結果

問題 No.3344 Common Tangent Line
コンテスト
ユーザー rurun
提出日時 2025-11-13 22:18:24
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 1,080 ms / 3,000 ms
コード長 5,955 bytes
コンパイル時間 1,147 ms
コンパイル使用メモリ 108,836 KB
実行使用メモリ 7,716 KB
最終ジャッジ日時 2025-11-13 22:19:07
合計ジャッジ時間 26,996 ms
ジャッジサーバーID
（参考情報） 		judge5 / judge1
このコードへのチャレンジ
（要ログイン）
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 # 

// cf: https://github.com/drken1215/algorithm/blob/master/Geometry/common_tanline.cpp

//
// 2 円の共通接線
//a
// verified:
//   AOJ Course CGL_7_G: Common Tangent
//     http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=CGL_7_G&lang=ja
//
//   AOJ 2201 Immortal Jewels
//     http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=2201
//


#include <iostream>
#include <vector>
#include <cmath>
#include <iomanip>
#include <algorithm>
using namespace std;


//------------------------------//
// 基本要素 (点, 線分, 円)
//------------------------------//

using DD = long double;
const DD INF = 1LL<<60;      // to be set appropriately
const DD EPS = 1e-10;        // to be set appropriately
const DD PI = acosl(-1.0);
DD torad(int deg) {return (DD)(deg) * PI / 180;}
DD todeg(DD ang) {return ang * 180 / PI;}

/* Point */
struct Point {
    DD x, y;
    Point(DD x = 0.0, DD y = 0.0) : x(x), y(y) {}
    friend ostream& operator << (ostream &s, const Point &p) {return s << '(' << p.x << ", " << p.y << ')';}
};
inline Point operator + (const Point &p, const Point &q) {return Point(p.x + q.x, p.y + q.y);}
inline Point operator - (const Point &p, const Point &q) {return Point(p.x - q.x, p.y - q.y);}
inline Point operator * (const Point &p, DD a) {return Point(p.x * a, p.y * a);}
inline Point operator * (DD a, const Point &p) {return Point(a * p.x, a * p.y);}
inline Point operator * (const Point &p, const Point &q) {return Point(p.x * q.x - p.y * q.y, p.x * q.y + p.y * q.x);}
inline Point operator / (const Point &p, DD a) {return Point(p.x / a, p.y / a);}
inline Point conj(const Point &p) {return Point(p.x, -p.y);}
inline Point rot(const Point &p, DD ang) {return Point(cos(ang) * p.x - sin(ang) * p.y, sin(ang) * p.x + cos(ang) * p.y);}
inline Point rot90(const Point &p) {return Point(-p.y, p.x);}
inline DD cross(const Point &p, const Point &q) {return p.x * q.y - p.y * q.x;}
inline DD dot(const Point &p, const Point &q) {return p.x * q.x + p.y * q.y;}
inline DD norm(const Point &p) {return dot(p, p);}
inline DD abs(const Point &p) {return sqrt(dot(p, p));}
inline DD amp(const Point &p) {DD res = atan2(p.y, p.x); if (res < 0) res += PI*2; return res;}
inline bool eq(const Point &p, const Point &q) {return abs(p - q) < EPS;}
inline bool operator < (const Point &p, const Point &q) {return (abs(p.x - q.x) > EPS ? p.x < q.x : p.y < q.y);}
inline bool operator > (const Point &p, const Point &q) {return (abs(p.x - q.x) > EPS ? p.x > q.x : p.y > q.y);}
inline Point operator / (const Point &p, const Point &q) {return p * conj(q) / norm(q);}

/* Line */
struct Line : vector<Point> {
    Line(Point a = Point(0.0, 0.0), Point b = Point(0.0, 0.0)) {
        this->push_back(a);
        this->push_back(b);
    }
    friend ostream& operator << (ostream &s, const Line &l) {return s << '{' << l[0] << ", " << l[1] << '}';}
};

/* Circle */
struct Circle : Point {
    DD r;
    Circle(Point p = Point(0.0, 0.0), DD r = 0.0) : Point(p), r(r) {}
    friend ostream& operator << (ostream &s, const Circle &c) {return s << '(' << c.x << ", " << c.y << ", " << c.r << ')';}
};



//------------------------------//
// 接線
//------------------------------//

// tanline
vector<Point> tanline(const Point &p, const Circle &c) {
    vector<Point> res;
    DD d = norm(p - c);
    DD l = d - c.r * c.r;
    if (l < -EPS) return res;
    if (l <= 0.0) l = 0.0;
    Point cq = (p - c) * (c.r * c.r / d);
    Point qs = rot90((p - c) * (c.r * sqrt(l) / d));
    Point s1 = c + cq + qs, s2 = c + cq - qs;
    res.push_back(s1);
    res.push_back(s2);
    return res;
}

// common tanline, a and b must be different!
// Line[0] is tangent point in a
vector<Line> comtanline(Circle a, Circle b) {
    vector<Line> res;
    // intersect
    if (abs(a - b) > abs(a.r - b.r) + EPS) {
        if (abs(a.r - b.r) < EPS) {
            Point dir = b - a;
            dir = rot90(dir * (a.r / abs(dir)));
            res.push_back(Line(a + dir, b + dir));
            res.push_back(Line(a - dir, b - dir));
        }
        else {
            Point p = a * -b.r + b * a.r;
            p = p * (1.0 / (a.r - b.r));
            vector<Point> bs = tanline(p, a);
            vector<Point> as = tanline(p, b);
            for (int i = 0; i < min(as.size(), bs.size()); ++i) {
                res.push_back(Line(bs[i], as[i]));
            }
        }
    }
    // inscribed
    else if (abs(abs(a - b) - abs(a.r - b.r)) <= EPS) {
        Point dir = b - a;
        if (a.r > b.r) dir = dir * (a.r / abs(dir));
        else dir = dir * (-a.r / abs(dir));
        Point p = a + dir;
        res.push_back(Line(p, p + rot90(dir)));
    }
    // disjoint
    if (abs(a - b) > a.r + b.r + EPS) {
        Point p = a * b.r + b * a.r;
        p = p * (1.0 / (a.r + b.r));
        vector<Point> bs = tanline(p, a);
        vector<Point> as = tanline(p, b);
        for (int i = 0; i < min(as.size(), bs.size()); ++i) {
            res.push_back(Line(bs[i], as[i]));
        }
    }
    // circumscribed
    else if (abs(abs(a - b) - (a.r + b.r)) <= EPS) {
        Point dir = b - a;
        dir = dir * (a.r / abs(dir));
        Point p = a + dir;
        res.push_back(Line(p, p + rot90(dir)));
    }
    return res;
}



//------------------------------//
// Examples
//------------------------------//

void solve() {
    Circle p, q;
    cin >> p.x >> p.y >> p.r >> q.x >> q.y >> q.r;
    auto l = comtanline(p, q);
    long double ans = 0;
    for (auto line : l) {
      long double x1 = line[0].x, y1 = line[0].y;
      long double x2 = line[1].x, y2 = line[1].y;
      long double sum = (1-x1)*(y2-y1)-(1-y1)*(x2-x1);
      long double a = abs(y2-y1), b = abs(-(x2-x1)), c = abs(-x1*(y2-y1)+y1*(x2-x1));
      ans += abs(sum/max({a, b, c}));
      //cout << x1 << " " << y1 << " " << x2 << " " << y2 << endl;
    }
    cout << fixed << setprecision(15) << ans << endl;
}

int main() {
	int n;
	cin >> n;
	while (n--) {
		solve();
	}
}
0