UVALive 7281 求凸包 并判断点是否在凸包内

题解

二分判断点在凸包内，把凸包分成以p0为顶点的tot-2个三角形，判断是否有一个三角形把所要判断的点包住

#include<cstdio>
#include<iostream>
#include<cmath>
#include<cstdlib>
#include<cstring>
#include<algorithm>
using namespace std;
int n,m,tot;
struct point
{
    double x,y;
}p[100000],a[100000],b[100000];
bool cmp(point A,point B)
{
    if(A.x!=B.x)
    return A.x<B.x;
    return A.y<B.y;
}
point operator -(point A,point B)
{
    point c;
    c.x=A.x-B.x;
    c.y=A.y-B.y;
    return c;
}
double cross(point A,point B)
{
    return A.x*B.y-B.x*A.y;
}
void dopack()
{
    tot=0;
    for(int i=1;i<=n;i++)
    {
        while(tot>1&&cross(p[tot-1]-p[tot-2],a[i]-p[tot-2])<=0)tot--;
        p[tot++]=a[i];
    }
    int k=tot;
    for(int i=n-1;i>0;i--)
    {
        while(tot>k&&cross(p[tot-1]-p[tot-2],a[i]-p[tot-2])<=0)tot--;
        p[tot++]=a[i];
    }
    if(n>1)tot--;
}
bool check(point A)
{
    int l=1,r=tot-2,mid;
    while(l<=r)
    {
        mid=(l+r)>>1;
        double a1=cross(p[mid]-p[0],A-p[0]);
        double a2=cross(p[mid+1]-p[0],A-p[0]);
        if(a1>=0&&a2<=0)
        {
            if(cross(p[mid+1]-p[mid],A-p[mid])>=0)return true;
            return false;
        }
        else if(a1<0)
        {
            r=mid-1;
        }
        else
        {
            l=mid+1;
        }
    }
    return false;
}
int main()
{
    while(cin>>n)
    {
        for(int i=1;i<=n;i++)
        {
            scanf("%lf%lf",&a[i].x,&a[i].y);
        }
        sort(a+1,a+1+n,cmp);
        dopack();
        scanf("%d",&m);
        int ans=0;
        for(int i=1;i<=m;i++)
        {
            scanf("%lf%lf",&b[i].x,&b[i].y);
            if(check(b[i]))ans++;
        }
        printf("%d\n",ans);
    }
    return 0;
}