UVAoj 1342 - That Nice Euler Circuit

题解：
欧拉定理：E + 2 - V = F
总结：
1.跟着刘汝佳一步一步学习计算几何
2.对于一个实际问题，先想出解题思路，并且严格明确每一个步骤，最终脱离实际问题，以代码的思想实现

#include<cstdio>#include<cmath>#include<iostream>#include<cstring>#include<algorithm>#include<vector>#include<set>using namespace std;struct Point {  double x, y;  Point(double x=0, double y=0):x(x),y(y) { }};const double eps = 1e-10;int dcmp(double x) {  if(fabs(x) < eps) return 0; else return x < 0 ? -1 : 1;}typedef Point Vector;Vector operator + (const Vector& A, const Vector& B) { return Vector(A.x+B.x, A.y+B.y); }Vector operator - (const Point& A, const Point& B) { return Vector(A.x-B.x, A.y-B.y); }Vector operator * (const Vector& A, double p) { return Vector(A.x*p, A.y*p); }bool operator < (const Point& a, const Point& b) {  return a.x < b.x || (a.x == b.x && a.y < b.y);}bool operator == (const Point& a, const Point &b) {  return dcmp(a.x-b.x) == 0 && dcmp(a.y-b.y) == 0;}bool operator != (const Point& a, const Point &b) {  return !(a == b);}double Dot(const Vector& A, const Vector& B) { return A.x*B.x + A.y*B.y; }double Length(const Vector& A) { return sqrt(Dot(A, A)); }double Angle(const Vector& A, const Vector& B) { return acos(Dot(A, B) / Length(A) / Length(B)); }double Cross(const Vector& A, const Vector& B) { return A.x*B.y - A.y*B.x; }Point GetLineIntersection(const Point& P, const Point& v, const Point& Q, const Point& w) {  Vector u = P-Q;  double t = Cross(w, u) / Cross(v, w);  return P+v*t;}Vector Rotate(const Vector& A, double rad) {  return Vector(A.x*cos(rad)-A.y*sin(rad), A.x*sin(rad)+A.y*cos(rad));}bool SegmentProperIntersection(const Point& a1, const Point& a2, const Point& b1, const Point& b2) {  double c1 = Cross(a2-a1,b1-a1), c2 = Cross(a2-a1,b2-a1),  c3 = Cross(b2-b1,a1-b1), c4=Cross(b2-b1,a2-b1);  return dcmp(c1)*dcmp(c2)<0 && dcmp(c3)*dcmp(c4)<0;}bool OnSegment(const Point& p, const Point& a1, const Point& a2) {  return dcmp(Cross(a1-p, a2-p)) == 0 && dcmp(Dot(a1-p, a2-p)) < 0;}bool _OnSegment(const Point& p, const Point& a1, const Point& a2) {  return dcmp(Cross(a1-p, a2-p)) == 0 && dcmp(Dot(a1-p, a2-p)) < 0         && p != a1 && p != a2;}Point read_point(){  double x, y;  scanf("%lf%lf", &x, &y);  return Point(x,y);}#define MAXN 305int n,e,cnt;Point p[MAXN],v[MAXN * MAXN];set<Point>se;int main(){    int kcas = 0;    while(scanf("%d",&n) && n)    {        e = n - 1;        for(int i = 0;i < n;i++)            v[i] = p[i] = read_point();        cnt = n;        for(int i = 2;i < n - 1;i++)            for(int u = 0;u < i - 1;u++)                if(SegmentProperIntersection(p[i],p[i + 1],p[u],p[u + 1]))                    v[cnt++] = GetLineIntersection(p[i],p[i + 1] - p[i],p[u],p[u + 1] - p[u]);        sort(v,v + cnt);        cnt = unique(v,v + cnt) - v;        for(int i = 0;i < n - 1;i++)            for(int j = 0;j < cnt;j++)                if(OnSegment(v[j],p[i],p[i + 1]))                    e++;        printf("Case %d: There are %d pieces.\n",++kcas,e + 2 - cnt);    }}