結果

問題 No.1999 Lattice Teleportation
ユーザー woodywoody
提出日時 2022-07-04 23:47:27
言語 C++14
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 403 ms / 2,000 ms
コード長 8,917 bytes
コンパイル時間 4,473 ms
コンパイル使用メモリ 239,268 KB
実行使用メモリ 12,208 KB
最終ジャッジ日時 2024-12-14 19:06:10
合計ジャッジ時間 11,685 ms
ジャッジサーバーID
（参考情報） 		judge4 / judge5
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ファイルパターン 結果
sample AC * 4
other AC * 29
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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>
#include<atcoder/all>
#define rep(i,b) for(int i=0;i<b;i++)
#define rrep(i,b) for(int i=b-1;i>=0;i--)
#define rep1(i,b) for(int i=1;i<b;i++)
#define repx(i,x,b) for(int i=x;i<b;i++)
#define fore(i,a) for(auto i:a)
#define fore1(i,a) for(auto &i:a)
#define rng(x) (x).begin(), (x).end()
#define rrng(x) (x).rbegin(), (x).rend()
#define sz(x) ((int)(x).size())
#define pb push_back
#define fi first
#define se second
using namespace std;
using namespace atcoder;
using ll = long long;
template<typename T> using mpq = priority_queue<T, vector<T>, greater<T>>;
template<typename T> bool chmax(T &a, const T &b) { if (a<b) { a=b; return 1; } return 0; }
template<typename T> bool chmin(T &a, const T &b) { if (b<a) { a=b; return 1; } return 0; }
template<typename T> ll sumv(const vector<T>&a){ll res(0);for(auto&&x:a)res+=x;return res;}
bool yn(bool a) { if(a) {cout << "Yes" << endl; return 1;} else {cout << "No" << endl; return 0;}}
#define dame { cout << "No" << endl; return 0;}
#define dame1 { cout << -1 << endl; return 0;}
#define test(x) cout << "test" << x << endl;
#define deb(x,y) cout << x << " " << y << endl;
#define deb3(x,y,z) cout << x << " " << y << " " << z << endl;
#define deb4(x,y,z,x2) cout << x << " " << y << " " << z << " " << x2 << endl;
#define out cout << ans << endl;
#define outv fore(yans , ans) cout << yans << "\n";
#define show(x) cerr<<#x<<" = "<<x<<endl;
#define showv(v) {fore(vy , v) {cout << vy << " ";} cout << endl;}
#define showv2(v) fore(vy , v) cout << vy << "\n";
using pll = pair<ll,ll>;
using pil = pair<int,ll>;
using pli = pair<ll,int>;
using pii = pair<int,int>;
using tp = tuple<int ,int ,int>;
using vi = vector<int>;
using vl = vector<ll>;
using vs = vector<string>;
using vb = vector<bool>;
using vpii = vector<pii>;
using vpli = vector<pli>;
using vpll = vector<pll>;
using vpil = vector<pil>;
using vvi = vector<vector<int>>;
using vvl = vector<vector<ll>>;
using vvs = vector<vector<string>>;
using vvb = vector<vector<bool>>;
using vvpii = vector<vector<pii>>;
using vvpli = vector<vector<pli>>;
using vvpll = vector<vpll>;
using vvpil = vector<vpil>;
using mint = modint1000000007;
using vm = vector<mint>;
using vvm = vector<vector<mint>>;
vector<int> dx={1,0,-1,0,1,1,-1,-1},dy={0,1,0,-1,1,-1,1,-1};
ll gcd(ll a, ll b) { return a?gcd(b%a,a):b;}
ll lcm(ll a, ll b) { return a/gcd(a,b)*b;}
const double eps = 1e-10;
const ll LINF = 1001002003004005006ll;
const int INF = 1001001001;
struct rational{
    ll num,den;
 
    rational(ll num_=0,ll den_=0){
        if (num_ == 0){
            num = num_;
            den = den_;
            if (den_ != 0) den = den_ / abs(den_);
        }else if(den_ == 0){
            num = num_ / abs(num_);
            den = 0;
        }else{
            ll d = gcd(abs(num_),abs(den_));
            num = num_/d;
            den = den_/d;
 
            // if((num_ < 0 && den_ > 0) || (num_ > 0 && den_ < 0)) num *= -1;
        }
    }
 
    rational operator+(rational const other) const{
        if (den == 0 || other.den == 0) return rational(1,0);
        assert(abs(other.num) < LLONG_MAX/den);
        assert(abs(num) < LLONG_MAX/other.den);
        ll p,q;
        p = num*other.den + den*other.num;
        q = den*other.den;
        return rational(p,q);
    }
 
    rational operator-(rational const other) const{
        if (den == 0 || other.den == 0) return rational(1,0);
        assert(abs(other.num) < LLONG_MAX/den);
        assert(abs(num) < LLONG_MAX/other.den);
        ll p,q;
        p = num*other.den - den*other.num;
        q = den*other.den;
        return rational(p,q);
    }
 
    rational operator*(rational const other) const{
        if (den == 0 || other.den == 0) return rational(1,0);
        if (other.num == 0) return rational(num,den);
        assert(abs(num) < LLONG_MAX/abs(other.num));
        assert(other.den < LLONG_MAX/den);
        ll p,q;
        p = num*other.num;
        q = den*other.den;
        return rational(p,q);
    }
 
    rational operator/(rational const other) const{
        rational r(other.den , other.num);
        return *this * r;
    }
 
