結果

問題 No.3344 Common Tangent Line
コンテスト
ユーザー 👑 potato167
提出日時 2025-11-14 00:03:55
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 419 ms / 3,000 ms
コード長 4,778 bytes
コンパイル時間 2,355 ms
コンパイル使用メモリ 202,608 KB
実行使用メモリ 7,716 KB
最終ジャッジ日時 2025-11-14 00:04:26
合計ジャッジ時間 27,840 ms
ジャッジサーバーID
（参考情報） 		judge5 / 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 * 1
other AC * 40
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>
using namespace std;
using ll=long long;
const ll ILL=2167167167167167167;
const int INF=2100000000;
#define rep(i,a,b) for (int i=(int)(a);i<(int)(b);i++)
#define all(p) p.begin(),p.end()
template<class T> using _pq = priority_queue<T, vector<T>, greater<T>>;
template<class T> int LB(vector<T> &v,T a){return lower_bound(v.begin(),v.end(),a)-v.begin();}
template<class T> int UB(vector<T> &v,T a){return upper_bound(v.begin(),v.end(),a)-v.begin();}
template<class T> bool chmin(T &a,T b){if(b<a){a=b;return 1;}else return 0;}
template<class T> bool chmax(T &a,T b){if(a<b){a=b;return 1;}else return 0;}
template<class T> void So(vector<T> &v) {sort(v.begin(),v.end());}
template<class T> void Sore(vector<T> &v) {sort(v.begin(),v.end(),[](T x,T y){return x>y;});}
bool yneos(bool a,bool upp=false){if(a){cout<<(upp?"YES\n":"Yes\n");}else{cout<<(upp?"NO\n":"No\n");}return a;}
template<class T> void vec_out(vector<T> &p,int ty=0){
    if(ty==2){cout<<'{';for(int i=0;i<(int)p.size();i++){if(i){cout<<",";}cout<<'"'<<p[i]<<'"';}cout<<"}\n";}
    else{if(ty==1){cout<<p.size()<<"\n";}for(int i=0;i<(int)(p.size());i++){if(i) cout<<" ";cout<<p[i];}cout<<"\n";}}
template<class T> T vec_min(vector<T> &a){assert(!a.empty());T ans=a[0];for(auto &x:a) chmin(ans,x);return ans;}
template<class T> T vec_max(vector<T> &a){assert(!a.empty());T ans=a[0];for(auto &x:a) chmax(ans,x);return ans;}
template<class T> T vec_sum(vector<T> &a){T ans=T(0);for(auto &x:a) ans+=x;return ans;}
int pop_count(long long a){int res=0;while(a){res+=(a&1),a>>=1;}return res;}
template<class T> T square(T a){return a * a;}

// https://github.com/kth-competitive-programming/kactl/tree/main/content/geometry
template<class T> ll sgn(T x) { return (x > 0) - (x < 0); }
template<class T> struct Point {
    using P = Point;
    T x, y;
    explicit Point(T x = 0, T y = 0) : x(x), y(y) {}
    bool operator<(P p) const { return tie(x, y) < tie(p.x, p.y); }
    bool operator==(P p) const { return tie(x, y) == tie(p.x, p.y); }
    P operator+(P p) const { return P(x + p.x, y + p.y); }
    P operator-(P p) const { return P(x - p.x, y - p.y); }
    P operator*(T d) const { return P(x * d, y * d); }
    P operator/(T d) const { return P(x / d, y / d); }
    T dot(P p) const { return x * p.x + y * p.y; }
    T cross(P p) const { return x * p.y - y * p.x; }
    T cross(P a, P b) const { return (a - *this).cross(b - *this); }
    T dist2() const { return x * x + y * y; }
    double dist() const { return sqrt(dist2()); }
    // angle to x-axis in interval [-pi, pi]
    double angle() const { return atan2(y, x); }
    P unit() const { return *this / dist(); }  // makes dist()=1
    P perp() const { return P(-y, x); }        // rotates +90 degrees
    P normal() const { return perp().unit(); }
    // returns point rotated 'a' radians ccw around the origin
    P rotate(double a) const {
        return P(x * cos(a) - y * sin(a), x * sin(a) + y * cos(a));
    }
    friend ostream& operator<<(ostream& os, P p) {
        return os << "(" << p.x << "," << p.y << ")";
    }
};

/* Finds the external tangents of two circles, or internal if r2 is negated. Can return 0, 1, or 2 tangents -- 0 if one circle contains the other (or overlaps it, in the internal case, or if the circles are the same);
 * 1 if the circles are tangent to each other (in which case .first = .second and the tangent line is perpendicular to the line between the centers).
 * .first and .second give the tangency points at circle 1 and 2 respectively.
 * To find the tangents of a circle with a point set r2 to 0. */

template<class P>
vector<pair<P, P>> tangents(P c1, double r1, P c2, double r2) {
    P d = c2 - c1;
    double dr = r1 - r2, d2 = d.dist2(), h2 = d2 - dr * dr;
    if(d2 == 0 || h2 < 0) return {};
    vector<pair<P, P>> out;
    for(double sign : {-1, 1}) {
        P v = (d * dr + d.perp() * sqrt(h2) * sign) / d2;
        out.push_back({c1 + v * r1, c2 + v * r2});
    }
    if(h2 == 0) out.pop_back();
    return out;
}

void solve();
// POP'N ROLL MUSIC / TOMOO
int main() {
    ios::sync_with_stdio(false);
    cin.tie(nullptr);

    int t = 1;
    cin >> t;
    rep(i, 0, t) solve();
}

void solve(){
    using ld = double;
    using P = Point<ld>;
    ld R1, R2;
    P C1, C2;
    cin >> C1.x >> C1.y >> R1;
    cin >> C2.x >> C2.y >> R2;
    auto tmp = tangents(C1, R1, C2, R2);
    for (auto a : tangents(C1, R1, C2, -R2)) tmp.push_back(a);
    ld ans = 0;
    for (auto [p, q] : tmp){
       //cout << p << " " << q << "\n";
        ld a = q.y - p.y;
        ld b = p.x - q.x;
        ld c = a * p.x + b * p.y;
        c *= -1;
        ld m = max(abs(a), max(abs(b), abs(c)));
        ans += abs(a + b + c) / m;
    }
    cout << fixed << setprecision(20) << ans << "\n";
}
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