#877190 (C++17) No.2336 Do you like typical problems?

• 問題: No.2336 Do you like typical problems?
• ユーザー: Forested
• 提出日時: 2023-06-02 22:20:58
• 言語: C++17 (gcc 12.3.0 + boost 1.83.0)
• 結果: AC
• 実行時間: 429 ms / 2,000 ms
• コード長: 13,183 bytes
• コンパイル時間: 1,804 ms
• コンパイル使用メモリ: 141,560 KB
• 実行使用メモリ: 9,472 KB
• 最終ジャッジ日時: 2024-06-08 23:41:18
• 合計ジャッジ時間: 5,748 ms
• ジャッジサーバーID （参考情報）: judge2 / judge5

入力	結果	実行時間; 実行使用メモリ
testcase_00	AC	2 ms; 5,248 KB
testcase_01	AC	2 ms; 5,376 KB
testcase_02	AC	2 ms; 5,376 KB
testcase_03	AC	2 ms; 5,376 KB
testcase_04	AC	2 ms; 5,376 KB
testcase_05	AC	2 ms; 5,376 KB
testcase_06	AC	2 ms; 5,376 KB
testcase_07	AC	2 ms; 5,376 KB
testcase_08	AC	5 ms; 5,376 KB
testcase_09	AC	4 ms; 5,376 KB
testcase_10	AC	5 ms; 5,376 KB
testcase_11	AC	5 ms; 5,376 KB
testcase_12	AC	4 ms; 5,376 KB
testcase_13	AC	425 ms; 9,344 KB
testcase_14	AC	429 ms; 9,472 KB
testcase_15	AC	428 ms; 9,472 KB
testcase_16	AC	416 ms; 9,344 KB
testcase_17	AC	408 ms; 9,472 KB
testcase_18	AC	125 ms; 6,400 KB
testcase_19	AC	138 ms; 6,400 KB
testcase_20	AC	413 ms; 9,472 KB

ソースコード

#ifndef LOCAL
#define FAST_IO
#endif

// ============
#include <algorithm>
#include <array>
#include <bitset>
#include <cassert>
#include <cmath>
#include <iomanip>
#include <iostream>
#include <list>
#include <map>
#include <numeric>
#include <queue>
#include <random>
#include <set>
#include <stack>
#include <string>
#include <tuple>
#include <unordered_map>
#include <unordered_set>
#include <utility>
#include <vector>

#define OVERRIDE(a, b, c, d, ...) d
#define REP2(i, n) for (i32 i = 0; i < (i32)(n); ++i)
#define REP3(i, m, n) for (i32 i = (i32)(m); i < (i32)(n); ++i)
#define REP(...) OVERRIDE(__VA_ARGS__, REP3, REP2)(__VA_ARGS__)
#define PER(i, n) for (i32 i = (i32)(n) - 1; i >= 0; --i)
#define ALL(x) begin(x), end(x)

using namespace std;

using u32 = unsigned int;
using u64 = unsigned long long;
using i32 = signed int;
using i64 = signed long long;
using f64 = double;
using f80 = long double;

template <typename T>
using Vec = vector<T>;

template <typename T>
bool chmin(T &x, const T &y) {
    if (x > y) {
        x = y;
        return true;
    }
    return false;
}
template <typename T>
bool chmax(T &x, const T &y) {
    if (x < y) {
        x = y;
        return true;
    }
    return false;
}

#ifdef INT128

using u128 = __uint128_t;
using i128 = __int128_t;

istream &operator>>(istream &is, i128 &x) {
    i64 v;
    is >> v;
    x = v;
    return is;
}
ostream &operator<<(ostream &os, i128 x) {
    os << (i64)x;
    return os;
}
istream &operator>>(istream &is, u128 &x) {
    u64 v;
    is >> v;
    x = v;
    return is;
}
ostream &operator<<(ostream &os, u128 x) {
    os << (u64)x;
    return os;
}

#endif

[[maybe_unused]] constexpr i32 INF = 1000000100;
[[maybe_unused]] constexpr i64 INF64 = 3000000000000000100;
struct SetUpIO {
    SetUpIO() {
#ifdef FAST_IO
        ios::sync_with_stdio(false);
        cin.tie(nullptr);
#endif
        cout << fixed << setprecision(15);
    }
} set_up_io;
// ============

