2019 ICPC Malaysia National H题

Posted 2022-02-05 ccsu-kid

题意：给定n个点，求出这些点构成的凸包，然后逆时针输出，另外还有q次询问，每次询问一个点是否在凸包里。

题解：二维凸包裸题，直接利用叉积判断点是否在凸包内即可，时间复杂度n2，不知为何这题给了15s，然后我代码只跑了15ms

#include <bits/stdc++.h>
using namespace std;
double eps=1e-15;
double pi=acos(-1);
struct Point
    double x,y;
    Point(double x=0,double y=0):x(x),y(y)
;
typedef Point Vector;
Vector operator + (Vector A,Vector B)return Vector(A.x+B.x,A.y+B.y);
Vector operator - (Vector A,Vector B)return Vector(A.x-B.x,A.y-B.y);
Vector operator * (Vector A,double B)return Vector(A.x*B,A.y*B);
Vector operator / (Vector A,double B)return Vector(A.x/B,A.y/B);
int dcmp(double x)
    if(fabs(x)<eps)return 0;
    else return x<0?-1:1;

bool operator < (const Point &a,const Point &b)
    return dcmp(a.x-b.x)<0||(dcmp(a.x-b.x)==0&&dcmp(a.y-b.y)<0);

bool operator == (const Point &a,const Point &b)
    return dcmp(a.x-b.x)==0&&dcmp(a.y-b.y)==0;

double Cross(Vector A,Vector B)
    return A.x*B.y-A.y*B.x;

double Dot(Vector A,Vector B)
    return A.x*B.x+A.y*B.y;

Vector Rotate(Vector A,double rad)
    return Vector(A.x*cos(rad)-A.y*sin(rad),A.x*sin(rad)+A.y*cos(rad));

int tubao(Point *p,int n,Point *ch)//求凸包，返回凸包数组的长度
    sort(p,p+n);
    int m=0;
    for(int i=0;i<n;i++)
        while(m>1&&Cross(ch[m-1]-ch[m-2],p[i]-ch[m-2])<=0)m--;
        ch[m++]=p[i];
    
    int k=m;
    for(int i=n-2;i>=0;i--)
        while(m>k&&Cross(ch[m-1]-ch[m-2],p[i]-ch[m-2])<=0)m--;
        ch[m++]=p[i];
    
    if(n>1)m--;
    return m;

void readp(Point &A)
    scanf("%lf%lf",&A.x,&A.y);

bool onsegment(Point p,Point a1,Point a2)
    if(p==a1||p==a2)return false;
    return dcmp(Cross(a1-p,a2-p))==0&&dcmp(Dot(a1-p,a2-p))<0;

bool segmentcross(Point a1,Point a2,Point b1,Point b2)
    if(a1==b1||a1==b2||a2==b1||a2==b2)return true;
    double c1=Cross(a2-a1,b1-a1),c2=Cross(a2-a1,b2-a1),
           c3=Cross(b2-b1,a1-b1),c4=Cross(b2-b1,a2-b1);
    return dcmp(c1)*dcmp(c2)<0&&dcmp(c3)*dcmp(c4)<0;

int intubao(Point *ch,int n,Point p)//判断p点是否在凸包内
    Vector A,B;
    int flag=0;
    for(int i=0;i<n;i++)
        A=ch[(i+1)%n]-ch[i];
        B=p-ch[i];
        /*if(onsegment(p,ch[i],ch[(i+1)%n]))//这题说了点在凸包上视为在凸包外
            flag=-1;
            break;
        */
        if(Cross(A,B)>0)
            flag++;
        
    
    if(flag==-1||flag==n)return 1;
    return 0;

int T,n,q,m;
Point p1[10005],ch1[10005];
struct node
    double x,y;
g[1005];
int main()
    scanf("%d",&T);
    int kase=0;
    while(T--)
        scanf("%d%d",&n,&q);
        for(int i=0;i<n;i++)
            readp(p1[i]);
        
        int m1=tubao(p1,n,ch1);
        for(int i=1;i<=q;i++)
            scanf("%lf%lf",&g[i].x,&g[i].y);
        
        printf("Case %d\n",++kase);
        for(int i=0;i<m1;i++)
            printf("%d %d\n",(int)ch1[i].x,(int)ch1[i].y);
        
        printf("%d %d\n",(int)ch1[0].x,(int)ch1[0].y);
        for(int i=1;i<=q;i++)
            Point t;
            t.x=g[i].x;
            t.y=g[i].y;
            printf("%d %d ",(int)t.x,(int)t.y);
            if(intubao(ch1,m1,t))printf("is unsafe!\n");
            else printf("is safe!\n");
        
        printf("\n");