ZOJ 1010 Area 求任意多边形面积

主要判断是否是多边形：1、n<3 ； 2、非相邻两条线段不相交

#include <iostream>
#include <cmath>
#include <stdio.h>
using namespace std;
#define eps 1e-8
int sig(double x)
{
    if(x<-eps) return -1;
    if(x>eps) return 1;
    return 0;
}
struct point
{
    double x,y;
} p[1005];

struct line
{
    point p;
    point q;
    line()
    {

    }
    line(point aa,point bb)
    {
        p=aa;
        q=bb;
    }
};
int inside(point o,line L)
{
    double xl=min(L.p.x,L.q.x);
    double xr=max(L.p.x,L.q.x);
    double yl=min(L.p.y,L.q.y);
    double yr=max(L.p.y,L.q.y);
    if(sig(o.x-xl)>=0&&sig(xr-o.x)>=0&&sig(o.y-yl)>=0&&sig(yr-o.y)>=0)
        return 1;
    else
        return 0;
}

int banana(line u,line v)
{
    point ret=u.p;
    double t=((u.p.x-v.p.x)*(v.p.y-v.q.y)-(u.p.y-v.p.y)*(v.p.x-v.q.x))/((u.p.x-u.q.x)*(v.p.y-v.q.y)-(u.p.y-u.q.y)*(v.p.x-v.q.x));
    ret.x+=(u.q.x-u.p.x)*t;
    ret.y+=(u.q.y-u.p.y)*t;
    if(inside(ret,u)&&inside(ret,v)) return 1;
    return 0;
}
double det(point p0,point p1,point p2)
{
    return (p1.x-p0.x)*(p2.y-p0.y)-(p1.y-p0.y)*(p2.x-p0.x);
}
//求多边形面积
double ploygon_area(int n)
{
    double s=0.0;
    for(int i=1; i < n-1; i++)
        s += det(p[0],p[i],p[i+1]);
    return 0.5*fabs(s);
}

int main()
{
    int i,n,ca=1,j,yy=0;
    while(scanf("%d",&n)!=EOF,n)
    {
        for(i=0; i<n; i++)
            scanf("%lf%lf",&p[i].x,&p[i].y);
        if(yy==1) printf("
");
        yy=1;
        printf("Figure %d: ",ca++);
        if(n<3)
        {
            printf("Impossible
");
            continue;
        }
        p[n]=p[0];
        int flag=0;
        for(i=0;i<n;i++)
        {
            for(j=i+2;j<n;j++)
            {
                if(i==(j+1)%n) continue;
                if(banana(line(p[i],p[i+1]),line(p[j],p[j+1]))) {flag=1;break;}
            }
            if(flag) break;
        }
        if(flag)
        {
            printf("Impossible
");
            continue;
        }
        double ans=ploygon_area(n);
        printf("%.2f
",ans);
    }
    return 0;
}