#ifdef DEBUGF
#else
#define DBG(x) (void)0
#endif

// ============

#include <cassert>
#include <iostream>
#include <type_traits>

// ============

constexpr bool is_prime(unsigned n) {
    if (n == 0 || n == 1) {
        return false;
    }
    for (unsigned i = 2; i * i <= n; ++i) {
        if (n % i == 0) {
            return false;
        }
    }
    return true;
}

constexpr unsigned mod_pow(unsigned x, unsigned y, unsigned mod) {
    unsigned ret = 1, self = x;
    while (y != 0) {
        if (y & 1) {
            ret = (unsigned) ((unsigned long long) ret * self % mod);
        }
        self = (unsigned) ((unsigned long long) self * self % mod);
        y /= 2;
    }
    return ret;
}

template <unsigned mod>
constexpr unsigned primitive_root() {
    static_assert(is_prime(mod), "`mod` must be a prime number.");
    if (mod == 2) {
        return 1;
    }

    unsigned primes[32] = {};
    int it = 0;
    {
        unsigned m = mod - 1;
        for (unsigned i = 2; i * i <= m; ++i) {
            if (m % i == 0) {
                primes[it++] = i;
                while (m % i == 0) {
                    m /= i;
                }
            }
        }
        if (m != 1) {
            primes[it++] = m;
        }
    }
    for (unsigned i = 2; i < mod; ++i) {
        bool ok = true;
        for (int j = 0; j < it; ++j) {
            if (mod_pow(i, (mod - 1) / primes[j], mod) == 1) {
                ok = false;
                break;
            }
        }
        if (ok)
            return i;
    }
    return 0;
}

// y >= 1
template <typename T>
constexpr T safe_mod(T x, T y) {
    x %= y;
    if (x < 0) {
        x += y;
    }
    return x;
}

// y != 0
template <typename T>
constexpr T floor_div(T x, T y) {
    if (y < 0) {
        x *= -1;
        y *= -1;
    }
    if (x >= 0) {
        return x / y;
    } else {
        return -((-x + y - 1) / y);
    }
}

// y != 0
template <typename T>
constexpr T ceil_div(T x, T y) {
    if (y < 0) {
        x *= -1;
        y *= -1;
    }
    if (x >= 0) {
        return (x + y - 1) / y;
    } else {
        return -(-x / y);
    }
}
// ============

template <unsigned mod>
class ModInt {
    static_assert(mod != 0, "`mod` must not be equal to 0.");
    static_assert(
        mod < (1u << 31),
        "`mod` must be less than (1u << 31) = 2147483648.");

    unsigned val;

public:
    static constexpr unsigned get_mod() {
        return mod;
    }
    
    constexpr ModInt() : val(0) {}
    template <typename T, std::enable_if_t<std::is_signed_v<T>> * = nullptr>
    constexpr ModInt(T x) : val((unsigned) ((long long) x % (long long) mod + (x < 0 ? mod : 0))) {}
    template <typename T, std::enable_if_t<std::is_unsigned_v<T>> * = nullptr>
    constexpr ModInt(T x) : val((unsigned) (x % mod)) {}

    static constexpr ModInt raw(unsigned x) {
        ModInt<mod> ret;
        ret.val = x;
        return ret;
    }

    constexpr unsigned get_val() const {
        return val;
    }

    constexpr ModInt operator+() const {
        return *this;
    }
    constexpr ModInt operator-() const {
        return ModInt<mod>(0u) - *this;
    }

    constexpr ModInt &operator+=(const ModInt &rhs) {
        val += rhs.val;
        if (val >= mod)
            val -= mod;
        return *this;
    }
    constexpr ModInt &operator-=(const ModInt &rhs) {
        if (val < rhs.val)
            val += mod;
        val -= rhs.val;
        return *this;
    }
    constexpr ModInt &operator*=(const ModInt &rhs) {
        val = (unsigned long long)val * rhs.val % mod;
        return *this;
    }
    constexpr ModInt &operator/=(const ModInt &rhs) {
        val = (unsigned long long)val * rhs.inv().val % mod;
        return *this;
    }

