結果

問題 No.1999 Lattice Teleportation
ユーザー tokusakurai
提出日時 2022-07-02 12:59:25
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 79 ms / 2,000 ms
コード長 6,203 bytes
コンパイル時間 2,262 ms
コンパイル使用メモリ 205,100 KB
最終ジャッジ日時 2025-01-30 03:55:35
ジャッジサーバーID
（参考情報） 		judge1 / judge2
このコードへのチャレンジ
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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;
#define rep(i, n) for (int i = 0; i < n; i++)
#define rep2(i, x, n) for (int i = x; i <= n; i++)
#define rep3(i, x, n) for (int i = x; i >= n; i--)
#define each(e, v) for (auto &e : v)
#define pb push_back
#define eb emplace_back
#define all(x) x.begin(), x.end()
#define rall(x) x.rbegin(), x.rend()
#define sz(x) (int)x.size()
using ll = long long;
using pii = pair<int, int>;
using pil = pair<int, ll>;
using pli = pair<ll, int>;
using pll = pair<ll, ll>;
template <typename T>
bool chmax(T &x, const T &y) {
    return (x < y) ? (x = y, true) : false;
}
template <typename T>
bool chmin(T &x, const T &y) {
    return (x > y) ? (x = y, true) : false;
}
template <typename T>
int flg(T x, int i) {
    return (x >> i) & 1;
}
template <typename T>
void print(const vector<T> &v, T x = 0) {
    int n = v.size();
    for (int i = 0; i < n; i++) cout << v[i] + x << (i == n - 1 ? '\n' : ' ');
    if (v.empty()) cout << '\n';
}
template <typename T>
void printn(const vector<T> &v, T x = 0) {
    int n = v.size();
    for (int i = 0; i < n; i++) cout << v[i] + x << '\n';
}
template <typename T>
int lb(const vector<T> &v, T x) {
    return lower_bound(begin(v), end(v), x) - begin(v);
}
template <typename T>
int ub(const vector<T> &v, T x) {
    return upper_bound(begin(v), end(v), x) - begin(v);
}
template <typename T>
void rearrange(vector<T> &v) {
    sort(begin(v), end(v));
    v.erase(unique(begin(v), end(v)), end(v));
}
template <typename T>
vector<int> id_sort(const vector<T> &v, bool greater = false) {
    int n = v.size();
    vector<int> ret(n);
    iota(begin(ret), end(ret), 0);
    sort(begin(ret), end(ret), [&](int i, int j) { return greater ? v[i] > v[j] : v[i] < v[j]; });
    return ret;
}
template <typename S, typename T>
pair<S, T> operator+(const pair<S, T> &p, const pair<S, T> &q) {
    return make_pair(p.first + q.first, p.second + q.second);
}
template <typename S, typename T>
pair<S, T> operator-(const pair<S, T> &p, const pair<S, T> &q) {
    return make_pair(p.first - q.first, p.second - q.second);
}
template <typename S, typename T>
istream &operator>>(istream &is, pair<S, T> &p) {
    S a;
    T b;
    is >> a >> b;
    p = make_pair(a, b);
    return is;
}
template <typename S, typename T>
ostream &operator<<(ostream &os, const pair<S, T> &p) {
    return os << p.first << ' ' << p.second;
}
struct io_setup {
    io_setup() {
        ios_base::sync_with_stdio(false);
        cin.tie(NULL);
        cout << fixed << setprecision(15);
    }
} io_setup;
const int inf = (1 << 30) - 1;
const ll INF = (1LL << 60) - 1;
const int MOD = 1000000007;
// const int MOD = 998244353;
template <typename T>
int type(pair<T, T> p) {
    if (p.first == 0 && p.second == 0) return 0;
    if (p.second < 0 || (p.second == 0 && p.first > 0)) return -1;
    return 1;
}
template <typename T>
bool compare_arg(pair<T, T> p, pair<T, T> q) {
