Problem: Example

Input

3
0 1
0 0 0 1
0 1 0 2
0 2 0 3


Output

6.0000000000000000

Solution (in CPP):

Solution:
#include "bits/stdc++.h"
using namespace std;
using ld = long double;
const ld eps = 1e-9;

typedef ld  Weight;
struct Edge {
	int src, dest;
	int cap, rev;
	Weight weight;
	bool operator < (const Edge &rhs) const { return weight > rhs.weight; }
};


/* ??????????????¬ */

#include <complex>

typedef complex<ld> Point;
#define rep(i,n) for(int i=0;i<(int)(n);i++)
#define all(x) (x).begin(),(x).end()


const ld pi = acos(-1.0);
const ld dtop = pi / 180.;
const ld ptod = 1. / dtop;

namespace std {
	bool operator<(const Point &lhs, const Point &rhs) {
		if (lhs.real() < rhs.real() - eps) return true;
		if (lhs.real() > rhs.real() + eps) return false;
		return lhs.imag() < rhs.imag();
	}
}

// ????????\???
Point input_Point() {
	ld x, y;
	cin >> x >> y;
	return Point(x, y);
}

// ????????????????????????
bool eq(const ld a, const ld b) {
	return (abs(a - b) < eps);
}

// ??????
ld dot(const Point& a, const Point& b) {
	return real(conj(a) * b);
}

// ??????
ld cross(const Point& a, const Point& b) {
	return imag(conj(a) * b);
}

// ??´????????????
class Line {
public:
	Point a, b;
	Line() : a(Point(0, 0)), b(Point(0, 0)) {}
	Line(Point a, Point b) : a(a), b(b) {}
	Point operator[](const int _num)const {
		if (_num == 0)return a;
		else if (_num == 1)return b;
		else {
			assert(false);
			return Point();
		}
	}
};

// ????????????
class Circle {
public:
	Point p;
	ld r;
	Circle() : p(Point(0, 0)), r(0) {}
	Circle(Point p, ld r) : p(p), r(r) {}
};

// ccw
// 1: a,b,c??????????¨???¨?????????????????¶
//-1: a,b,c???????¨???¨?????????????????¶
// 2: c,a,b???????????´???????????¶
//-2: a,b,c???????????´???????????¶
// 0: a,c,b???????????´???????????¶
int ccw(const Point& a, const Point &b, const Point &c) {
	const Point nb(b - a);
	const Point nc(c - a);
	if (cross(nb, nc) > eps) return 1;   // a,b,c??????????¨???¨?????????????????¶
	if (cross(nb, nc) < -eps) return -1; // a,b,c???????¨???¨?????????????????¶
	if (dot(nb, nc) < 0) return 2;       // c,a,b???????????´???????????¶
	if (norm(nb) < norm(nc)) return -2;  // a,b,c???????????´???????????¶
	return 0;                          // a,c,b???????????´???????????¶
}


/* ???????????? */

// ??´?????¨??´??????????????????
bool isis_ll(const Line& l, const Line& m) {
	return !eq(cross(l.b - l.a, m.b - m.a), 0);
}

// ??´?????¨?????????????????????
bool isis_ls(const Line& l, const Line& s) {
	return isis_ll(l, s) &&
		(cross(l.b - l.a, s.a - l.a) * cross(l.b - l.a, s.b - l.a) < eps);
}

// ????????¨?????????????????????
bool isis_ss(const Line& s, const Line& t) {
	return ccw(s.a, s.b, t.a) * ccw(s.a, s.b, t.b) <= 0 &&
		ccw(t.a, t.b, s.a) * ccw(t.a, t.b, s.b) <= 0;
}

// ????????´????????????
bool isis_lp(const Line& l, const Point& p) {
	return (abs(cross(l.b - p, l.a - p)) < eps);
}

// ?????????????????????
bool isis_sp(const Line& s, const Point& p) {
	return (abs(s.a - p) + abs(s.b - p) - abs(s.b - s.a) < eps);
}

// ??????????¶?
Point proj(const Line &l, const Point& p) {
	ld t = dot(p - l.a, l.b - l.a) / norm(l.a - l.b);
	return l.a + t * (l.b - l.a);
}