    rational operator+=(rational const other){
        *this = *this + other;
        return *this;
    }
 
    rational operator-=(rational const other){
        *this = *this - other;
        return *this;
    }
 
    rational operator*=(rational const other){
        *this = *this * other;
        return *this;
    }
 
    rational operator/=(rational const other){
        *this = *this / other;
        return *this;
    }
 
    bool operator>(rational const other) const{
        if (den == 0){
            if (other.den == 0) return false;
            else return true;
        }else if(other.den == 0){
            return false;
        }
        assert(abs(num) < LLONG_MAX/other.den);
        assert(abs(other.num) < LLONG_MAX/den);
        return num*other.den > den*other.num;
    }
 
    bool operator<(rational const other) const{
        int ta,tb;
        if (den >= 0 && num >= 0) ta = 0;
        else if (den < 0 && num >= 0) ta = 1;
        else if (den <= 0 && num < 0) ta = 2;
        else ta = 3;
        if (other.den >= 0 && other.num >= 0) tb = 0;
        else if (other.den < 0 && other.num >= 0) tb = 1;
        else if (other.den <= 0 && other.num < 0) tb = 2;
        else tb = 3;
        if (ta != tb) return ta < tb;
        if (den == 0){
            if (other.den == 0) return false;
            else{
                return false;
            }
        }else if(other.den == 0){
            return true;
        }
        assert(abs(num) < LLONG_MAX/abs(other.den));
        assert(abs(other.num) < LLONG_MAX/abs(den));
        return num*other.den < den*other.num;
    }
 
    bool operator>=(rational const other) const{
        if (den == 0){
            if (other.den == 0) return true;
            else return true;
        }else if(other.den == 0){
            return false;
        }
        assert(abs(num) < LLONG_MAX/other.den);
        assert(abs(other.num) < LLONG_MAX/den);
        return num*other.den >= den*other.num;
    }
 
    bool operator<=(rational const other) const{
        if (den == 0){
            if (other.den == 0) return true;
            else return false;
        }else if(other.den == 0){
            return true;
        }
        assert(abs(num) < LLONG_MAX/other.den);
        assert(abs(other.num) < LLONG_MAX/den);
        return num*other.den <= den*other.num;
    }
 
    bool operator==(rational const other) const{
        return (num == other.num) && (den == other.den);
    }
 
    bool operator!=(rational const other) const{
        return (num != other.num) || (den != other.den);
    }
};
 
// rational(a,b) でa/bを既約分数の状態で管理。a,bは共に64bit型整数であるが、四足演算にてa*b >= LLONG_MAX となる場合には警告が出る。
// a*b < 0の時、a<0 , b>0で管理。
// a == 0 の時　(0,1)、b == 0 の時 (1,0)で管理。
struct vec{
    ll x,y;
    vec(ll x=0,ll y=0) : x(x),y(y) {}
    vec operator+(const vec& ot) {
        vec ret(x+ot.x , y+ot.y);
        return ret;
    }
    vec operator-(const vec& ot) {
        vec ret(x-ot.x , y-ot.y);
        return ret;
    }
    vec operator*(const vec& ot) {
        vec ret(x*ot.x , y*ot.y);
        return ret;
    }
};
struct vec3{
    ll x,y,z;
    vec3(ll x=0,ll y=0,ll z=0) : x(x),y(y),z(z) {}
    vec3 operator+(const vec3& ot) {
        vec3 ret(x+ot.x , y+ot.y , z+ot.z);
        return ret;
    }
    vec3 operator-(const vec3& ot) {
        vec3 ret(x-ot.x , y-ot.y , z-ot.z);
        return ret;
    }
    vec3 operator*(const vec3& ot) {
        vec3 ret(x*ot.x , y*ot.y , z*ot.z);
        return ret;
    }
};
ll dot(vec a,vec b){
    return a.x*b.x + a.y*b.y;
}
ll dot3(vec3 a,vec3 b){
    return a.x*b.x + a.y*b.y + a.z*b.z;
}
mint crs(vec a,vec b){
    pair<mint , mint> va = {a.x , a.y};
    pair<mint , mint> vb = {b.x , b.y};
    return va.fi*vb.se - va.se*vb.fi;
}
vec3 crs3(vec3 a,vec3 b){
    ll x = a.y*b.z - a.z*b.y;
    ll y = a.z*b.x - a.x*b.z;
    ll z = a.x*b.y - a.y*b.x;
    return vec3(x , y , z);
}
int main(){
    int n; cin>>n;
    mpq<pair<rational , ll>> q;
    rep(i,n){
        ll a,b; cin>>a>>b;
        rational r(b,a),r2(-b,-a);
        ll d = gcd(abs(a),abs(b));
        q.push({r , d});
        q.push({r2 , d});
    }
    vl a(2*n+1) , b(2*n+1);
    mint sump = 0;
    rep(i,2*n){
        rational r = q.top().fi;
        ll d = q.top().se;
        q.pop();
        a[i+1] = a[i] + d * r.den;
        b[i+1] = b[i] + d * r.num;
        sump += abs(d);
    }
    mint area = 0;
    rep1(i,2*n-1){
        vec v1(a[i] - a[0] , b[i] - b[0]);
        vec v2(a[i+1] - a[0] , b[i+1] - b[0]);
        mint tmpa = crs(v1 , v2) / 2;
        area += tmpa;
    }
    mint ans = area + 1 + sump/2;
    cout << ans.val() << endl;
    return 0;
}
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