結果

問題 No.1999 Lattice Teleportation
ユーザー 沙耶花
提出日時 2022-07-01 23:39:41
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 194 ms / 2,000 ms
コード長 4,201 bytes
コンパイル時間 2,316 ms
コンパイル使用メモリ 207,296 KB
最終ジャッジ日時 2025-01-30 03:37:09
ジャッジサーバーID
（参考情報） 		judge1 / judge2
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ファイルパターン 結果
sample AC * 4
other AC * 29
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 #
プレゼンテーションモードにする

#include <bits/stdc++.h>
using namespace std;
using pll = pair<long long, long long>;
// modint
template<int MOD> struct Fp {
    long long val;
    constexpr Fp(long long v = 0) noexcept : val(v % MOD) {
        if (val < 0) val += MOD;
    }
    constexpr int getmod() const { return MOD; }
    constexpr Fp operator - () const noexcept {
        return val ? MOD - val : 0;
    }
    constexpr Fp operator + (const Fp& r) const noexcept { return Fp(*this) += r; }
    constexpr Fp operator - (const Fp& r) const noexcept { return Fp(*this) -= r; }
    constexpr Fp operator * (const Fp& r) const noexcept { return Fp(*this) *= r; }
    constexpr Fp operator / (const Fp& r) const noexcept { return Fp(*this) /= r; }
    constexpr Fp& operator += (const Fp& r) noexcept {
        val += r.val;
        if (val >= MOD) val -= MOD;
        return *this;
    }
    constexpr Fp& operator -= (const Fp& r) noexcept {
        val -= r.val;
        if (val < 0) val += MOD;
        return *this;
    }
    constexpr Fp& operator *= (const Fp& r) noexcept {
        val = val * r.val % MOD;
        return *this;
    }
    constexpr Fp& operator /= (const Fp& r) noexcept {
        long long a = r.val, b = MOD, u = 1, v = 0;
        while (b) {
            long long t = a / b;
            a -= t * b, swap(a, b);
            u -= t * v, swap(u, v);
        }
        val = val * u % MOD;
        if (val < 0) val += MOD;
        return *this;
    }
    constexpr bool operator == (const Fp& r) const noexcept {
        return this->val == r.val;
    }
    constexpr bool operator != (const Fp& r) const noexcept {
        return this->val != r.val;
    }
    friend constexpr istream& operator >> (istream& is, Fp<MOD>& x) noexcept {
        is >> x.val;
        x.val %= MOD;
        if (x.val < 0) x.val += MOD;
        return is;
    }
    friend constexpr ostream& operator << (ostream& os, const Fp<MOD>& x) noexcept {
        return os << x.val;
    }
    friend constexpr Fp<MOD> modpow(const Fp<MOD>& r, long long n) noexcept {
        if (n == 0) return 1;
        if (n < 0) return modpow(modinv(r), -n);
        auto t = modpow(r, n / 2);
        t = t * t;
        if (n & 1) t = t * r;
        return t;
    }
    friend constexpr Fp<MOD> modinv(const Fp<MOD>& r) noexcept {
        long long a = r.val, b = MOD, u = 1, v = 0;
        while (b) {
            long long t = a / b;
            a -= t * b, swap(a, b);
            u -= t * v, swap(u, v);
        }
        return Fp<MOD>(u);
    }
};
const int MOD = 1000000007;
using mint = Fp<MOD>;
mint calc_area(vector<pll> vp) {
    int N = vp.size();
    mint res = 0;
    for (int i = 0; i < N; ++i) {
        mint px = vp[i].first, py = vp[(i+1)%N].first;
        mint qx = vp[i].second, qy = vp[(i+1)%N].second;
        res += px * qy - py * qx;
    }
    return res;
}
long long GCD(long long x, long long y) {
    if (y == 0) return x;
    else return GCD(y, x % y);
}
int main() {
    int N;
    cin >> N;
    vector<long long> X(N), Y(N);
    for (int i = 0; i < N; ++i){
        cin >> X[i] >> Y[i];
        if(Y[i]<0){
            X[i]*=-1;
            Y[i]*=-1;
        }
    }
    {
        vector<long long> x,y;
        for(int i=0;i<N;i++){
            if(X[i]!=0||Y[i]!=0){
                x.push_back(X[i]);
                y.push_back(Y[i]);
            }
        }
        swap(x,X);
        swap(y,Y);
        N = X.size();
    }
    if(N==0){
        cout<<1<<endl;
        return 0;
    }
    vector<int> ids(N);
    iota(ids.begin(), ids.end(), 0);
    sort(ids.begin(), ids.end(), [&](int i, int j) {
        return Y[i]*X[j] < Y[j]*X[i];
    });
    vector<pll> vp;
    vp.emplace_back(0, 0);
    for (auto i : ids) {
        auto p = vp.back();
        vp.emplace_back(p.first + X[i], p.second + Y[i]);
    }
    auto p = vp.back();
    int M = vp.size();
    for (int i = 1; i < M-1; ++i) {
        vp.emplace_back(p.first - vp[i].first, p.second - vp[i].second);
    }
    mint S = calc_area(vp);
    mint B = 0;
    for (int i = 0; i < vp.size(); ++i) {
        long long dx = vp[(i+1)%vp.size()].first - vp[i].first;
        long long dy = vp[(i+1)%vp.size()].second - vp[i].second;
        dx = abs(dx), dy = abs(dy);
        long long g = GCD(dx, dy);
        B += g;
    }
    mint res = (S + B) / 2;
    res = res+1;
    cout << res << endl;
}
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