poj3449（判断直线相交）

题目链接：https://vjudge.net/problem/POJ-3449

题意：给出若干几何体，判断每个几何体与其它几何体的相交情况，并依次输出。

思路：

首先要知道的是根据正方形对角线的两个点怎么求其它两个点，比如已知(x0,y0),(x2,y2)，那么：

x1+x3=x0+x2,

x1-x3=y2-y0,

y1+y3=y0+y2,

y1-y3=x0-x2

之后就暴力枚举了，枚举所有几何体的所有边，用线段相交判断几何体相交。这题的输入输出很恶心。

AC代码：

#include<cstdio>
#include<algorithm>
#include<cstdlib>
#include<cmath>
#include<vector>
#include<cstring>
using namespace std;

const double eps=1e-8;
int sgn(double x){
    if(abs(x)<eps) return 0;
    else if(x<0) return -1;
    else return 1;
}

struct Point{
    double x,y;
    Point(){}
    Point(double xx,double yy){
        x=xx,y=yy;
    }
    Point operator + (const Point& b)const{
        return Point(x+b.x,y+b.y);
    }
    Point operator - (const Point& b)const{
        return Point(x-b.x,y-b.y);
    }
    double operator ^ (const Point& b)const{
        return x*b.y-y*b.x;
    }
};

struct Line{
    Point s,e;
    Line(){}
    Line(Point ss,Point ee){
        s=ss,e=ee;
    }
};

bool inter(Line l1,Line l2){
    return
        max(l1.s.x,l1.e.x)>=min(l2.s.x,l2.e.x)&&
        max(l2.s.x,l2.e.x)>=min(l1.s.x,l1.e.x)&&
        max(l1.s.y,l1.e.y)>=min(l2.s.y,l2.e.y)&&
        max(l2.s.y,l2.e.y)>=min(l1.s.y,l1.e.y)&&
        sgn((l2.s-l1.e)^(l1.s-l1.e))*sgn((l2.e-l1.e)^(l1.s-l1.e))<=0&&
        sgn((l1.s-l2.e)^(l2.s-l2.e))*sgn((l1.e-l2.e)^(l2.s-l2.e))<=0;
}

struct node{
    char id;
    int num;
    Point pt[25];
}sp[30];

bool cmp(node a,node b){
    return a.id<b.id;
}

bool check(node a,node b){
    for(int i=0;i<a.num;++i)
        for(int j=0;j<b.num;++j)
            if(inter(Line(a.pt[i],a.pt[(i+1)%a.num]),Line(b.pt[j],b.pt[(j+1)%b.num])))
                return true;
    return false;
}

vector<char> vc;
int n;
char str[30];

