POJ 3449 Geometric Shapes【计算几何+判线段相交】

题目链接

题意：有一堆多边形，问每个多边形和哪些其他多边形相交。

讲道理是个水题……就是输入输出麻烦了点，中间判下线段相交就行。

线段相交的模板：

// 判断一个数是否为0bool zero(double x){    if (fabs(x)<eps)    return true;    else    return false;}// 求矢量p0->p1, p0->p2的叉积double xmult(Point p1,Point p2,Point p0){    return (p1.x-p0.x)*(p2.y-p0.y)-(p2.x-p0.x)*(p1.y-p0.y); }// 判点是否在线段上,包括端点int dot_online_in(Point p,Line l){     return zero(xmult(p,l.a,l.b))&&(l.a.x-p.x)*(l.b.x-p.x)<eps&&(l.a.y-p.y)*(l.b.y-p.y)<eps;}//判两点在线段同侧,点在线段上返回0int same_side(Point p1,Point p2,Line l){    return xmult(l.a,p1,l.b)*xmult(l.a,p2,l.b)>eps; }// 判两点在线段异侧int opposite_side(Point p1,Point p2,Line l){    return xmult(l.a,p1,l.b)*xmult(l.a,p2,l.b)<-eps; }// 判线段相交，包括端点和部分重合int intersect_in(Line u,Line v){     if (!dots_inline(u.a,u.b,v.a)||!dots_inline(u.a,u.b,v.b))        return !same_side(u.a,u.b,v)&&!same_side(v.a,v.b,u);     return dot_online_in(u.a,v)||dot_online_in(u.b,v)||dot_online_in(v.a,u)||dot_online_in(v.b,u); }// 判线段相交，不包括端点和部分重合int intersect_ex(Line u,Line v){     return opposite_side(u.a,u.b,v)&&opposite_side(v.a,v.b,u); }

