QOJ.ac
QOJ
ID | 题目 | 提交者 | 结果 | 用时 | 内存 | 语言 | 文件大小 | 提交时间 | 测评时间 |
---|---|---|---|---|---|---|---|---|---|
#723013 | #9434. Italian Cuisine | telgs | WA | 38ms | 3800kb | C++23 | 18.2kb | 2024-11-07 20:56:00 | 2024-11-07 20:56:07 |
Judging History
answer
// #pragma GCC optimize(2)
#include<iostream>
#include<algorithm>
#include<cstring>
#include<vector>
#include<set>
#include<unordered_map>
#include<queue>
#include<iomanip>
#include<cmath>
#define IOS ios::sync_with_stdio(false),cin.tie(0),cout.tie(0)
using namespace std;
using ll=long long;
using pii=pair<ll,ll>;
using ld=long double;
constexpr ll N=1e6+10,mod=1e8-3;
constexpr ld inf=1e18,eps=1e-5,INF=9e18,PI=3.1514926535;
ll n;
// using point_t=long long;
using point_t=long double;
// 点与向量
template<typename T> struct point{
T x,y;
bool operator==(const point &a) const{
return (abs(x-a.x)<=eps && abs(y-a.y)<=eps);
}
bool operator<(const point &a) const{
if(abs(x-a.x)<=eps) return y<a.y-eps;
return x<a.x-eps;
}
bool operator>(const point &a) const{
return !(*this<a||*this==a);
}
point operator+(const point &a) const{
return {x+a.x,y+a.y};
}
point operator-(const point &a) const{
return {x-a.x,y-a.y};
}
point operator-() const{
return {-x,-y};}
point operator*(const T k) const{
return {k*x,k*y};
}
point operator/(const T k) const{
return {x/k,y/k};
}
// 点积
T operator*(const point &a) const{return x*a.x+y*a.y;
}
// 叉积,注意优先级
T operator^(const point &a) const{
return x*a.y-y*a.x;
}
// to-left 测试
int toleft(const point &a) const{
const auto t=(*this)^a;
return (t>eps)-(t<-eps);
}
// 向量长度的平方
T len2() const{
return (*this)*(*this);
}
// 两点距离的平方
T dis2(const point &a) const{
return (a-(*this)).len2();
}
// 涉及浮点数
// 向量长度
long double len() const{
return sqrtl(len2());
}
// 两点距离
long double dis(const point &a) const{
return sqrtl(dis2(a));
}
// 向量夹角
long double ang(const point &a) const{
return acosl(max(-1.0l,min(1.0l,((*this)*a)/(len()*a.len()))));
}
// 逆时针旋转(给定角度)
point rot(const long double rad) const{
return {x*cos(rad)-y*sin(rad),x*sin(rad)+y*cos(rad)};
}
// 逆时针旋转(给定角度的正弦与余弦)
point rot(const long double cosr,const long double sinr) const{
return {x*cosr-y*sinr,x*sinr+y*cosr};
}
};
using Point=point<point_t>;
// 极角排序
struct argcmp{
bool operator()(const Point &a,const Point &b) const{
const auto quad=[](const Point &a){
if (a.y<-eps) return 1;
if (a.y>eps) return 4;if (a.x<-eps) return 5;
if (a.x>eps) return 3;
return 2;
};
const int qa=quad(a),qb=quad(b);
if (qa!=qb) return qa<qb;
const auto t=a^b;
// if (abs(t)<=eps) return a*a<b*b-eps;
// 不同长度的向量需要分开
return t>eps;
}
};
// 直线
template<typename T> struct line{
point<T> p,v;
// p 为直线上一点,v 为方向向量
bool operator==(const line &a) const{
return v.toleft(a.v)==0&&v.toleft(p-a.p)==0;
}
// to-left 测试