int main(){
    while(scanf("%s",str),str[0]!='.'){
        sp[0].id=str[0];
        scanf("%s",str);
        if(strcmp(str,"square")==0){
            sp[0].num=4;
            scanf(" (%lf,%lf)",&sp[0].pt[0].x,&sp[0].pt[0].y);
            scanf(" (%lf,%lf)",&sp[0].pt[2].x,&sp[0].pt[2].y);
            sp[0].pt[1].x=(sp[0].pt[0].x+sp[0].pt[2].x+(sp[0].pt[2].y-sp[0].pt[0].y))/2;
            sp[0].pt[3].x=(sp[0].pt[0].x+sp[0].pt[2].x-(sp[0].pt[2].y-sp[0].pt[0].y))/2;
            sp[0].pt[1].y=(sp[0].pt[0].y+sp[0].pt[2].y+(sp[0].pt[0].x-sp[0].pt[2].x))/2;
            sp[0].pt[3].y=(sp[0].pt[0].y+sp[0].pt[2].y-(sp[0].pt[0].x-sp[0].pt[2].x))/2;
        }
        else if(strcmp(str,"rectangle")==0){
            sp[0].num=4;
            scanf(" (%lf,%lf)",&sp[0].pt[0].x,&sp[0].pt[0].y);
            scanf(" (%lf,%lf)",&sp[0].pt[1].x,&sp[0].pt[1].y);
            scanf(" (%lf,%lf)",&sp[0].pt[2].x,&sp[0].pt[2].y);
            sp[0].pt[3].x=sp[0].pt[2].x+(sp[0].pt[0].x-sp[0].pt[1].x);
            sp[0].pt[3].y=sp[0].pt[2].y+(sp[0].pt[0].y-sp[0].pt[1].y);
        }
        else if(strcmp(str,"line")==0){
            sp[0].num=2;
            scanf(" (%lf,%lf)",&sp[0].pt[0].x,&sp[0].pt[0].y);
            scanf(" (%lf,%lf)",&sp[0].pt[1].x,&sp[0].pt[1].y);
        }
        else if(strcmp(str,"triangle")==0){
            sp[0].num=3;
            scanf(" (%lf,%lf)",&sp[0].pt[0].x,&sp[0].pt[0].y);
            scanf(" (%lf,%lf)",&sp[0].pt[1].x,&sp[0].pt[1].y);
            scanf(" (%lf,%lf)",&sp[0].pt[2].x,&sp[0].pt[2].y);
        }
        else{
            scanf("%d",&sp[0].num);
            for(int i=0;i<sp[0].num;++i)
                scanf(" (%lf,%lf)",&sp[0].pt[i].x,&sp[0].pt[i].y);
        }
        n=1;
        while(scanf("%s",str),str[0]!='-'){
            sp[n].id=str[0];
            scanf("%s",str);
            if(strcmp(str,"square")==0){
                sp[n].num=4;
                scanf(" (%lf,%lf)",&sp[n].pt[0].x,&sp[n].pt[0].y);
                scanf(" (%lf,%lf)",&sp[n].pt[2].x,&sp[n].pt[2].y);
                sp[n].pt[1].x=(sp[n].pt[0].x+sp[n].pt[2].x+(sp[n].pt[2].y-sp[n].pt[0].y))/2;
                sp[n].pt[3].x=(sp[n].pt[0].x+sp[n].pt[2].x-(sp[n].pt[2].y-sp[n].pt[0].y))/2;
                sp[n].pt[1].y=(sp[n].pt[0].y+sp[n].pt[2].y+(sp[n].pt[0].x-sp[n].pt[2].x))/2;
                sp[n].pt[3].y=(sp[n].pt[0].y+sp[n].pt[2].y-(sp[n].pt[0].x-sp[n].pt[2].x))/2;
            }
            else if(strcmp(str,"rectangle")==0){
                sp[n].num=4;
                scanf(" (%lf,%lf)",&sp[n].pt[0].x,&sp[n].pt[0].y);
                scanf(" (%lf,%lf)",&sp[n].pt[1].x,&sp[n].pt[1].y);
                scanf(" (%lf,%lf)",&sp[n].pt[2].x,&sp[n].pt[2].y);
                sp[n].pt[3].x=sp[n].pt[2].x+(sp[n].pt[0].x-sp[n].pt[1].x);
                sp[n].pt[3].y=sp[n].pt[2].y+(sp[n].pt[0].y-sp[n].pt[1].y);
            }
            else if(strcmp(str,"line")==0){
                sp[n].num=2;
                scanf(" (%lf,%lf)",&sp[n].pt[0].x,&sp[n].pt[0].y);
                scanf(" (%lf,%lf)",&sp[n].pt[1].x,&sp[n].pt[1].y);
            }
            else if(strcmp(str,"triangle")==0){
                sp[n].num=3;
                scanf(" (%lf,%lf)",&sp[n].pt[0].x,&sp[n].pt[0].y);
                scanf(" (%lf,%lf)",&sp[n].pt[1].x,&sp[n].pt[1].y);
                scanf(" (%lf,%lf)",&sp[n].pt[2].x,&sp[n].pt[2].y);
            }
            else{
                scanf("%d",&sp[n].num);
                for(int i=0;i<sp[n].num;++i)
                    scanf(" (%lf,%lf)",&sp[n].pt[i].x,&sp[n].pt[i].y);
            }
            ++n;
        }
        sort(sp,sp+n,cmp);
        for(int i=0;i<n;++i){
            printf("%c ",sp[i].id);
            vc.clear();
            for(int j=0;j<n;++j)
                if(j!=i)
                    if(check(sp[i],sp[j]))
                        vc.push_back(sp[j].id);
            if(vc.size()==0){
                printf("has no intersections\n");
            }
            else if(vc.size()==1){
                printf("intersects with %c\n",vc[0]);
            }
            else if(vc.size()==2){
                printf("intersects with %c and %c\n",vc[0],vc[1]);
            }
            else{
                printf("intersects with ");
                for(int j=0;j<vc.size()-1;++j)
                    printf("%c, ",vc[j]);
                printf("and %c\n",vc[vc.size()-1]);
            }
        }
        printf("\n");
    }
    return 0;
}