Problem:
Problem H: Monster Trap

Once upon a time when people still believed in magic, there was a great wizard Aranyaka
Gondlir. After twenty years of hard training in a deep forest, he had finally mastered ultimate
magic, and decided to leave the forest for his home.

Arriving at his home village, Aranyaka was very surprised at the extraordinary desolation. A
gloom had settled over the village. Even the whisper of the wind could scare villagers. It was a
mere shadow of what it had been.

What had happened? Soon he recognized a sure sign of an evil monster that is immortal. Even
the great wizard could not kill it, and so he resolved to seal it with magic. Aranyaka could cast
a spell to create a monster trap: once he had drawn a line on the ground with his magic rod,
the line would function as a barrier wall that any monster could not get over. Since he could
only draw straight lines, he had to draw several lines to complete a monster trap, i.e., magic
barrier walls enclosing the monster. If there was a gap between barrier walls, the monster could
easily run away through the gap.

For instance, a complete monster trap without any gaps is built by the barrier walls in the left
figure, where “M” indicates the position of the monster. In contrast, the barrier walls in the
right figure have a loophole, even though it is almost complete.

Your mission is to write a program to tell whether or not the wizard has successfully sealed the
monster.

Input

The input consists of multiple data sets, each in the following format.

n
x1 y1 x'1 y'1
x2 y2 x'2 y'2
...
xn yn x'n y'n

The first line of a data set contains a positive integer n, which is the number of the line segments
drawn by the wizard. Each of the following n input lines contains four integers x, y, x', and
y', which represent the x- and y-coordinates of two points (x, y) and (x', y' ) connected by a line
segment. You may assume that all line segments have non-zero lengths. You may also assume
that n is less than or equal to 100 and that all coordinates are between -50 and 50, inclusive.

For your convenience, the coordinate system is arranged so that the monster is always on the
origin (0, 0). The wizard never draws lines crossing (0, 0).

You may assume that any two line segments have at most one intersection point and that no
three line segments share the same intersection point. You may also assume that the distance
between any two intersection points is greater than 10-5.

An input line containing a zero indicates the end of the input.

Output

For each data set, print “yes” or “no” in a line. If a monster trap is completed, print “yes”.
Otherwise, i.e., if there is a loophole, print “no”.

Sample Input

8
-7 9 6 9
-5 5 6 5
-10 -5 10 -5
-6 9 -9 -6
6 9 9 -6
-1 -2 -3 10
1 -2 3 10
-2 -3 2 -3
8
-7 9 5 7
-5 5 6 5
-10 -5 10 -5
-6 9 -9 -6
6 9 9 -6
-1 -2 -3 10
1 -2 3 10
-2 -3 2 -3
0

Output for the Sample Input

yes
no

Solution in C++ (judge verdict: Runtime Error)

#include<bits/stdc++.h>
#define f first
#define s second
#define mp make_pair
#define pi M_PI
#define inf 1<<30
#define eps (1e-11)
#define MAX 1000
#define equals(a,b) (fabs((a)-(b))<eps)
using namespace std;

class Point{
public:
  double x,y;
  Point(double x=0,double y=0):x(x),y(y){}

  Point operator+(Point p){ return Point(x+p.x,y+p.y);}
  Point operator-(Point p){ return Point(x-p.x,y-p.y);}
  Point operator*(double k){ return Point(x*k,y*k);}
  Point operator/(double k){ return Point(x/k,y/k);}
  bool operator<(Point p)const{ return (x!=p.x ? x<p.x : y<p.y);}
  bool operator==(Point p)const{ return fabs(x-p.x)<eps && fabs(y-p.y)<eps;}

  double abs(){ return sqrt(norm());}
  double norm(){ return (x*x+y*y);}
};
typedef Point Vector;
typedef vector<Point> Polygon;

class Segment{
public:
  Point p1,p2;
  Segment(Point p1=Point(),Point p2=Point()):p1(p1),p2(p2){}
};
typedef Segment Line;

double norm(Vector a){ return (a.x*a.x+a.y*a.y);}
double abs(Vector a){ return sqrt(norm(a));}
double dot(Vector a,Vector b){ return (a.x*b.x+a.y*b.y);}
double cross(Vector a,Vector b){ return (a.x*b.y-a.y*b.x);}

