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<cstdio>#include<cmath>#include<algorithm>using namespace std;#define LL long longconst 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);}