//???????±??????????????????????
Point reflect(const Line &l, const Point &p) {
	Point pr = proj(l, p);
	return pr * 2.l - p;
}

// ??´?????¨??´????????????
Point is_ll(const Line &s, const Line& t) {
	Point sv = s.b - s.a, tv = t.b - t.a;
	assert(cross(sv, tv) != 0);
	return s.a + sv * cross(tv, t.a - s.a) / cross(tv, sv);
}
// ??´?????¨??´????????????
vector<Point> is_ll2(const Line &s, const Line& t) {
	Point sv = s.b - s.a, tv = t.b - t.a;
	if (cross(sv, tv) != 0)return vector<Point>(1, is_ll(s, t));
	else {
		vector<Point>ans;
		for (int k = 0; k < 2; ++k) {
			if (isis_sp(s, t[k]) && find(ans.begin(), ans.end(), t[k]) == ans.end())ans.push_back(t[k]);
			if (isis_sp(t, s[k]) && find(ans.begin(), ans.end(), s[k]) == ans.end())ans.push_back(s[k]);
		}
		return ans;
	}
}
// ????????¨???????????????
//???????????£????????¨???????????¨assert(false)
Point is_ss(const Line &s, const Line& t) {
	if (isis_ss(s, t)) {
		for (int k = 0; k < 2; ++k) {
			for (int l = 0; l < 2; ++l) {
				if (s[k] == t[l])return s[k];
			}
		}
		return is_ll(s, t);
	}
	else {
		//??????isis_ss?????????
		assert(false);
		return Point(0, 0);
	}
}
// ????????¨???????????????
vector<Point> is_ss2(const Line &s, const Line& t) {
	vector<Point> kouho(is_ll2(s, t));
	vector<Point>ans;
	for (auto p : kouho) {
		if (isis_sp(s, p) && isis_sp(t, p))ans.emplace_back(p);
	}
	return ans;
}
// ??´?????¨???????????¢
ld dist_lp(const Line& l, const Point& p) {
	return abs(p - proj(l, p));
}

//??´?????¨??´???????????¢
ld dist_ll(const Line& l, const Line& m) {
	return isis_ll(l, m) ? 0 : dist_lp(l, m.a);
}

// ??´?????¨??????????????¢
ld dist_ls(const Line& l, const Line& s) {
	return isis_ls(l, s) ? 0 : min(dist_lp(l, s.a), dist_lp(l, s.b));
}

// ????????¨???????????¢
ld dist_sp(const Line& s, const Point& p) {
	Point r = proj(s, p);
	return isis_sp(s, r) ? abs(r - p) : min(abs(s.a - p), abs(s.b - p));
}

// ????????¨??????????????¢
ld dist_ss(const Line& s, const Line& t) {
	if (isis_ss(s, t)) return 0;
	return min({ dist_sp(s, t.a), dist_sp(s, t.b), dist_sp(t, s.a), dist_sp(t, s.b) });
}


//??´?????¨??´?????????????????????????????????
Line bisection(const Line &s, const Line &t) {
	const Point laglanju(is_ll(s, t));
	const Point avec = !(abs(laglanju - s[0])<eps) ? s[0] - laglanju : s[1] - laglanju;
	const Point bvec = !(abs(laglanju - t[0])<eps) ? t[0] - laglanju : t[1] - laglanju;

	return Line(laglanju, laglanju + (abs(bvec)*avec + abs(avec)*bvec) / (abs(avec) + abs(bvec)));
}


//???????????´?????????????????????
//???????????´??????????????§???????????¨????¢?????????¨?????????
Point  inner_center(const vector<Line>&ls) {
	vector<Point>vertics;
	for (int i = 0; i <static_cast<int>(ls.size()); ++i) {
		vertics.push_back(is_ll(ls[i], ls[(i + 1) % 3]));
	}
	if (vertics[0] == vertics[1] || vertics[1] == vertics[2] || vertics[2] == vertics[0])return vertics[0];
	Line bi1(bisection(Line(vertics[0], vertics[1]), Line(vertics[0], vertics[2])));
	Line bi2(bisection(Line(vertics[1], vertics[2]), Line(vertics[1], vertics[0])));
	if (bi1[0] == bi2[0])return bi1[0];
	else {
		return is_ll(bi1, bi2);
	}
}

