結果

問題 No.1596 Distance Sum in 2D Plane
ユーザー scol_kpscol_kp
提出日時 2021-07-09 22:10:01
言語 C++17
(gcc 12.3.0 + boost 1.83.0)
結果
AC  
実行時間 71 ms / 2,000 ms
コード長 8,811 bytes
コンパイル時間 2,042 ms
コンパイル使用メモリ 203,008 KB
実行使用メモリ 12,548 KB
最終ジャッジ日時 2023-09-14 09:18:55
合計ジャッジ時間 4,054 ms
ジャッジサーバーID
(参考情報)
judge11 / judge15
このコードへのチャレンジ(β)

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 15 ms
12,476 KB
testcase_01 AC 16 ms
12,408 KB
testcase_02 AC 68 ms
12,416 KB
testcase_03 AC 71 ms
12,428 KB
testcase_04 AC 69 ms
12,480 KB
testcase_05 AC 68 ms
12,480 KB
testcase_06 AC 69 ms
12,360 KB
testcase_07 AC 70 ms
12,476 KB
testcase_08 AC 68 ms
12,544 KB
testcase_09 AC 68 ms
12,548 KB
testcase_10 AC 69 ms
12,364 KB
testcase_11 AC 59 ms
12,284 KB
testcase_12 AC 60 ms
12,372 KB
testcase_13 AC 61 ms
12,476 KB
testcase_14 AC 2 ms
4,380 KB
testcase_15 AC 2 ms
4,380 KB
testcase_16 AC 1 ms
4,376 KB
testcase_17 AC 2 ms
4,376 KB
testcase_18 AC 2 ms
4,376 KB
testcase_19 AC 1 ms
4,380 KB
権限があれば一括ダウンロードができます

ソースコード

diff #

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

using ll = long long;
using Vi = std::vector<int>;
using Vl = std::vector<ll>;
using Pii = std::pair<int, int>;
using Pll = std::pair<ll, ll>;

constexpr int I_INF = std::numeric_limits<int>::max();
constexpr ll L_INF = std::numeric_limits<ll>::max();

template <typename T1, typename T2>
inline bool chmin(T1& a, const T2& b) {
    if (a > b) {
        a = b;
        return true;
    }
    return false;
}
template <typename T1, typename T2>
inline bool chmax(T1& a, const T2& b) {
    if (a < b) {
        a = b;
        return true;
    }
    return false;
}

template <std::ostream& os = std::cout>
class Prints {
private:
    class __Prints {
    public:
        __Prints(const char* sep, const char* term) : sep(sep), term(term) {}
        template <class... Args>
#if __cplusplus >= 201703L
        auto operator()(const Args&... args) const -> decltype((os << ... << std::declval<Args>()), void()) {
#else
        void operator()(const Args&... args) const {
#endif
            print(args...);
        }
        template <typename T>
#if __cplusplus >= 201703L
        auto pvec(const T& vec, size_t sz) const -> decltype(os << std::declval<decltype(std::declval<T>()[0])>(), void()) {
#else
        void pvec(const T& vec, size_t sz) const {
#endif
            for (size_t i = 0; i < sz; i++)
                os << vec[i] << (i == sz - 1 ? term : sep);
        }
        template <typename T>
#if __cplusplus >= 201703L
        auto pmat(const T& mat, size_t h, size_t w) const -> decltype(os << std::declval<decltype(std::declval<T>()[0][0])>(), void()) {
#else
        void pmat(const T& mat, size_t h, size_t w) const {
#endif
            for (size_t i = 0; i < h; i++)
                for (size_t j = 0; j < w; j++)
                    os << mat[i][j] << (j == w - 1 ? term : sep);
        }

    private:
        const char *sep, *term;
        void print() const { os << term; }
        void print_rest() const { os << term; }
        template <class T, class... Tail>
        void print(const T& head, const Tail&... tail) const { os << head, print_rest(tail...); }
        template <class T, class... Tail>
        void print_rest(const T& head, const Tail&... tail) const { os << sep << head, print_rest(tail...); }
    };

public:
    Prints() {}
    __Prints operator()(const char* sep = " ", const char* term = "\n") const { return __Prints(sep, term); }
};

Prints<> prints;
Prints<std::cerr> prints_err;

//%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

template <std::int_fast64_t Modulus>
class ModInt {
    using i64 = std::int_fast64_t;

private:
    i64 m_value;

public:
    constexpr ModInt(const i64 x = 0) noexcept : m_value(x) {
        if (m_value < -Modulus || m_value >= Modulus) m_value %= Modulus;
        if (m_value < 0) m_value += Modulus;
    }

    constexpr i64 const& value() const noexcept { return m_value; }

    constexpr ModInt& operator+=(const ModInt rhs) noexcept {
        m_value += rhs.m_value;
        if (m_value >= Modulus) {
            m_value -= Modulus;
        }
        return *this;
    }
    constexpr ModInt& operator-=(const ModInt rhs) noexcept {
        if (m_value < rhs.m_value) {
            m_value += Modulus;
        }
        m_value -= rhs.m_value;
        return *this;
    }
    constexpr ModInt& operator*=(const ModInt rhs) noexcept {
        m_value *= rhs.m_value;
        if (m_value >= Modulus) m_value %= Modulus;
        return *this;
    }
    constexpr ModInt& operator/=(ModInt rhs) noexcept {
        *this *= rhs.inv();
        return *this;
    }

