BZOJ 1091([SCOI2003]分割多边形-分割直线)

Description

Input

Output

Sample Input

Sample Output

HINT

Source

直接把多边形伸长成2点都在矩形上的线段，这种话每次取时把之前的线段割一下。

注意伸长时保证向量方向

#include<cstdio>
#include<cstring>
#include<cstdlib>
#include<algorithm>
#include<functional>
#include<iostream>
#include<cmath>
#include<cctype>
#include<ctime>
using namespace std;
#define For(i,n) for(int i=1;i<=n;i++)
#define Fork(i,k,n) for(int i=k;i<=n;i++)
#define Rep(i,n) for(int i=0;i<n;i++)
#define ForD(i,n) for(int i=n;i;i--)
#define RepD(i,n) for(int i=n;i>=0;i--)
#define Forp(x) for(int p=pre[x];p;p=next[p])
#define Lson (x<<1)
#define Rson ((x<<1)+1)
#define MEM(a) memset(a,0,sizeof(a));
#define MEMI(a) memset(a,127,sizeof(a));
#define MEMi(a) memset(a,128,sizeof(a));
#define INF (2139062143)
#define F (1000000007)
#define MP make_pair
#define MAXP (500+10)
#define MAXN (500+10)
#define MAXM (500+10)
#define eps (1e-6)
long long mul(long long a,long long b){return (a*b)%F;}
long long add(long long a,long long b){return (a+b)%F;}
long long sub(long long a,long long b){return (a-b+(a-b)/F*F+F)%F;}
typedef long long ll;
int n,m,p;
double sqr(double x){return x*x;}
int dcmp(double a,double b=0){if (fabs(a-b)<=eps) return 0;else if (a<b) return -1;return 1;}
struct P
{
    double x,y;
    P(){}
    P(double _x,double _y):x(_x),y(_y){}
    friend istream& operator>>(istream& cin,P &a){cin>>a.x>>a.y;return cin;}
    friend ostream& operator<<(ostream& cout,P &a){cout<<a.x<<‘ ‘<<a.y;return cout;}
    friend bool operator==(P a,P b){return dcmp(a.x,b.x)==0&&dcmp(a.y,b.y)==0;    }
}a[MAXP];
struct V
{
    double x,y;
    V(){}
    V(double _x,double _y):x(_x),y(_y){}
    V(P a,P b):x(b.x-a.x),y(b.y-a.y){}
    friend V operator*(double a,V b){return V(a*b.x,a*b.y);}
    friend V operator-(P a,P b){return V(b.x-a.x,b.y-a.y); }
    friend double operator*(V a,V b){return a.x*b.y-a.y*b.x;}
    friend double operator^(V a,V b){return a.x*b.x+a.y*b.y;}
    friend P operator+(P a,V b){return P(a.x+b.x,a.y+b.y);    }
    friend double dis2(V a){return sqr(a.x)+sqr(a.y);    }
};
struct L
{
    P p;
    V v;    
    L(){}
    L(P _A,V _B):p(_A),v(_B){}
    friend bool parallel(L a,L b) {return (dcmp(a.v.x*b.v.y,a.v.y*b.v.x))==0;}
    friend P intersect(L a,L b) //直线交点
    {
        V &v=a.v,&w=b.v,u=V(b.p,a.p);
        double t=(w*u)/(v*w);
        P c=a.p+t*v; return c;
    }
    friend bool inleft(P a,L b){return dcmp(b.v*V(b.p,a))>=0;    }
    void print(){cout<<p.x<<‘ ‘<<p.y<<‘ ‘<<v.x<<‘ ‘<<v.y<<endl;    }
}l[MAXP],lrec[4];
bool inrec(P a){return (dcmp(a.x)>=0&&dcmp(a.x,n)<=0&&dcmp(a.y)>=0&&dcmp(a.y,m)<=0);}
L through_rec_line(L l)
{
    int siz=0;P st[3];
    if (dcmp(l.v.x)==0) return L(P(l.p.x,l.v.y>0?0:m),V(0,(l.v.y>0?1:-1)*m));
    if (dcmp(l.v.y)==0) return L(P(l.v.x>0?0:n,l.p.y),V((l.v.x>0?1:-1)*n,0)); //至此保证不平行坐标系 
    Rep(i,4)
    {
        if (parallel(lrec[i],l)) continue;
        st[++siz]=intersect(lrec[i],l);
        if (!inrec(st[siz])) siz--;
        if (siz==2)
        { 
            if (st[1]==st[2]) siz--;
            else
            {
                V a=V(st[1],st[2]);
                if (dcmp(a^l.v)<0) return L(st[2],V(st[2],st[1]));
                return L(st[1],a); 
            }
        }
    }
}
bool b[MAXP]={0};
double ans=1e300;
int cut_list[MAXN];
void dfs(double tot,int siz)
{
    if (tot>ans) return;
    if (siz==p) 
    {
    //  Rep(i,siz) cout<<cut_list[i]<<‘ ‘;printf("%.3lf\n",ans);
        ans=min(ans,tot); 
        return;
    }
     
    /*  
    if (siz==2)
    {
        if (cut_list[0]==2&&cut_list[1]==1) 
        {
            cout<<‘ ‘;
        }
    }*/
   
    For(i,p)
        if (!b[i])
        {
            L x=through_rec_line(l[i]);
            For(j,p)
                if (!parallel(l[j],x)&&b[j])
                {
                    P p=intersect(x,l[j]);
                    if (dcmp(V(p,x.p)^V(p,x.p+x.v))<0)
                    {
                        if (!inleft(x.p,l[j])) x=L(p,V(p,x.p+x.v));
                        else if (!inleft(x.p+x.v,l[j])) x=L(x.p,V(x.p,p));
                    }
                }
            b[i]=1;
            cut_list[siz]=i;
        /*
            Rep(j,siz) printf("\t");
            cout<<i<<endl; 
            printf("%.3lf\n",tot+sqrt(dis2(x.v)));
          */ 
            dfs(tot+sqrt(dis2(x.v)),siz+1);
            b[i]=0;
        }
}
int main()
{
//  freopen("bzoj1091.in","r",stdin);
//  freopen("bzoj1091.out","w",stdout);
     
    cin>>n>>m>>p;
    ForD(i,p) cin>>a[i];memcpy(a+p+1,a+1,sizeof(P)*p);
    For(i,p) l[i]=L(a[i],V(a[i],a[i+1]));memcpy(l+p+1,l+1,sizeof(L)*p);
 
    lrec[0]=L(P(0,0),V(n,0)),lrec[1]=L(P(n,0),V(0,m)),lrec[2]=L(P(n,m),V(-n,0)),lrec[3]=L(P(0,m),V(0,-m));
    For(i,p) l[i]=through_rec_line(l[i]); 
 
//  For(i,p) l[i].print();
 
    dfs(0,0);
     
     
    printf("%.3lf\n",ans);
    return 0;
}