//???????????´?????????????????????
//???????????´??????????????§???????????¨????¢?????????¨?????????
vector<Point>  ex_center(const vector<Line>&ls) {
	vector<Point>vertics;
	for (int i = 0; i < static_cast<int>(ls.size()); ++i) {
		vertics.push_back(is_ll(ls[i], ls[(i + 1) % 3]));
	}
	if (abs(vertics[0] - vertics[1])<eps || abs(vertics[1] - vertics[2])<eps || (abs(vertics[2] - vertics[0])<eps))return vector<Point>();
	vector<Point>ecs;
	for (int i = 0; i < 3; ++i) {
		Line bi1(bisection(Line(vertics[i], vertics[i] * 2.0l - vertics[(i + 2) % 3]), Line(vertics[i], vertics[(i + 1) % 3])));
		Line bi2(bisection(Line(vertics[(i + 1) % 3], vertics[(i + 1) % 3] * 2.0l - vertics[(i + 2) % 3]), Line(vertics[(i + 1) % 3], vertics[i])));
		ecs.push_back(is_ll(bi1, bi2));
	}
	return ecs;
}


//a,b:??????
//c:????????§??????
//???????????´?????????????????¢?????????????±??????????
vector<Point>  same_dis(const vector<Line>&ls) {
	vector<Point>vertics;
	vertics.push_back(is_ll(ls[0], ls[2]));
	vertics.push_back(is_ll(ls[1], ls[2]));

	if (abs(vertics[0] - vertics[1]) < eps)return vector<Point>{vertics[0]};
	Line bis(bisection(ls[0], ls[1]));
	vector<Point>ecs;

	Line abi(bisection(Line(vertics[0], vertics[1]), ls[0]));
	ecs.push_back(is_ll(bis, abi));


	Line bbi(bisection(Line(vertics[0], 2.l*vertics[0] - vertics[1]), ls[0]));
	ecs.push_back(is_ll(bis, bbi));

	return ecs;
}
/* ??? */

// ?????¨????????????
vector<Point> is_cc(const Circle& c1, const Circle& c2) {
	vector<Point> res;
	ld d = abs(c1.p - c2.p);
	ld rc = (d * d + c1.r * c1.r - c2.r * c2.r) / (2 * d);
	ld dfr = c1.r * c1.r - rc * rc;
	if (abs(dfr) < eps) dfr = 0.0;
	else if (dfr < 0.0) return res; // no intersection
	ld rs = sqrt(dfr);
	Point diff = (c2.p - c1.p) / d;
	res.push_back(c1.p + diff * Point(rc, rs));
	if (dfr != 0.0) res.push_back(c1.p + diff * Point(rc, -rs));
	return res;
}

//???????????????????????????
/*  0 => out
1 => on
2 => in*/
int is_in_Circle(const Circle &cir, const  Point& p) {
	ld dis = abs(cir.p - p);
	if (dis > cir.r + eps)return 0;
	else if (dis < cir.r - eps)return 2;
	else return 1;
}
//???lc??????rc??????????????????
/*0 => out
1 => on
2 => in*/
int Circle_in_Circle(const Circle &lc, const  Circle&rc) {
	ld dis = abs(lc.p - rc.p);
	if (dis < rc.r - lc.r - eps)return 2;
	else if (dis>rc.r - lc.r + eps)return 0;
	else return 1;
}

// ?????¨??´????????????
vector<Point> is_lc(const Circle& c, const Line& l) {
	vector<Point> res;
	ld d = dist_lp(l, c.p);
	if (d < c.r + eps) {
		ld len = (d > c.r) ? 0.0 : sqrt(c.r * c.r - d * d); //safety;
		Point nor = (l.a - l.b) / abs(l.a - l.b);
		res.push_back(proj(l, c.p) + len * nor);
		res.push_back(proj(l, c.p) - len * nor);
	}
	return res;
}

