POJ3178 计算几何+DP

//一些点一些圆，过圆不能连线，相邻点不能连线，问最多连几条线 
//计算几何模板+区间dp
//关键是判断圆和线段是否相交 
#include <cstdio>
#include <cmath>
#include <algorithm>
#define N 500
#define ll long long
#define sqr(x) ((x)*(x))
using namespace std;
bool ok[N][N];
ll n,m,r,f[N][N];
struct poi
{
    ll x,y;
    poi(ll X,ll Y)
    {
        x=X;y=Y;
    }
    poi()
    {
    }
} p[N],q[N];
ll cro(poi a,poi b)
{
    return (a.x*b.y-a.y*b.x);
}
ll dot(poi a,poi b)
{
    return a.x*b.x+a.y*b.y;
}
poi tr(poi a,poi b)
{
    return poi(a.x-b.x,a.y-b.y);
}
double dis(poi a,poi b)
{
    return sqrt((double)(sqr(a.x-b.x)+sqr(a.y-b.y)));
}
bool cmp(poi a,poi b)
{
    return (a.x<b.x)||(a.x==b.x && a.y<b.y);
}
bool cmp2(poi a,poi b)
{
    return cro(tr(a,p[1]),tr(b,p[1]))>0;
}
bool check(poi a,poi b)
{
    double C=dis(a,b);
    for(int i=1;i<=m;i++)
    {
        double A=dis(q[i],a);
        double B=dis(q[i],b);
        double COSA=(B*B+C*C-A*A)/(2*B*C);
        double COSB=(A*A+C*C-B*B)/(2*A*C);
        if(COSA<1e-10||COSB<1e-10){
            if(A<1.0*r+1e-10||B<1.0*r+1e-10)return 0;
            else continue;
        }
        double SINA=sqrt(1-COSA*COSA);
        double H=B*SINA;
        if(H<1.0*r+1e-10)return 0;
    }
    return 1;
}
int main()
{
    scanf("%d%d%d",&n,&m,&r);
    for(int i=1;i<=n;i++)
        scanf("%d%d",&p[i].x,&p[i].y);
    sort(p+1,p+1+n,cmp);
    sort(p+2,p+1+n,cmp2);
    for(int i=1;i<=m;i++)
        scanf("%d%d",&q[i].x,&q[i].y);
    for(int i=1;i<=n;i++)
        for(int j=i+2;j<=n;j++)
        if(i!=1 || j!=n)
            ok[i][j]=check(p[i],p[j]);
    for(int len=2;len<=n;len++)
        for(int start=1;start<=n;start++){
            ll end=start+len;
            for(int k=start+1;k<min(end,n);k++)
                f[start][end]=max(f[start][end],f[start][k]+f[k][end]);
            f[start][end]+=ok[start][end];
        }
    printf("%d\n",f[1][n]);
}