#include <iostream>#include <cstdio>#include <cstring>#include <algorithm>#include <string>#include <cmath>#include <vector>#include <queue>#include <set>#include <map>using namespace std;#define ll long long#define zero(x) (((x)>0?(x):-(x))<eps)const double eps=1e-8;char ch;struct Point{    double x,y;};struct Shape{    string kind;    int n;    Point point[30];    int cnt;    int intersect[30];}shape[30];bool vis[30];double xmult(Point p1,Point p2,Point p0){    return (p1.x-p0.x)*(p2.y-p0.y)-(p2.x-p0.x)*(p1.y-p0.y); }int dots_inline(Point p1,Point p2,Point p3){    return zero(xmult(p1,p2,p3));}int dot_online_in(Point p,Point p1,Point p2){     return zero(xmult(p,p1,p2))&&(p1.x-p.x)*(p2.x-p.x)<eps&&(p1.y-p.y)*(p2.y-p.y)<eps;}int same_side(Point p1,Point p2,Point p3,Point p4){    return xmult(p3,p1,p4)*xmult(p3,p2,p4)>eps; }int intersect_in(Point p1,Point p2,Point p3,Point p4){     if (!dots_inline(p1,p2,p3)||!dots_inline(p1,p2,p4))        return !same_side(p1,p2,p3,p4)&&!same_side(p3,p4,p1,p2);     return dot_online_in(p1,p3,p4)||dot_online_in(p2,p3,p4)||dot_online_in(p3,p1,p2)||dot_online_in(p4,p1,p2); }void input(int id,string ss){    if (ss=="square"){        shape[id].n=4;        getchar();        scanf("%lf,%lf",&shape[id].point[1].x,&shape[id].point[1].y);        getchar();        getchar();        getchar();        scanf("%lf,%lf",&shape[id].point[3].x,&shape[id].point[3].y);        getchar();        getchar();        double x1,y1,x2,y2,x3,y3,x4,y4;        x1=shape[id].point[1].x;        y1=shape[id].point[1].y;        x3=shape[id].point[3].x;        y3=shape[id].point[3].y;        x2=(x1+x3+y3-y1)/2;        x4=(x1+x3+y1-y3)/2;        y2=(y1+y3+x1-x3)/2;        y4=(y1+y3-x1+x3)/2;        shape[id].point[2].x=x2;        shape[id].point[2].y=y2;        shape[id].point[4].x=x4;        shape[id].point[4].y=y4;        shape[id].point[shape[id].n+1]=shape[id].point[1];    }    else if (ss=="rectangle"){        shape[id].n=4;        for (int i=1;i<=3;i++){            getchar();            scanf("%lf,%lf",&shape[id].point[i].x,&shape[id].point[i].y);            getchar();            getchar();        }        shape[id].point[4].x=shape[id].point[3].x+shape[id].point[1].x-shape[id].point[2].x;        shape[id].point[4].y=shape[id].point[3].y+shape[id].point[1].y-shape[id].point[2].y;        shape[id].point[shape[id].n+1]=shape[id].point[1];    }    else if (ss=="line"){        shape[id].n=2;        for (int i=1;i<=2;i++){            getchar();            scanf("%lf,%lf",&shape[id].point[i].x,&shape[id].point[i].y);            getchar();            getchar();        }        shape[id].point[shape[id].n+1]=shape[id].point[1];    }    else if (ss=="triangle"){        shape[id].n=3;        for (int i=1;i<=3;i++){            getchar();            scanf("%lf,%lf",&shape[id].point[i].x,&shape[id].point[i].y);            getchar();            getchar();        }        shape[id].point[shape[id].n+1]=shape[id].point[1];    }    else if (ss=="polygon"){        scanf("%d",&shape[id].n);        getchar();        for (int i=1;i<=shape[id].n;i++){            getchar();            scanf("%lf,%lf",&shape[id].point[i].x,&shape[id].point[i].y);            getchar();            getchar();        }        shape[id].point[shape[id].n+1]=shape[id].point[1];    }}int main(){    // freopen("1.txt","r",stdin);    while (scanf("%c",&ch)!=EOF){        getchar();        memset(vis,false,sizeof(vis));        for (int i=0;i<26;i++){            shape[i].cnt=0;            memset(shape[i].intersect,0,sizeof(shape[i].intersect));        }        if (ch=='.')    break;        string ss;        cin>>ss;        int id=ch-'A';        shape[id].kind=ss;        vis[id]=true;        getchar();        input(id,ss);        while (scanf("%c",&ch)!=EOF){            getchar();            if (ch=='-')    break;            id=ch-'A';            cin>>ss;            shape[id].kind=ss;            getchar();            vis[id]=true;            input(id,ss);        }        for (int i=0;i<26;i++){            if (!vis[i])    continue;            for (int j=i+1;j<26;j++){                if (!vis[j])    continue;                bool flag=false;                for (int k1=1;k1<=shape[i].n;k1++){                    for (int k2=1;k2<=shape[j].n;k2++){                        if (intersect_in(shape[i].point[k1],shape[i].point[k1+1],shape[j].point[k2],shape[j].point[k2+1])){                            flag=true;                            break;                        }                    }                    if (flag)                        break;                }                if (flag){                    shape[i].intersect[++shape[i].cnt]=j;                    shape[j].intersect[++shape[j].cnt]=i;                }            }        }        for (int i=0;i<26;i++){            if (!vis[i])    continue;            if (shape[i].cnt==0){                printf("%c has no intersections\n",i+'A');                continue;            }            if (shape[i].cnt==1){                printf("%c intersects with %c\n",i+'A',shape[i].intersect[1]+'A');                continue;            }            if (shape[i].cnt==2){                if (shape[i].intersect[1]>shape[i].intersect[2])                    swap(shape[i].intersect[1],shape[i].intersect[2]);                printf("%c intersects with %c and %c\n",i+'A',shape[i].intersect[1]+'A',shape[i].intersect[2]+'A');                continue;            }            sort(shape[i].intersect+1,shape[i].intersect+shape[i].cnt+1);            printf("%c intersects with ",i+'A');            for (int j=1;j<=shape[i].cnt;j++){                // B intersects with S, W, and X                if (j==shape[i].cnt){                    printf("and %c\n",shape[i].intersect[j]+'A');                }                else{                    printf("%c, ",shape[i].intersect[j]+'A');                }            }        }        putchar('\n');    }}