[模板]计算几何

Posted 2020-08-26 Aireen Ye

凸包

#include<set> 
#include<cmath>
#include<ctime>
#include<queue>
#include<stack>
#include<cstdio>
#include<vector>
#include<cstring>
#include<cstdlib>
#include<iostream>
#include<algorithm>
#define N 100001
#define eps 1e-11
using namespace std;
struct point{
    int x,y;double t;
}a[N],v[N];
int n,u,vn;
inline double sqr(int k){
    return (double)(k*k);
}
inline point dec(point x,point y){
    return (point){x.x-y.x,x.y-y.y,0.0};
}
inline int mult(point x,point y){
    return x.x*y.y-y.x*x.y;
}
inline double dis(point x,point y){
    return sqrt(sqr(abs(x.x-y.x))+sqr(abs(x.y-y.y)));
}
inline bool cmp(point x,point y){
    if(fabs(x.t-y.t)<eps)
        return dis(x,a[1])>dis(y,a[1]); 
    return x.t<y.t;
} 
inline void convex(){
    u=1;
    for(int i=2;i<=n;i++)
        if((a[i].x<a[u].x)||(a[i].x==a[u].x&&a[i].y<a[u].y)) u=i;
    a[0]=a[u];a[u]=a[1];a[1]=a[0];
    for(int i=2;i<=n;i++)
        a[i].t=atan2(a[i].y-a[1].y,a[i].x-a[1].x);
    sort(a+2,a+1+n,cmp);
    v[++vn]=a[1];v[++vn]=a[2];a[++n]=a[1];
    for(int i=3;i<=n;i++){
        if(fabs(a[i].t-a[i-1].t)<eps)
            continue;
        while(vn>1&&mult(dec(a[i],v[vn-1]),dec(v[vn],v[vn-1]))>0) vn--;
        v[++vn]=a[i];
    }
}
inline void init(){
    scanf("%d",&n);
    for(int i=1;i<=n;i++)
        scanf("%d%d",&a[i].x,&a[i].y);
    convex();
}
int main(){
    freopen("convex.in","r",stdin);
    freopen("convex.out","w",stdout);
    init();
    fclose(stdin);
    fclose(stdout);
    return 0;
}

旋转卡壳

#include<set> 
#include<cmath>
#include<ctime>
#include<queue>
#include<stack>
#include<cstdio>
#include<vector>
#include<cstring>
#include<cstdlib>
#include<iostream>
#include<algorithm>
#define N 1000001
using namespace std;
struct point{
    int x,y;
}a[N];
int n;
inline point dec(point x,point y){
    return (point){x.x-y.x,x.y-y.y};
}
inline int mult(point x,point y){
    return x.x*y.y-x.y*y.x;
}
inline double sqr(int k){
    return (double)(k*k);
}
inline double dis(point x){
    return sqrt(sqr(x.x)+sqr(x.y));
}
inline int Next(int k){
    if(++k>n) return 1;
    return k;
}
inline double rorate(){
    double di,dia=0.0;
    if(n==1) return dia;
    for(int i=1,j=2;i<=n;i++){
        while(mult(dec(a[Next(i)],a[i]),dec(a[j],a[i]))<mult(dec(a[Next(i)],a[i]),dec(a[Next(j)],a[i])))
            j=Next(j);
        di=dis(dec(a[i],a[j]));
        if(di>dia) dia=di;
        di=dis(dec(a[Next(i)],a[Next(j)]));
        if(di>dia) dia=di;
    }
    return dia;
}
inline void init(){
    scanf("%d",&n);
    for(int i=1;i<=n;i++)
        scanf("%d%d",&a[i].x,&a[i].y);
    printf("%lf\n",rorate());
}
int main(){
    freopen("rorate.in","r",stdin);
    freopen("rorate.out","w",stdout);
    init();
    fclose(stdin);
    fclose(stdout);
    return 0;
}