Los Valley - P1663 - Mountain - half plane post

https://www.luogu.org/problemnew/show/P1663

Characters given to the mountain, find the lowest point you can see all over the place.

It is a cross half-plane.

Paste family portrait:

#include<bits/stdc++.h>
using namespace std;
typedef long long ll;

//不要输出-0.0之类的数

const double eps=1e-8;
const double inf=1e9;
const double pi=acos(-1.0);     //小数点后15位精度，和atan2相同

//判断浮点数的符号
inline int cmp(double x) {
    return (fabs(x)<eps)?0:((x>0.0)?1:-1);
}

inline double sqr(double x) {
    return x*x;
}

struct Point {
    double x,y;
    Point() {};
    Point(const double x,const double y):x(x),y(y) {};

    friend Point operator+(const Point &a,const Point &b) {
        return Point(a.x+b.x,a.y+b.y);
    }
    friend Point operator-(const Point &a,const Point &b) {
        return Point(a.x-b.x,a.y-b.y);
    }
    friend Point operator*(const Point &p,const double k) {
        return Point(p.x*k,p.y*k);
    }
    friend Point operator*(const double k,const Point &p) {
        return Point(p.x*k,p.y*k);
    }
    friend Point operator/(const Point &p,const double k) {
        return Point(p.x/k,p.y/k);
    }
    inline double angle() {
        //返回向量的倾斜角，[-pi, pi]
        return atan2(y,x);
    }
};

double det(const Point &a,const Point &b) {
    return a.x*b.y-a.y*b.x;
}
double dot(const Point &a,const Point &b) {
    return a.x*b.x+a.y*b.y;
}

//半平面交，O(nlogn)
vector<Point> halfplane_intersection(vector<Halfplane> v) {
    sort(v.begin(),v.end(),compare);
    deque<Halfplane> q;
    deque<Point> ans;
    q.push_back(v[0]);

    int vs=v.size();
    for(int i=1;i<vs;++i){
        if(cmp((v[i].second-v[i].first).angle()-(v[i-1].second-v[i-1].first).angle())==0)
            continue;
        while(!ans.empty()&&!satisfy(ans.back(),v[i])){
            ans.pop_back();
            q.pop_back();
        }
        while(!ans.empty()&&!satisfy(ans.front(),v[i])){
            ans.pop_front();
            q.pop_front();
        }
        ans.push_back(intersect_point(q.back(),v[i]));
        q.push_back(v[i]);
    }
    while(!ans.empty()&&!satisfy(ans.back(),q.front())){
        ans.pop_back();
        q.pop_back();
    }
    while(!ans.empty()&&!satisfy(ans.front(),q.back())){
        ans.pop_front();
        q.pop_front();
    }
    ans.push_back(intersect_point(q.back(),q.front()));
    return vector<Point>(ans.begin(),ans.end());
}

void solve() {
    int n;
    scanf("%d",&n);
    double x[5005],y[5005];
    for(int i=1;i<=n;i++){
        scanf("%lf%lf",&x[i],&y[i]);
    }
    vector<Halfplane> hp;
    hp.push_back(Halfplane(Point(x[1],inf),Point(x[1],y[1])));
    hp.push_back(Halfplane(Point(x[n],y[n]),Point(x[n],inf)));
    hp.push_back(Halfplane(Point(x[n],inf),Point(x[1],inf)));
    for(int i=2;i<=n;i++){
        hp.push_back(Halfplane(Point(x[i-1],y[i-1]),Point(x[i],y[i])));
    }

    /*for(int i=0;i<(int)hp.size();i++){
        printf("Point1 %d: (%.4f, %4f)\n",i+1,hp[i].first.x,hp[i].first.y);
        printf("Point2 %d: (%.4f, %4f)\n",i+1,hp[i].second.x,hp[i].second.y);

        puts("");
    }*/

    double ans=inf;
    vector<Point> hpi=halfplane_intersection(hp);
    int hs=hpi.size();
    for(int i=0;i<hs;i++){
        //printf("Point %d: (%.4f, %4f)\n",i+1,hpi[i].x,hpi[i].y);
        ans=min(ans,hpi[i].y);
    }
    printf("%8f\n",ans);
}

int main() {
#ifdef Yinku
    freopen("Yinku.in","r",stdin);
#endif // Yinku
    solve();
    return 0;
}