int ccw(Point p0,Point p1,Point p2){
  Vector a=p1-p0;
  Vector b=p2-p0;
  if(cross(a,b)>eps)return 1;
  if(cross(a,b)<-eps)return -1;
  if(dot(a,b)<-eps)return 2;
  if(a.norm()<b.norm())return -2;
  return 0;
}

bool intersect(Point p1,Point p2,Point p3,Point p4){
  return (ccw(p1,p2,p3)*ccw(p1,p2,p4)<=0 &&
          ccw(p3,p4,p1)*ccw(p3,p4,p2)<=0);
}

bool intersect(Segment s1,Segment s2){
  return intersect(s1.p1,s1.p2,s2.p1,s2.p2);
}

Point getCrossPointSS(Segment s1,Segment s2){
  Vector base=s2.p2-s2.p1;
  double d1=abs(cross(base,s1.p1-s2.p1));
  double d2=abs(cross(base,s1.p2-s2.p1));
  double t=d1/(d1+d2);
  return (s1.p1+(s1.p2-s1.p1)*t);
}

int contains(Polygon g,Point p){
  int n=g.size();
  bool x=false;
  for(int i=0;i<n;i++){
    Vector a=g[i]-p,b=g[(i+1)%n]-p;
    if(abs(cross(a,b))<eps && dot(a,b)<eps)return 1;
    if(a.y>b.y)swap(a,b);
    if(a.y<eps && eps<b.y && cross(a,b)>eps)x=!x;
  }
  if(x)return 2;
  return 0;
}

typedef vector<vector<int> > Graph;

Graph SegmentArrangement(vector<Segment> v,vector<Point> &ps){
  for(int i=0;i<v.size();i++){
    ps.push_back(v[i].p1);
    ps.push_back(v[i].p2);
    for(int j=i+1;j<v.size();j++){
      if(intersect(v[i],v[j]))ps.push_back(getCrossPointSS(v[i],v[j]));
    }
  }
  sort(ps.begin(),ps.end());
  ps.erase(unique(ps.begin(),ps.end()),ps.end());
  Graph g(ps.size());
  for(int i=0;i<v.size();i++){
    vector<pair<double,int> > list;
    for(int j=0;j<ps.size();j++)
      if(ccw(v[i].p1,v[i].p2,ps[j])==0)
        list.push_back(mp(norm(v[i].p1-ps[j]),j));
    sort(list.begin(),list.end());
    for(int j=0;j<list.size()-1;j++){
      int a=list[j].s,b=list[j+1].s;
      g[a].push_back(b);
      g[b].push_back(a);
    }
  }
  return g;
}

Graph g;
vector<Point> vp;
bool checked[MAX];
bool visited[MAX];
vector<int> v;
string ans="no";

void dfs(int now,int before){
  v.push_back(now);
  if(visited[now]){
    int s;
    for(int i=0;i<v.size();i++){
      if(v[i]==now){
        s=i+1;
        break;
      }
    }
    Polygon p;
    for(int i=s;i<v.size();i++)p.push_back(vp[v[i]]);
    if(contains(p,Point(0,0))!=0)ans="yes";
  }
  else {
    visited[now]=true;
    for(int i=0;i<g[now].size();i++){
      int next=g[now][i];
      if(next==before)continue;
      if(!checked[next])dfs(next,now);
    }
    visited[now]=false;
  }
  v.pop_back();
  checked[now]=true;
}

int main()
{
  int n;
  
  while(1){
    cin>>n;
    if(n==0)break;
    vector<Segment> v;
    for(int i=0;i<n;i++){
      int a,b,c,d;
      cin>>a>>b>>c>>d;
      v.push_back(Segment(Point(a,b),Point(c,d)));
    }
    vp.clear();
    g=SegmentArrangement(v,vp);
    ans="no";
    fill(checked,checked+MAX,0);
    for(int i=0;i<vp.size();i++){
      fill(visited,visited+MAX,0);
      v.clear();
      if(!checked[i])dfs(i,-1);
    }
    cout<<ans<<endl;
  }
  return 0;
}