int toleft(const point<T> &a) const{
return v.toleft(a-p);
}
// 半平面交算法定义的排序
bool operator<(const line &a) const{
if (abs(v^a.v)<=eps&&v*a.v>=-eps) return toleft(a.p)==-1;
return argcmp()(v,a.v);
}
// 涉及浮点数
// 直线交点
point<T> inter(const line &a) const{
return p+v*((a.v^(p-a.p))/(v^a.v));
}
// 点到直线距离
long double dis(const point<T> &a) const{
return abs(v^(a-p))/v.len();
}
// 点在直线上的投影
point<T> proj(const point<T> &a) const{
return p+v*((v*(a-p))/(v*v));
}
};
using Line=line<point_t>;
//线段
template<typename T> struct segment{
point<T> a,b;
bool operator<(const segment &s) const{
return make_pair(a,b)<make_pair(s.a,s.b);
}
// 判定性函数建议在整数域使用// 判断点是否在线段上
// -1 点在线段端点 | 0 点不在线段上 | 1 点严格在线段上
int is_on(const point<T> &p) const{
if (p==a||p==b) return -1;
return (p-a).toleft(p-b)==0&&(p-a)*(p-b)<-eps;
}
// 判断线段直线是否相交
// -1 直线经过线段端点 | 0 线段和直线不相交 | 1 线段和直线严格相交
int is_inter(const line<T> &l) const{
if (l.toleft(a)==0||l.toleft(b)==0) return -1;
return l.toleft(a)!=l.toleft(b);
}
// 判断两线段是否相交
// -1 在某一线段端点处相交 | 0 两线段不相交 | 1 两线段严格相交
int is_inter(const segment<T> &s)const{
if (is_on(s.a)||is_on(s.b)||s.is_on(a)||s.is_on(b)) return -1;
const line<T> l={a,b-a},ls={s.a,s.b-s.a};
return l.toleft(s.a)*l.toleft(s.b)==-1&&ls.toleft(a)*ls.toleft(b)==-1;
}
// 点到线段距离
long double dis(const point<T> &p) const{
if((p-a)*(b-a)<-eps||(p-b)*(a-b)<-eps) return min(p.dis(a),p.dis(b));
const line<T> l={a,b-a};
return l.dis(p);
}
// 两线段间距离
long double dis(const segment<T> &s) const{
if(is_inter(s)) return 0;
return min({dis(s.a),dis(s.b),s.dis(a),s.dis(b)});
}
};
using Segment=segment<point_t>;
// 圆
struct Circle{
Point c;
long double r;
bool operator==(const Circle &a) const{
return c==a.c && abs(r-a.r)<=eps;
}
// 周长
long double circ() const{
return 2*PI*r;
}
// 面积
long double area() const{
return PI*r*r;
}
// 点与圆的关系
// -1 圆上 | 0 圆外 | 1 圆内
int is_in(const Point &p) const{
const long double d=p.dis(c);
return abs(d-r)<=eps?-1:d<r-eps;
}
// 直线与圆关系
// 0 相离 | 1 相切 | 2 相交
int relation(const Line &l) const{
const long double d=l.dis(c);
if(d>r+eps) return 0;
if(abs(d-r)<=eps) return 1;
return 2;
}
// 圆与圆关系
// -1 相同 | 0 相离 | 1 外切 | 2 相交 | 3 内切 | 4 内含
int relation(const Circle &a) const{
if(*this==a) return -1;
const long double d=c.dis(a.c);
if(d>r+a.r+eps) return 0;
if(abs(d-r-a.r)<=eps) return 1;
if(abs(d-abs(r-a.r))<=eps) return 3;
if(d<abs(r-a.r)-eps) return 4;
return 2;
}
// 直线与圆的交点
vector<Point> inter(const Line &l) const{
const long double d=l.dis(c);
const Point p=l.proj(c);
const int t=relation(l);
if (t==0) return vector<Point>();
if (t==1) return vector<Point>{p};
const long double k=sqrt(r*r-d*d);
return vector<Point>{p-(l.v/l.v.len())*k,p+(l.v/l.v.len())*k};
}
// 圆与圆交点
vector<Point> inter(const Circle &a) const{
const long double d=c.dis(a.c);
