#677558 (C++14) No.1596 Distance Sum in 2D Plane

• 問題: No.1596 Distance Sum in 2D Plane
• ユーザー: Mazesoba
• 提出日時: 2021-07-11 19:09:11
• 言語: C++14 (gcc 13.3.0 + boost 1.89.0)
• 結果: AC
• 実行時間: 222 ms / 2,000 ms
• コード長: 4,575 bytes
• コンパイル時間: 1,590 ms
• コンパイル使用メモリ: 167,656 KB
• 実行使用メモリ: 6,784 KB
• 最終ジャッジ日時: 2024-07-02 03:11:09
• 合計ジャッジ時間: 5,698 ms
• ジャッジサーバーID （参考情報）: judge5 / judge1

ファイルパターン	結果
sample	AC * 3
other	AC * 17

ソースコード

// 問題の URL を書いておく
// 

#include <bits/stdc++.h>

using namespace std;

//#define ENABLE_PRINT

#if defined(ENABLE_PRINT)

#define Print(v) \
do {\
    cerr << #v << ": " << v << endl; \
}while(0)

#define PrintVec(v) \
do {\
    for(int __i = 0; __i < v.size(); ++__i) \
    { \
        cerr << #v << "[" << __i << "]: " << v[__i] << endl; \
    }\
}while(0)

#define P(fmt, ...) fprintf(stderr, fmt, __VA_ARGS__)
#define LP fprintf(stderr, "L: %d\n", __LINE__)

#else

#define Print(v) ((void)0)
#define PrintVec(v) ((void)0)
#define P(fmt, ...) ((void)0)
#define LP ((void)0)

#endif

#define rep(i, n) for(int i = 0; i < (int)(n); ++i)

using ll = long long;

namespace internal {

struct modint_base {};
struct static_modint_base : modint_base {};

template <class T> using is_modint = std::is_base_of<modint_base, T>;
template <class T> using is_modint_t = std::enable_if_t<is_modint<T>::value>;

}  // namespace internal

template <int m, std::enable_if_t<(1 <= m)>* = nullptr>
struct static_modint : internal::static_modint_base {
    using mint = static_modint;

  public:
    static constexpr int mod() { return m; }
    static mint raw(int v) {
        mint x;
        x._v = v;
        return x;
    }

    static_modint() : _v(0) {}
    static_modint(int v) {
        long long x = (long long)(v % (long long)(umod()));
        if (x < 0) x += umod();
        _v = (unsigned int)(x);
    }
    static_modint(bool v) { _v = ((unsigned int)(v) % umod()); }

    unsigned int val() const { return _v; }

    mint& operator++() {
        _v++;
        if (_v == umod()) _v = 0;
        return *this;
    }
    mint& operator--() {
        if (_v == 0) _v = umod();
        _v--;
        return *this;
    }
    mint operator++(int) {
        mint result = *this;
        ++*this;
        return result;
    }
    mint operator--(int) {
        mint result = *this;
        --*this;
        return result;
    }

    mint& operator+=(const mint& rhs) {
        _v += rhs._v;
        if (_v >= umod()) _v -= umod();
        return *this;
    }
    mint& operator-=(const mint& rhs) {
        _v -= rhs._v;
        if (_v >= umod()) _v += umod();
        return *this;
    }
    mint& operator*=(const mint& rhs) {
        unsigned long long z = _v;
        z *= rhs._v;
        _v = (unsigned int)(z % umod());
        return *this;
    }
    mint& operator/=(const mint& rhs) { return *this = *this * rhs.inv(); }

    mint operator+() const { return *this; }
    mint operator-() const { return mint() - *this; }

    mint pow(long long n) const {
        assert(0 <= n);
        mint x = *this, r = 1;
        while (n) {
            if (n & 1) r *= x;
            x *= x;
            n >>= 1;
        }
        return r;
    }
    mint inv() const {
        if (prime) {
            assert(_v);
            return pow(umod() - 2);
        } else {
            abort();
        }
    }

    friend mint operator+(const mint& lhs, const mint& rhs) {
        return mint(lhs) += rhs;
    }
    friend mint operator-(const mint& lhs, const mint& rhs) {
        return mint(lhs) -= rhs;
    }
    friend mint operator*(const mint& lhs, const mint& rhs) {
        return mint(lhs) *= rhs;
    }
    friend mint operator/(const mint& lhs, const mint& rhs) {
        return mint(lhs) /= rhs;
    }
    friend bool operator==(const mint& lhs, const mint& rhs) {
        return lhs._v == rhs._v;
    }
    friend bool operator!=(const mint& lhs, const mint& rhs) {
        return lhs._v != rhs._v;
    }

  private:
    unsigned int _v;
    static constexpr unsigned int umod() { return m; }
    static constexpr bool prime = true;
};

using modint1000000007 = static_modint<1000000007>;

using mint = modint1000000007;

const int NMax = 200005 * 2;
mint facts[NMax];
mint invs[NMax];

mint comb(int n, int m)
{
    return invs[m] * facts[n] * invs[n - m];
}

void setup()
{
    facts[0] = 1;
    invs[0] = 1;
    rep(i, NMax - 1)
    {
        facts[i + 1] = facts[i] * (i + 1);
        invs[i + 1] = facts[i + 1].inv();
    }
}

int main(int, const char**)
{
    setup();

    int N, M;
    cin >> N >> M;

    auto ans = comb(2 * N, N) * N * 2;
    rep(i, M)
    {
        int t, x, y;
        cin >> t >> x >> y;
        auto d0 = comb(x + y, x);
        if(t == 1)
        {
            auto d1 = comb((N - (x + 1)) + (N - y), (N - y));
            ans -= d0 * d1;
        }
        else
        {
            auto d1 = comb((N - x) + (N - (y + 1)), (N - x));
            ans -= d0 * d1;
        }
    }
    cout << ans.val() << endl;

    return 0;
}