// ?????¨??????????????¢
vector<Point> is_sc(const Circle& c, const Line& l) {
	vector<Point> v = is_lc(c, l), res;
	for (Point p : v)
		if (isis_sp(l, p)) res.push_back(p);
	return res;
}

// ?????¨????????\???
vector<Line> tangent_cp(const Circle& c, const Point& p) {
	vector<Line> ret;
	Point v = c.p - p;
	ld d = abs(v);
	ld l = sqrt(norm(v) - c.r * c.r);
	if (isnan(l)) { return ret; }
	Point v1 = v * Point(l / d, c.r / d);
	Point v2 = v * Point(l / d, -c.r / d);
	ret.push_back(Line(p, p + v1));
	if (l < eps) return ret;
	ret.push_back(Line(p, p + v2));
	return ret;
}

// ?????¨????????\???
vector<Line> tangent_cc(const Circle& c1, const Circle& c2) {
	vector<Line> ret;
	if (abs(c1.p - c2.p) - (c1.r + c2.r) > -eps) {
		Point center = (c1.p * c2.r + c2.p * c1.r) / (c1.r + c2.r);
		ret = tangent_cp(c1, center);
	}
	if (abs(c1.r - c2.r) > eps) {
		Point out = (-c1.p * c2.r + c2.p * c1.r) / (c1.r - c2.r);
		vector<Line> nret = tangent_cp(c1, out);
		ret.insert(ret.end(), all(nret));
	}
	else {
		Point v = c2.p - c1.p;
		v /= abs(v);
		Point q1 = c1.p + v * Point(0, 1) * c1.r;
		Point q2 = c1.p + v * Point(0, -1) * c1.r;
		ret.push_back(Line(q1, q1 + v));
		ret.push_back(Line(q2, q2 + v));
	}
	return ret;
}
//??????????????????????????¢???
ld two_Circle_area(const Circle&l, const Circle&r) {
	ld dis = abs(l.p - r.p);
	if (dis > l.r + r.r)return 0;
	else if (dis + r.r < l.r) {
		return r.r*r.r*pi;
	}
	else if (dis + l.r < r.r) {
		return l.r*l.r*pi;
	}
	else {
		ld ans = (l.r)*(l.r)*acos((dis*dis + l.r*l.r - r.r*r.r) / (2 * dis*l.r)) +
			(r.r)*(r.r)*acos((dis*dis + r.r*r.r - l.r*l.r) / (2 * dis*r.r)) -
			sqrt(4 * dis*dis*l.r*l.r - (dis*dis + l.r*l.r - r.r*r.r)*(dis*dis + l.r*l.r - r.r*r.r)) / 2;
		return ans;
	}

}

/* ????§???¢ */

typedef vector<Point> Polygon;

// ??¢???
ld area(const Polygon &p) {
	ld res = 0;
	int n = p.size();
	rep(j, n) res += cross(p[j], p[(j + 1) % n]);
	return res / 2;
}

//????§???¢????????¢??????
bool is_counter_clockwise(const Polygon &poly) {
	ld angle = 0;
	int n = poly.size();
	rep(i, n) {
		Point a = poly[i], b = poly[(i + 1) % n], c = poly[(i + 2) % n];
		angle += arg((c - b) / (b - a));
	}
	return angle > eps;
}

// ??????????????????
/*0 => out
1 => on
2 => in*/
int is_in_Polygon(const Polygon &poly, const  Point& p) {
	ld angle = 0;
	int n = poly.size();
	rep(i, n) {
		Point a = poly[i], b = poly[(i + 1) % n];
		if (isis_sp(Line(a, b), p)) return 1;
		angle += arg((b - p) / (a - p));
	}
	return eq(angle, 0) ? 0 : 2;
}
//??????????????????2?????????
enum { out, on, in };
int convex_contains(const Polygon &P, const Point &p) {
	const int n = P.size();
	Point g = (P[0] + P[n / 3] + P[2 * n / 3]) / 3.0l; // inner-point
	int a = 0, b = n;
	while (a + 1 < b) { // invariant: c is in fan g-P[a]-P[b]
		int c = (a + b) / 2;
		if (cross(P[a] - g, P[c] - g) > 0) { // angle < 180 deg
			if (cross(P[a] - g, p - g) > 0 && cross(P[c] - g, p - g) < 0) b = c;
			else                                                  a = c;
		}
		else {
			if (cross(P[a] - g, p - g) < 0 && cross(P[c] - g, p - g) > 0) a = c;
			else                                                  b = c;
		}
	}
	b %= n;
	if (cross(P[a] - p, P[b] - p) < 0) return 0;
	if (cross(P[a] - p, P[b] - p) > 0) return 2;
	return 1;
}

