353;
using mint = Modular<std::integral_constant<decay<decltype(md)>::type, md>>;

#define endl "\n"

int maxn = (int)1e6 + 1;
vector<mint> fac;

const mint p = mint(1) / 2;

void precompute_factorial() {
    fac.resize(maxn + 1);

    fac[0] = 1;
    for (int i = 1; i < maxn; i++) {
        fac[i] = i * fac[i - 1];
    }
}

mint comb(int n, int r) {
    if (r < 0 || r > n) {
        return 0;
    }
    return fac[n] / (fac[n - r] * fac[r]);
}

void solve() {
    int n, q;
    cin >> n >> q;
    vector<int> a(n), b(n);
    for (int i = 0; i < n; i++) {
        cin >> a[i];
    }
    for (int i = 0; i < n; i++) {
        cin >> b[i];
    }

    int ta = accumulate(a.begin(), a.end(), 0);
    int tb = accumulate(b.begin(), b.end(), 0);

    for (int zz = 0; zz < q; zz++) {
        int l, r;
        cin >> l >> r;
        l--, r--;
        int la = 0, lb = 0;
        for (int i = l; i <= r; i++) {
            la += a[i], lb += b[i];
        }
        int ra = ta - la;
        int rb = tb - lb;

        mint ans = 0;
        for (int x = 0; x <= lb; x++) {
            mint lhs = comb(lb, x) * power(p, lb);
            for (int y = 0; y < la - ra + x; y++) {
                mint rhs = comb(rb, y) * power(p, rb);
                ans += lhs * rhs;
            }
        }
        cout << ans << " ";
    }
    cout << endl;
}

int main() {
    precompute_factorial();
    solve();
    return 0;
}