    constexpr ModInt& operator++() noexcept {
        *this += 1;
        return *this;
    }
    constexpr ModInt operator++(int) noexcept {
        ModInt res = *this;
        *this += 1;
        return res;
    }
    constexpr ModInt& operator--() noexcept {
        *this -= 1;
        return *this;
    }
    constexpr ModInt operator--(int) noexcept {
        ModInt res = *this;
        *this -= 1;
        return res;
    }

    constexpr ModInt inv() const noexcept {
        i64 q = m_value;
        i64 b = Modulus, u = 1, v = 0;
        i64 tmp = 0;
        while (b) {
            i64 t = q / b;
            q -= t * b;
            tmp = q, q = b, b = tmp;
            u -= t * v;
            tmp = u, u = v, v = tmp;
        }
        if (u < -Modulus || u >= Modulus) u %= Modulus;
        if (u < 0) u += Modulus;
        return u;
    }

    constexpr ModInt pow(i64 k) const noexcept {
        ModInt res = 1;
        ModInt tmp = 0;
        if (k < 0) {
            tmp = this->inv();
            k = -k;
        } else {
            tmp = *this;
        }
        for (; k > 0; k >>= 1) {
            if (k & 1) res *= tmp;
            tmp *= tmp;
        }
        return res;
    }

    friend constexpr ModInt operator+(const ModInt& a) noexcept {
        return a;
    }
    friend constexpr ModInt operator-(const ModInt& a) noexcept {
        return ModInt(0) - a;
    }
    friend constexpr ModInt operator+(const ModInt& lhs, const ModInt& rhs) noexcept {
        return ModInt<Modulus>(lhs) += rhs;
    }
    friend constexpr ModInt operator-(const ModInt& lhs, const ModInt& rhs) noexcept {
        return ModInt<Modulus>(lhs) -= rhs;
    }
    friend constexpr ModInt operator*(const ModInt& lhs, const ModInt& rhs) noexcept {
        return ModInt<Modulus>(lhs) *= rhs;
    }
    friend constexpr ModInt operator/(const ModInt& lhs, const ModInt& rhs) noexcept {
        return ModInt<Modulus>(lhs) /= rhs;
    }

    friend constexpr bool operator<(const ModInt& lhs, const ModInt& rhs) noexcept {
        return lhs.m_value < rhs.m_value;
    }
    friend constexpr bool operator>(const ModInt& lhs, const ModInt& rhs) noexcept {
        return lhs.m_value > rhs.m_value;
    }
    friend constexpr bool operator<=(const ModInt& lhs, const ModInt& rhs) noexcept {
        return lhs.m_value <= rhs.m_value;
    }
    friend constexpr bool operator>=(const ModInt& lhs, const ModInt& rhs) noexcept {
        return lhs.m_value >= rhs.m_value;
    }

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

    friend std::istream& operator>>(std::istream& is, ModInt& rhs) {
        i64 a;
        is >> a;
        rhs = a;
        return is;
    }
    friend std::ostream& operator<<(std::ostream& os, const ModInt& rhs) {
        os << rhs.m_value;
        return os;
    }
};

template <std::int_fast64_t Modulus>
class ModComb {
    using i64 = int_fast64_t;
    using Vm = std::vector<ModInt<Modulus>>;

private:
    Vm fac, inv, finv;

public:
    explicit ModComb(i64 n) noexcept : fac(n + 1), inv(n + 1), finv(n + 1) {
        fac[0] = fac[1] = 1;
        finv[0] = finv[1] = 1;
        inv[1] = 1;
        for (i64 i = 2; i < n + 1; ++i) {
            fac[i] = fac[i - 1] * i;
            inv[i] = Modulus - inv[Modulus % i] * (Modulus / i);
            finv[i] = finv[i - 1] * inv[i];
        }
    }

    ModInt<Modulus> comb(i64 n, i64 k) const noexcept {
        ModInt<Modulus> res;
        if (n < k || n < 0 || k < 0)
            res = 0;
        else
            res = fac[n] * finv[n - k] * finv[k];
        return res;
    }

    ModInt<Modulus> perm(i64 n, i64 k) const noexcept {
        ModInt<Modulus> res;
        if (n < k || n < 0 || k < 0)
            res = 0;
        else
            res = fac[n] * finv[n - k];
        return res;
    }

    ModInt<Modulus> get_fac(i64 n) const noexcept { return fac[n]; }
    ModInt<Modulus> get_finv(i64 n) const noexcept { return finv[n]; }
};


constexpr long long MOD = 1000000007;
using Mint = ModInt<MOD>;

void solve() {
    ll N, M;
    cin >> N >> M;
    ModComb<MOD> mc(N * 2);
    Mint ans = mc.comb(N * 2, N) * (N * 2);
    for (ll i = 0; i < M; i++) {
        ll t, x, y;
        cin >> t >> x >> y;
        if (t == 1) {
            ans -= mc.comb(x + y, x) * mc.comb((N - x - 1) + (N - y), N - x - 1);
        } else {
            ans -= mc.comb(x + y, x) * mc.comb((N - x) + (N - y - 1), N - x);
        }
    }
    prints()(ans);
}

//%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

int main() {
#ifdef FASTIO
    std::cin.tie(nullptr), std::cout.tie(nullptr);
    std::ios::sync_with_stdio(false);
#endif
#ifdef FILEINPUT
    std::ifstream ifs("./in_out/input.txt");
    std::cin.rdbuf(ifs.rdbuf());
#endif
#ifdef FILEOUTPUT
    std::ofstream ofs("./in_out/output.txt");
    std::cout.rdbuf(ofs.rdbuf());
#endif
    std::cout << std::setprecision(18) << std::fixed;
    solve();
    std::cout << std::flush;
    return 0;
}
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