cf 1142 C

忽然觉得这个题很有必要写题解。

移项

y-x^2 = bx+c

那么其实就是找有多少条直线上方没有点

所以就是一个上凸壳有多少条直线/点.

绝妙啊！！！！

太妙了啊！！！！

神乎其技卧槽！！！

(我是傻逼)

#include <cstdio>
#include <cmath>
#include <algorithm>
#include <vector>
#include <set>
using namespace std;
typedef long long db;
const double eps=1e-6;
const double pi=acos(-1);
int sign(db k){
    if (k>eps) return 1; else if (k<-eps) return -1; return 0;
}
int cmp(db k1,db k2){return sign(k1-k2);}
struct point{
    db x,y;
    point operator + (const point &k1) const{return (point){k1.x+x,k1.y+y};}
    point operator - (const point &k1) const{return (point){x-k1.x,y-k1.y};}
    point operator * (db k1) const{return (point){x*k1,y*k1};}
    point operator / (db k1) const{return (point){x/k1,y/k1};}
    bool operator == (const point &k1) const{return cmp(x,k1.x)==0&&cmp(y,k1.y)==0;}
    bool operator <(const point &k1)const {
        int c=cmp(x,k1.x);
        if(c)return c==-1;
        return cmp(y,k1.y)==-1;
    }
};
db cross(point k1,point k2){return k1.x*k2.y-k1.y*k2.x;}
db dot(point k1,point k2){return k1.x*k2.x+k1.y*k2.y;}
int n;
vector<point> convexHull(vector<point> ps){
    int n = ps.size();if(n<=1)return ps;
    sort(ps.begin(),ps.end());
    vector<point> qs(n*2);int k=0;
    for(int i=0;i<n;qs[k++]=ps[i++])
        while (k>1&&cross(qs[k-1]-qs[k-2],ps[i]-qs[k-2])<=0)--k;
    for(int i=n-2,t=k;i>=0;qs[k++]=ps[i--])
        while (k>t&&cross(qs[k-1]-qs[k-2],ps[i]-qs[k-2])<=0)--k;
    qs.resize(k-1);
    return qs;
}
void getUDP(vector<point>A,vector<point>&U,vector<point>&D){
    db l=1e7,r=-1e7;
    for (int i=0;i<A.size();i++) l=min(l,A[i].x),r=max(r,A[i].x);
    int wherel,wherer;
    for (int i=0;i<A.size();i++) if (cmp(A[i].x,l)==0) wherel=i;
    for (int i=A.size();i;i--) if (cmp(A[i-1].x,r)==0) wherer=i-1;
    U.clear(); D.clear(); int now=wherel;
    while (1){D.push_back(A[now]); if (now==wherer) break; now++; if (now>=A.size()) now=0;}
    now=wherel;
    while (1){U.push_back(A[now]); if (now==wherer) break; now--; if (now<0) now=A.size()-1;}
}
vector<point>p,u,d;
db x,y;
int main(){
    scanf("%d",&n);
    db mx=0;
    for(int i=1;i<=n;i++){
        scanf("%lld%lld",&x,&y);
        p.push_back(point{x,y-x*x});
        mx+=x;
    }
    p=convexHull(p);
    getUDP(p,u,d);
    set<int>s;
    for(auto p:u)s.insert(p.x);
    printf("%d
",s.size()-1);
}