// ??????
//???????????????????????¨????????????????????§??¨???
Polygon convex_hull(vector<Point> ps) {
	int n = ps.size();
	int k = 0;
	sort(ps.begin(), ps.end());
	Polygon ch(2 * n);
	for (int i = 0; i < n; ch[k++] = ps[i++])
		while (k >= 2 && ccw(ch[k - 2], ch[k - 1], ps[i]) <= 0) --k;
	for (int i = n - 2, t = k + 1; i >= 0; ch[k++] = ps[i--])
		while (k >= t && ccw(ch[k - 2], ch[k - 1], ps[i]) <= 0) --k;
	ch.resize(k - 1);
	return ch;
}



//????????????
vector<Polygon> convex_cut(const Polygon &ps, const Line& l) {
	int n = ps.size();
	Polygon q;
	Polygon r;
	rep(i, n) {
		Point a = ps[i], b = ps[(i + 1) % n];
		Line m = Line(a, b);
		if (ccw(l.a, l.b, a) != -1) q.push_back(a);
		if (ccw(l.a, l.b, a) != 1) r.push_back(a);
		if (ccw(l.a, l.b, a) * ccw(l.a, l.b, b) < 0 && isis_ll(l, m)) {
			q.push_back(is_ll(l, m));
			r.push_back(is_ll(l, m));
		}
	}
	const vector<Polygon>polys{ q,r };
	return polys;
}


/* ??¢??¬??????????????? */
void add_Point(vector<Point> &ps, const Point p) {
	for (Point q : ps) if (abs(q - p) < eps) return;
	ps.push_back(p);
}




typedef vector<Edge> Edges;
typedef vector<Edges> Graph;
typedef vector<Weight> Array;
typedef vector<Array> Matrix;

void add_edge(Graph &g, int src, int dest, int cap, Weight weight) {
	g[src].push_back(Edge{ src, dest, cap, (int)g[dest].size(), weight });
	g[dest].push_back(Edge{ dest, src, 0, (int)g[src].size() - 1, -weight });
}

Graph segment_arrangement(const vector<Line> &s, const vector<Point> &p) {
	int n = p.size(), m = s.size();
	Graph g(n);
	rep(i, m) {
		vector<pair<ld, int>> vec;
		rep(j, n) {
			if (isis_sp(s[i], p[j]))
				vec.emplace_back(abs(s[i].a - p[j]), j);
		}
		sort(all(vec));
		rep(j, vec.size() - 1) {
			int from = vec[j].second, to = vec[j + 1].second;
			add_edge(g, from, to, 1,static_cast<Weight>(abs(p[from] - p[to])));
		}
	}
	return g;
}
pair<vector<Point>,Graph> sennbunn_arrangement(const vector<Line>&s) {
	vector<Point>crss;
	for (int i = 0; i < static_cast<int>(s.size()); ++i) {
		for (int j = i + 1; j < static_cast<int>(s.size()); ++j) {
			if (isis_ss(s[i], s[j])) {
				crss.push_back(is_ll2(s[i], s[j])[0]);
			}
		}
	}
	for (int i = 0; i <static_cast<int>(s.size()); ++i) {
		crss.push_back(s[i][0]);
		crss.push_back(s[i][1]);
	}
	sort(crss.begin(), crss.end());
	crss.erase(unique(crss.begin(), crss.end()), crss.end());
	
