[ZOJ 1010] Area (计算几何)

题目链接：http://acm.zju.edu.cn/onlinejudge/showProblem.do?problemCode=1010

题目大意：给你n个点，问你顺次连线能否连成多边形？如果能，就输出多边形面积。

面积用向量的叉积去算。然后能否连成多边形就是看这条线跟之前的线有没有交点。

这些在大白书上都有板子。。

代码：

 #include <cstdio>
 #include <cstdlib>
 #include <string>
 #include <iostream>
 #include <cstring>
 #include <algorithm>
 #include <cctype>
 #include <vector>
 #include <map>
 #include <set>
 #include <iterator>
 #include <functional>
 #include <cmath>
 #include <numeric>
 #include <ctime>
 using namespace std;
 typedef long long LL;
 typedef pair<int,int> PII;
 typedef vector<int> VI;
 #define PB push_back
 #define MP make_pair
 #define SZ size()
 #define CL clear()
 #define AA first
 #define BB second
 #define EPS 1e-8
 #define ZERO(x) memset((x),0,sizeof(x))
 const int INF = ~0U>>;
 const double PI = acos(-1.0);

 struct POINT{
     double x,y;
     POINT(double ax=,double ay=):x(ax),y(ay) {}
 };
 typedef POINT VECTOR;

 POINT pts[];

 VECTOR operator- (POINT A,POINT B){
     return VECTOR(A.x-B.x,A.y-B.y);
 }

 double CROSS(VECTOR A,VECTOR B){
     return A.x*B.y-A.y*B.x;
 }

 double AREA(POINT *p,int n){
     double area = ;
     for(int i=;i<n-;i++){
         area += CROSS(p[i]-p[],p[i+]-p[]);
     }
     return area/;
 }

 bool SegmentProperIntersection(POINT a1,POINT a2,POINT b1,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 c1*c2<EPS && c3*c4<EPS;
 }

 int main(){
     int n;
     int kase = ;
     while( scanf("%d",&n), n ){
         if(kase!=) puts("");
         bool flag = true;
         for(int i=;i<n;i++){
             double a,b;
             scanf("%lf%lf",&a,&b);
             pts[i] = POINT(a,b);
             for(int j=;j<i-;j++){
                 if( SegmentProperIntersection(pts[j],pts[j+],pts[i-],pts[i])) flag = false;
             }
         }
         for(int j=;j<n-;j++){
             if( SegmentProperIntersection(pts[j],pts[j+],pts[],pts[n-])) flag = false;
         }
         double area = fabs(AREA(pts,n));
         if( n==||n== ){
             printf("Figure %d: Impossible\n",kase++);
             continue;
         }
         if(!flag) printf("Figure %d: Impossible\n",kase++);
         else printf("Figure %d: %.2f\n",kase++,area);
     }
     return ;
 }