    friend constexpr ModInt operator+(const ModInt &lhs, const ModInt &rhs) {
        return ModInt<mod>(lhs) += rhs;
    }
    friend constexpr ModInt operator-(const ModInt &lhs, const ModInt &rhs) {
        return ModInt<mod>(lhs) -= rhs;
    }
    friend constexpr ModInt operator*(const ModInt &lhs, const ModInt &rhs) {
        return ModInt<mod>(lhs) *= rhs;
    }
    friend constexpr ModInt operator/(const ModInt &lhs, const ModInt &rhs) {
        return ModInt<mod>(lhs) /= rhs;
    }

    constexpr ModInt pow(unsigned long long x) const {
        ModInt<mod> ret = ModInt<mod>::raw(1);
        ModInt<mod> self = *this;
        while (x != 0) {
            if (x & 1)
                ret *= self;
            self *= self;
            x >>= 1;
        }
        return ret;
    }
    constexpr ModInt inv() const {
        static_assert(is_prime(mod), "`mod` must be a prime number.");
        assert(val != 0);
        return this->pow(mod - 2);
    }

    friend std::istream &operator>>(std::istream &is, ModInt<mod> &x) {
        long long val;
        is >> val;
        x.val = val % mod + (val < 0 ? mod : 0);
        return is;
    }

    friend std::ostream &operator<<(std::ostream &os, const ModInt<mod> &x) {
        os << x.val;
        return os;
    }

    friend bool operator==(const ModInt &lhs, const ModInt &rhs) {
        return lhs.val == rhs.val;
    }
    
    friend bool operator!=(const ModInt &lhs, const ModInt &rhs) {
        return lhs.val != rhs.val;
    }
};

[[maybe_unused]] constexpr unsigned mod998244353 = 998244353;
[[maybe_unused]] constexpr unsigned mod1000000007 = 1000000007;

// ============
// ============

// ============

#include <cassert>
#include <vector>

// ============

#include <limits>
#include <utility>

template <typename T>
struct Add {
    using Value = T;
    static Value id() {
        return T(0);
    }
    static Value op(const Value &lhs, const Value &rhs) {
        return lhs + rhs;
    }
    static Value inv(const Value &x) {
        return -x;
    }
};

template <typename T>
struct Mul {
    using Value = T;
    static Value id() {
        return Value(1);
    }
    static Value op(const Value &lhs, const Value &rhs) {
        return lhs * rhs;
    }
    static Value inv(const Value &x) {
        return Value(1) / x;
    }
};

template <typename T>
struct Min {
    using Value = T;
    static Value id() {
        return std::numeric_limits<T>::max();
    }
    static Value op(const Value &lhs, const Value &rhs) {
        return std::min(lhs, rhs);
    }
};

template <typename T>
struct Max {
    using Value = T;
    static Value id() {
        return std::numeric_limits<Value>::min();
    }
    static Value op(const Value &lhs, const Value &rhs) {
        return std::max(lhs, rhs);
    }
};

template <typename T>
struct Xor {
    using Value = T;
    static Value id() {
        return T(0);
    }
    static Value op(const Value &lhs, const Value &rhs) {
        return lhs ^ rhs;
    }
    static Value inv(const Value &x) {
        return x;
    }
};

template <typename Monoid>
struct Reversible {
    using Value = std::pair<typename Monoid::Value, typename Monoid::Value>;
    static Value id() {
        return Value(Monoid::id(), Monoid::id());
    }
    static Value op(const Value &v1, const Value &v2) {
        return Value(
            Monoid::op(v1.first, v2.first),
            Monoid::op(v2.second, v1.second));
    }
};

// ============

template <typename CommutativeGroup>
class FenwickTree {
public:
    using Value = typename CommutativeGroup::Value;

private:
    std::vector<Value> data;

public:
    FenwickTree(int n) : data(n, CommutativeGroup::id()) {}

    void add(int idx, const Value &x) {
        assert(idx >= 0 && idx < (int) data.size());
        for (; idx < (int) data.size(); idx |= idx + 1) {
            data[idx] = CommutativeGroup::op(data[idx], x);
        }
    }