	return make_pair(crss,segment_arrangement(s, crss));
}

Graph Circle_arrangement(const vector<Circle> &c, const vector<Point> &p) {
	const int n = p.size(), m = c.size();
	Graph g(n);
	rep(i, m) {
		vector<pair<ld, int>> vec;
		rep(j, n) if (abs(abs(c[i].p - p[j]) - c[i].r) < eps)
			vec.emplace_back(arg(c[i].p - p[j]), j);
		sort(all(vec));
		rep(j, vec.size() - 1) {
			int from = vec[j].second, to = vec[j + 1].second;
			ld angle = vec[j + 1].first - vec[j].first;
			add_edge(g, from, to, 1,static_cast<Weight>(angle * c[i].r));
		}
		if (vec.size() >= 2) {
			int from = vec.back().second, to = vec.front().first;
			ld angle = vec.front().first - vec.back().first;
			add_edge(g, from, to, 1,static_cast<Weight>(angle * c[i].r));
		}
	}
	return g;
}

const int V = 1500;
Weight h[V];                //??????????????£???
Weight dist[V];             //???????????¢
int prevv[V], preve[V];  //??´???????????¨??????


#define REP(i,n) for(int i=0;i<(int)n;++i)
#define FOR(i,c) for(auto i=(c).begin();i!=(c).end();++i)
#define ALL(c) (c).begin(), (c).end()
const Weight INF =1e18;
Weight min_cost_flow(Graph &g, int s, int t, int f) {
	Weight res = 0;
	memset(h, 0, sizeof(h));
	typedef pair<Weight, int> P;
	while (f > 0) {
		priority_queue<P, vector<P>, greater<P> > que;
		fill(dist, dist + V, INF);
		dist[s] = 0;
		que.push(P(0, s));
		while (!que.empty()) {
			P p = que.top(); que.pop();
			int v = p.second;
			if (dist[v] < p.first) continue;
			REP(i, g[v].size()) {
				Edge &e = g[v][i];
				if (e.cap > 0 && dist[e.dest] > dist[v] + e.weight + h[v] - h[e.dest]+eps) {
					dist[e.dest] = dist[v] + e.weight + h[v] - h[e.dest];
					prevv[e.dest] = v;
					preve[e.dest] = i;
					que.push(P(dist[e.dest], e.dest));
				}
			}
		}
		if (dist[t] == INF) return -1;
		REP(v, V) h[v] =h[v]+ dist[v];

		int d = f;
		for (int v = t; v != s; v = prevv[v]) d = min(d, g[prevv[v]][preve[v]].cap);
		f -= d;
		res = res+d * h[t];
		for (int v = t; v != s; v = prevv[v]) {
			Edge &e = g[prevv[v]][preve[v]];
			e.cap -= d;
			g[v][e.rev].cap += d;
		}
	}
	return res;
}

int main() {
	int N; cin >> N;
	ld sx, sy; cin >> sx >> sy;
	Point sp;
	sp = Point(sx, sy);
	vector<Line>segs(N);
	ld aans = 0;
	for (int i = 0; i < N; ++i) {
		ld ax, ay, bx, by; cin >> ax >> ay >> bx >> by;
		segs[i] = Line(Point(ax, ay), Point(bx, by));
		aans += abs(segs[i].b - segs[i].a);
	}
	vector<pair<Point, Point>>pairs(N);
	for (int i = 0; i < N; ++i) {
		pairs[i] = make_pair(segs[i].a, segs[i].b);
	}

	const int start = 0;
	const int in = start + 1;
	const int out = in + pairs.size();
	const int goal = out + pairs.size();
	Graph aft(goal + 1);
	for (int i = 0; i < pairs.size(); ++i) {
		for (int j = 0; j < pairs.size(); ++j) {
			ld dis= abs(pairs[i].second - pairs[j].first);
			add_edge(aft, in + i, out + j, 1, dis);
		}
	}
	for (int i = 0; i < pairs.size(); ++i) {
		
		add_edge(aft, start, in+i, 1, 0);
		add_edge(aft, out+i, goal, 1, 0);
		
	}
	aans=aans+ min_cost_flow(aft, start, goal, pairs.size());
	cout << fixed<<setprecision(22)<<aans << endl;
	return 0;
}