Codeforces-961D

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题意

给出一些点，判断这些点能否都在小于等于两条直线上

思路

首先找出三个不在一条直线上的点，可以得到三条直线。
依次枚举每条直线可解。

代码

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#include <cstdio>
#include "stack"
#include "list"
#include <cstring>
#include <algorithm>
#include "iostream"
#include <cmath>
#include <vector>
#include "set"
#include "queue"
using namespace std;
#define FOP freopen("input.txt","r",stdin)
#define R index*2+1
#define Met(x,y) memset(x,y,sizeof x)
#define L index*2
typedef long long ll;
const ll MAXN =3e5+100;
const ll INF = 1e18;
const ll MOD = 1e9+7;

struct Point{
    ll x,y;
    bool exist;
    void read()
    {
        scanf("%lld%lld",&x,&y);
    }
    Point(double x_=0,double y_=0)
    {
        x=x_,y=y_;
    }
    Point operator -(const Point& rhs)
    {
        return Point(x-rhs.x,y-rhs.y);
    }
};
struct Line{
    ll A,B,C;
    Line(Point a,Point b)
    {
        A=b.y-a.y;
        B=a.x-b.x;
        C=b.x*a.y-a.x*b.y;
    }
    Line(){}
};
Point p[MAXN];
bool PointOnLine(Point a,Line b)
{
    return b.A*a.x+b.B*a.y+b.C==0;
}
int main(int argc, char const *argv[]) {
    // freopen("input.txt","r",stdin);
    ll n;
    cin>>n;
    for(int i=0;i<n;++i)
        p[i].read();
    if(n<=4)
    {
        puts("YES");
        return 0;
    }
    Line l[2];
    ll pp[3];
    pp[0]=0; pp[1]=1;
    Line tem(p[0],p[1]);
    bool flag=1;
    for(int i=2;i<n;++i)
        if (!PointOnLine(p[i],tem)) {
            pp[2]=i;
            flag=0;
        }
    if (flag) {
        puts("YES");
        return 0;
    }
    for(int i=0;i<3;++i)
    {
        l[0]=Line(p[pp[i]],p[pp[(i+1)%3]]);
        bool yes=1,al=0;
        for(int j=0;j<n;++j)
            if (al) {
                if(!PointOnLine(p[j],l[0]) && !PointOnLine(p[j],l[1]))
                {
                    yes=0;
                    break;
                }
            } else {
                if(i==2 && j==1)
                    i=i;
                if(PointOnLine(p[j],l[0]) || j==pp[(i+2)%3]) continue;
                al=1;
                l[1]=Line(p[j],p[pp[(i+2)%3]]);
            }
        if (yes) {
            puts("YES");
            return 0;
        }
    }
    puts("NO");
    return 0;
}