Poj 1113 Wall (凸包Graham)

题目链接：http://poj.org/problem?id=1113

解题报告参见  http://blog.csdn.net/lyy289065406/article/details/6648622

第一次写凸包的题，发现还有许多细节没有完全掌握。。。

公式：城堡围墙长度最小值 = 城堡顶点坐标构成的散点集的凸包总边长 + 半径为L的圆周长（推导见上述解题报告）

极角序

#include <stdio.h>#include <algorithm>#include <math.h>using namespace std;struct point{    double x,y;}; const double EPS=1e-8;const int MAX=1005;const double PI=acos(-1.0);point p[MAX],q[MAX],temp;int n,m;int DB (double x){    if (x>EPS)return 1;    if (x<-EPS)return -1;    return 0;}double Dis (point a,point b){    return sqrt((a.x-b.x)*(a.x-b.x)+(a.y-b.y)*(a.y-b.y));}//判断p在向量ab的哪一侧//右侧：返回正值//左侧：返回负值//在向量ab上返回0double cross(point a,point b,point p){    return (b.x-a.x)*(p.y-a.y)-(b.y-a.y)*(p.x-a.x);}int cmp (point a,point b){    double x=Dis(a,temp),y=Dis(b,temp);    int flag=DB(cross(temp,a,b));    if (flag)return flag == 1;    returnDB(x-y)<=0;} //求凸包函数//p:所有的点，n个,p[0]到p[n-1]//q:求完的凸包中的点，m个,q[0]到q[m-1]void Graham (point p[],int n,point q[],int &m){    point t;    int i,k=0,a,b;    for (i=1;i<n;i++)    {        a=DB(p[i].y-p[k].y);        b=DB(p[i].x-p[k].x);        if (a==-1 || !a && b==-1)k=i;    }    if (k!=0)t=p[0],p[0]=p[k],p[k]=t;    temp=p[0];    sort(p+1,p+n,cmp);    q[0]=p[0];    q[1]=p[1];    p[n]=p[0];    m=2;    for (i=2;i<=n;i++)    {        while (m>1 && DB(cross(q[m-2],q[m-1],p[i]))<=0)m--;        q[m++]=p[i];    }    m--;     //头尾是同一个点}int main (){int L,i;double ans=0;scanf("%d%d",&n,&L);for (i=0;i<n;i++)scanf("%lf%lf",&p[i].x,&p[i].y);Graham (p,n,q,m);for (i=0;i<m;i++)ans+=Dis(q[i],q[(i+1)%m]);ans+=PI*2*L;printf("%.0lf\n",ans);return 0;}

水平序

#include <stdio.h>#include <string.h>#include <algorithm>  #include <math.h>  using namespace std; const double PI=acos(-1.0);struct Point{      double x,y;void get(){scanf("%lf%lf",&x,&y);    }}pt[1005],ch[1005];int n,len;int DB (double d){if (fabs(d)<1e-8)return 0;return d>0?1:-1;}double Dis (Point p,Point ch){return sqrt((p.x-ch.x)*(p.x-ch.x)+(p.y-ch.y)*(p.y-ch.y));}double cross (Point p,Point ch,Point x){return (p.x-x.x)*(ch.y-x.y)-(ch.x-x.x)*(p.y-x.y);}int cmp (const void *a,const void *b){Point aa=*(Point *)a;Point bb=*(Point *)b;int y=DB(aa.y-bb.y);int x=DB(aa.x-bb.x);if (y == 0)return x==1?1:-1;return y;}void Graham (Point pt[],Point ch[],int &len,int n)      //只保存凸包顶点{int i,top=1;qsort(pt,n,sizeof(pt[0]),cmp);    ch[0]=pt[0];    ch[1]=pt[1];    for (i=2;i<n;i++)    {        while (top>0 && DB(cross(ch[top],pt[i],ch[top-1])) <= 0)            top--;        ch[++top]=pt[i];    }    int temp=top;    for (i=n-2;i>=0;i--)    {        while (top>temp && DB(cross(ch[top],pt[i],ch[top-1])) <= 0)            top--;        ch[++top]=pt[i];    }    len=top;}int main (){    int L,i;      double ans=0;    scanf("%d%d",&n,&L);      for (i=0;i<n;i++)          pt[i].get();    Graham (pt,ch,len,n);    for (i=0;i<len;i++)        ans+=Dis(ch[i],ch[(i+1)%len]);      ans+=PI*2*L;    printf("%.0lf\n",ans);    return 0;}