Codeforces Gym 101234H Split Game

按极角扫描，显然只有经过端点的时候数量才会改变。大力讨论一下，注意区分“转到这个点就改变”和“转过这个点才改变”两种情况。

#include
#include
#include
using namespace std;
#define LL long long
const int maxn=200010,eps=1e-8;
struct Vector
{
    LL x,y;
    void rd()
    {
        scanf("%I64d%I64d",&x,&y);
    }
    Vector operator + (const Vector &v) const
    {
        return (Vector){x+v.x,y+v.y};
    }
    Vector operator - (const Vector &v) const
    {
        return (Vector){x-v.x,y-v.y};
    }
}a[maxn];
LL cross(Vector v,Vector u)
{
    return v.x*u.y-v.y*u.x;
}
int f[maxn],del[maxn],n,ans,now;
int comp(int x,int y)
{
    return cross(a[x],a[y])>0;
}
int main()
{
    //freopen("a.in","r",stdin);
    int tem,nn=0;
    scanf("%d",&n);
    for (int i=1;i<=n;i++) a[i].rd();
    a[0]=a[n];
    a[n+1]=a[1];
    for (int i=1;i<=n;i++)
        if (!cross(a[i]-a[i-1],a[i+1]-a[i-1])) del[i]=1;
    for (int i=1;i<=n;i++)
        if (!del[i]) a[++nn]=a[i];
    n=nn;
    a[0]=a[n];
    a[n+1]=a[1];
    for (int i=1;i<=n;i++) f[i]=i;
    sort(f+1,f+n+1,comp);
    for (int i=1,j;i<=n;i=j)
    {
        tem=0;
        for (j=i;j<=n&&!cross(a[f[i]],a[f[j]]);j++)
        {
            if (cross(a[f[j]],a[f[j]-1])>=0&&cross(a[f[j]],a[f[j]+1])>0)
            {
                if (cross(a[f[j]-1]-a[f[j]],a[f[j]+1]-a[f[j]])>0) now++;
                else tem++;
            }
            if (cross(a[f[j]],a[f[j]-1])<0&&cross(a[f[j]],a[f[j]+1])<=0)
            {
                if (cross(a[f[j]-1]-a[f[j]],a[f[j]+1]-a[f[j]])<0) now--;
                else tem--;
            }
        }
        ans=max(ans,now);
        now+=tem;
        ans=max(ans,now);
    }
    printf("%d\n",ans+1);
}