poj-1584 判断凸包算法+极角排序+判断点在几何内外 模板

几何问题的重点
1 精度问题 有时答案一直错不是因为算法错误 而是精度没有处理好
2 代码能力 几何代码量较大 要不断练习熟能生巧，否则因为一个bug可能要查错很长时间

#include<cstdio>#include<cmath>#include<stack>#include<algorithm>using namespace std;struct point{    double x,y;}p[20000],tubao[20000];int n,mi;double r,x,y,minx,miny;bool cmp(point a,point b){    if(fabs((a.x-minx)*(b.y-miny)-(a.y-miny)*(b.x-minx))<=1e-8)return fabs(a.x-minx)<fabs(b.x-minx);    else return (a.x-minx)*(b.y-miny)-(a.y-miny)*(b.x-minx)>0;}//极角排序所用cmp函数bool toJudgeLeftOrRight(int p1,int p2,int p3){     point P1,P2;     P1.x = p[p3].x-p[p1].x;     P1.y = p[p3].y-p[p1].y;     P2.x = p[p2].x-p[p1].x;     P2.y = p[p2].y-p[p1].y;     if(fabs(P2.x*P1.y-P2.y*P1.x)<=1e-8||P2.x*P1.y-P2.y*P1.x>0)     return true;     else return false;}//判断点是否往左歪 判断凸包bool  grahamScan(){    mi = 0;    minx = p[mi].x;    miny = p[mi].y;    for(int i=0;i<n;i++)    if(p[i].y<p[mi].y){      mi = i;      minx = p[i].x;      miny = p[i].y;    }    else if(fabs(p[i].y-p[mi].y)<=1e-11&&p[i].x<p[mi].x)    {      mi = i;      minx = p[i].x;      miny = p[i].y;        }    sort(p,p+n,cmp);//极角排序    stack<int>st;    st.push(0);    st.push(1);    for(int i=2;i<n;i++)    {        while(st.size())        {          int p1,p2,p3 = i;          p2 = st.top();          st.pop();          p1 = st.top();          st.pop();          if(toJudgeLeftOrRight(p1,p2,p3))          {            st.push(p1);            st.push(p2);            st.push(i);            break;          }          else{            st.push(p1);          }        }    }    if(st.size()==n)return true;    else return false;}//判断凸包bool toJudgePointOutOrIn(){    int sum = 0;    for(int i=0;i<n;i++)    {      if(!(fabs((p[(i+1)%n].x - p[i].x))<=1e-11))      {        double k = (p[(i+1)%n].y - p[i].y)/(p[(i+1)%n].x - p[i].x),        b = p[i].y - k*p[i].x;        double X = (y-b)/k;         if(fabs(x-X)<=1e-11)return false;        else if(x-X<0)        {            double y1 = min(p[(i+1)%n].y,p[i].y);            double y2 = max(p[(i+1)%n].y,p[i].y);            if(y>y1&&(y<y2||fabs(y-y2)<=1e-11))sum++;        }      }      else{        if(fabs(x-p[i].x)<=1e-11)return false;        else if(x-p[i].x<0)        {            double y1 = min(p[(i+1)%n].y,p[i].y);            double y2 = max(p[(i+1)%n].y,p[i].y);            if(y>y1&&(y<y2||fabs(y-y2)<=1e-11))sum++;        }      }    }    if(sum%2)return true;    else return false;}//判断点是否在闭合几何内bool toJudgeCircal(){    for(int i=0;i<n;i++)    {       if(!(fabs((p[(i+1)%n].x - p[i].x))<=1e-11))      {        double k = (p[(i+1)%n].y - p[i].y)/(p[(i+1)%n].x - p[i].x),        b = p[i].y - k*p[i].x;        double R = fabs(y-k*x-b)/sqrt(1+k*k);        if(fabs(R-r)<=1e-11||R>r);        else return false;      }      else{         double R = fabs(p[i].x-x);         if(fabs(R-r)<=1e-11||R>r);         else return false;      }     }    return true;}//在前几步的基础上判断圆是否与凸包有交点int main(){    while(scanf("%d",&n))    {       if(n<3)break;       scanf("%lf%lf%lf",&r,&x,&y);       for(int i=0;i<n;i++)       scanf("%lf%lf",&p[i].x,&p[i].y);       if(grahamScan())       {        if(toJudgePointOutOrIn()){            if(toJudgeCircal())printf("PEG WILL FIT\n");            else printf("PEG WILL NOT FIT\n");            }        else printf("PEG WILL NOT FIT\n");       }       else printf("HOLE IS ILL-FORMED\n");     }    return 0;}