    Value sum(int r) const {
        assert(r >= 0 && r <= (int) data.size());
        Value ret = CommutativeGroup::id();
        for (; r > 0; r &= r - 1) {
            ret = CommutativeGroup::op(ret, data[r - 1]);
        }
        return ret;
    }

    Value sum(int l, int r) const {
        assert(l >= 0 && l <= r && r <= (int) data.size());
        return CommutativeGroup::op(sum(r), CommutativeGroup::inv(sum(l)));
    }
};

template <typename T>
using FenwickTreeAdd = FenwickTree<Add<T>>;
// ============

template <typename T>
class RangeAddRangeSum {
    int n;
    FenwickTree<Add<T>> ft0;
    FenwickTree<Add<T>> ft1;
    
public:
    RangeAddRangeSum(int n) : n(n), ft0(n + 1), ft1(n + 1) {}
    
    void add(int l, int r, const T &v) {
        assert(0 <= l && l <= r && r <= n);
        ft0.add(l, v);
        ft0.add(r, -v);
        ft1.add(l, -T(l) * v);
        ft1.add(r, T(r) * v);
    }
    
    T sum(int l, int r) const {
        assert(0 <= l && l <= r && r <= n);
        return T(r) * ft0.sum(r) + ft1.sum(r) - T(l) * ft0.sum(l) - ft1.sum(l);
    }
};
// ============
// ============

#include <algorithm>
#include <vector>

template <typename T>
class CoordinateCompression {
    std::vector<T> data;

    int size_sum() {
        return 0;
    }

    template <typename... Tail>
    int size_sum(const std::vector<T> &head, const Tail &...tail) {
        return (int) head.size() + size_sum(tail...);
    }

    void push() {}

    template <typename... Tail>
    void push(const std::vector<T> &head, const Tail &...tail) {
        for (const T &ele : head) {
            data.emplace_back(ele);
        }
        push(tail...);
    }

    void compress() {}

    template <typename... Tail>
    void compress(std::vector<T> &head, Tail &...tail) {
        for (T &ele : head) {
            ele = (T) (std::lower_bound(data.begin(), data.end(), ele) - data.begin());
        }
        compress(tail...);
    }

public:
    template <typename... V>
    CoordinateCompression(V &...v) {
        data.reserve(size_sum(v...));
        push(v...);
        std::sort(data.begin(), data.end());
        data.erase(std::unique(data.begin(), data.end()), data.end());
        compress(v...);
    }

    const T &operator[](const T &ele) const {
        return data[ele];
    }

    int size() const {
        return data.size();
    }
    
    bool contains(const T &ele) const {
        auto it = std::lower_bound(data.begin(), data.end(), ele);
        return it != data.end() && *it == ele;
    }
    
    T cc(const T &ele) const {
        return (T) (std::lower_bound(data.begin(), data.end(), ele) - data.begin());
    }
};
// ============

using Mint = ModInt<mod998244353>;

int main() {
    i32 n;
    cin >> n;
    Vec<i32> b(n), c(n);
    REP(i, n) {
        cin >> b[i] >> c[i];
        --b[i];
    }
    if (n == 1) {
        cout << 0 << '\n';
        exit(0);
    }
    CoordinateCompression<i32> cc(b, c);
    RangeAddRangeSum<Mint> rr(cc.size());
    REP(i, n) {
        rr.add(b[i], c[i], Mint(1) / Mint(cc[c[i]] - cc[b[i]]));
    }
    REP(i, cc.size() - 1) {
        Mint t = rr.sum(i, i + 1);
        rr.add(i, i + 1, t * (Mint(cc[i + 1] - cc[i] - 1)));
    }
    Mint eq;
    REP(i, n) {
        Mint s = rr.sum(b[i], c[i]);
        DBG(s);
        s -= Mint(1);
        s /= Mint(cc[c[i]] - cc[b[i]]);
        s /= Mint(n) * Mint(n - 1);
        eq += s;
    }
    Mint inv = (Mint(1) - eq) / Mint(2);
    Mint ex = inv * Mint(n) * Mint(n - 1) / Mint(2);
    REP(i, 1, n + 1) {
        ex *= Mint(i);
    }
    cout << ex << '\n';
}