    int a = type(p), b = type(q);
    if (a != b) return a < b;
    return p.first * q.second > q.first * p.second;
}
template <typename T>
void sort_arg(vector<pair<T, T>> &p) {
    sort(begin(p), end(p), compare_arg<T>);
}
template <int mod>
struct Mod_Int {
    int x;
    Mod_Int() : x(0) {}
    Mod_Int(long long y) : x(y >= 0 ? y % mod : (mod - (-y) % mod) % mod) {}
    static int get_mod() { return mod; }
    Mod_Int &operator+=(const Mod_Int &p) {
        if ((x += p.x) >= mod) x -= mod;
        return *this;
    }
    Mod_Int &operator-=(const Mod_Int &p) {
        if ((x += mod - p.x) >= mod) x -= mod;
        return *this;
    }
    Mod_Int &operator*=(const Mod_Int &p) {
        x = (int)(1LL * x * p.x % mod);
        return *this;
    }
    Mod_Int &operator/=(const Mod_Int &p) {
        *this *= p.inverse();
        return *this;
    }
    Mod_Int &operator++() { return *this += Mod_Int(1); }
    Mod_Int operator++(int) {
        Mod_Int tmp = *this;
        ++*this;
        return tmp;
    }
    Mod_Int &operator--() { return *this -= Mod_Int(1); }
    Mod_Int operator--(int) {
        Mod_Int tmp = *this;
        --*this;
        return tmp;
    }
    Mod_Int operator-() const { return Mod_Int(-x); }
    Mod_Int operator+(const Mod_Int &p) const { return Mod_Int(*this) += p; }
    Mod_Int operator-(const Mod_Int &p) const { return Mod_Int(*this) -= p; }
    Mod_Int operator*(const Mod_Int &p) const { return Mod_Int(*this) *= p; }
    Mod_Int operator/(const Mod_Int &p) const { return Mod_Int(*this) /= p; }
    bool operator==(const Mod_Int &p) const { return x == p.x; }
    bool operator!=(const Mod_Int &p) const { return x != p.x; }
    Mod_Int inverse() const {
        assert(*this != Mod_Int(0));
        return pow(mod - 2);
    }
    Mod_Int pow(long long k) const {
        Mod_Int now = *this, ret = 1;
        for (; k > 0; k >>= 1, now *= now) {
            if (k & 1) ret *= now;
        }
        return ret;
    }
    friend ostream &operator<<(ostream &os, const Mod_Int &p) { return os << p.x; }
    friend istream &operator>>(istream &is, Mod_Int &p) {
        long long a;
        is >> a;
        p = Mod_Int<mod>(a);
        return is;
    }
};
using mint = Mod_Int<MOD>;
int main() {
    int N;
    cin >> N;
    vector<pll> p1;
    rep(i, N) {
        ll x, y;
        cin >> x >> y;
        if (x == 0 && y == 0) continue;
        if (x < 0) x *= -1, y *= -1;
        p1.eb(x, y);
    }
    if (empty(p1)) {
        cout << "1\n";
        return 0;
    }
    N = sz(p1);
    sort_arg(p1);
    vector<pll> p2(2 * N + 1);
    pll p = pll(0, 0);
    p2[0] = p;
    rep(i, N) {
        p = p + p1[i];
        p2[i + 1] = p;
    }
    rep(i, N) {
        p = p - p1[i];
        p2[N + 1 + i] = p;
    }
    mint tw = mint(2).inverse();
    mint B = 0;
    rep(i, 2 * N) {
        auto [x1, y1] = p2[i];
        auto [x2, y2] = p2[i + 1];
        ll dx = abs(x1 - x2), dy = abs(y1 - y2);
        ll g = gcd(dx, dy);
        B += g;
    }
    mint S = 0;
    rep2(i, 1, 2 * N - 2) {
        auto [x1, y1] = p2[i] - p2[0];
        auto [x2, y2] = p2[i + 1] - p2[0];
        S += mint(x1) * mint(y2) - mint(x2) * mint(y1);
    }
    S *= tw;
    cout << S + B * tw + 1 << '\n';
}
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