const int t=relation(a);
if (t==-1||t==0||t==4) return vector<Point>();
Point e=a.c-c; e=e/e.len()*r;
if (t==1||t==3){
if(r*r+d*d-a.r*a.r>=-eps) return vector<Point>{c+e};
return vector<Point>{c-e};
}
const long double costh=(r*r+d*d-a.r*a.r)/(2*r*d),sinth=sqrt(1-
costh*costh);
return vector<Point>{c+e.rot(costh,-sinth),c+e.rot(costh,sinth)};
}
// 圆与圆交面积
long double inter_area(const Circle &a) const{
const long double d=c.dis(a.c);
const int t=relation(a);
if(t==-1) return area();
if(t<2) return 0;
if(t>2) return min(area(),a.area());
const long double costh1=(r*r+d*d-a.r*a.r)/(2*r*d),costh2=(a.r*a.r+d*d-
r*r)/(2*a.r*d);
const long double sinth1=sqrt(1-costh1*costh1),sinth2=sqrt(1-
costh2*costh2);
const long double th1=acos(costh1),th2=acos(costh2);
return r*r*(th1-costh1*sinth1)+a.r*a.r*(th2-costh2*sinth2);
}
// 过圆外一点圆的切线
vector<Line> tangent(const Point &a) const{
const int t=is_in(a);
if(t==1) return vector<Line>();
if(t==-1){
const Point v={-(a-c).y,(a-c).x};
return vector<Line>{{a,v}};
}
Point e=a-c; e=e/e.len()*r;
const long double costh=r/c.dis(a),sinth=sqrt(1-costh*costh);const Point t1=c+e.rot(costh,-sinth),t2=c+e.rot(costh,sinth);
return vector<Line>{{a,t1-a},{a,t2-a}};
}
// 两圆的公切线
vector<Line> tangent(const Circle &a) const{
const int t=relation(a);
vector<Line> lines;
if(t==-1||t==4) return lines;
if(t==1||t==3){
const Point p=inter(a)[0],v={-(a.c-c).y,(a.c-c).x};
lines.push_back({p,v});
}
const long double d=c.dis(a.c);
const Point e=(a.c-c)/(a.c-c).len();
if (t<=2){
const long double costh=(r-a.r)/d,sinth=sqrt(1-costh*costh);
const Point d1=e.rot(costh,-sinth),d2=e.rot(costh,sinth);
const Point u1=c+d1*r,u2=c+d2*r,v1=a.c+d1*a.r,v2=a.c+d2*a.r;
lines.push_back({u1,v1-u1}); lines.push_back({u2,v2-u2});
}
if (t==0){
const long double costh=(r+a.r)/d,sinth=sqrt(1-costh*costh);
const Point d1=e.rot(costh,-sinth),d2=e.rot(costh,sinth);
const Point u1=c+d1*r,u2=c+d2*r,v1=a.c-d1*a.r,v2=a.c-d2*a.r;
lines.push_back({u1,v1-u1}); lines.push_back({u2,v2-u2});
}
return lines;
}
// 圆的反演
tuple<int,Circle,Line> inverse(const Line &l) const{
const Circle null_c={{0.0,0.0},0.0};
const Line null_l={{0.0,0.0},{0.0,0.0}};
if (l.toleft(c)==0) return {2,null_c,l};
const Point v=l.toleft(c)==1?Point{l.v.y,-l.v.x}:Point{-l.v.y,l.v.x};
const long double d=r*r/l.dis(c);
const Point p=c+v/v.len()*d;
return {1,{(c+p)/2,d/2},null_l};
}
tuple<int,Circle,Line> inverse(const Circle &a) const{
const Circle null_c={{0.0,0.0},0.0};
const Line null_l={{0.0,0.0},{0.0,0.0}};
const Point v=a.c-c;
if (a.is_in(c)==-1){
const long double d=r*r/(a.r+a.r);
const Point p=c+v/v.len()*d;
return {2,null_c,{p,{-v.y,v.x}}};
}
if (c==a.c) return {1,{c,r*r/a.r},null_l};
const long double d1=r*r/(c.dis(a.c)-a.r),d2=r*r/(c.dis(a.c)+a.r);
const Point p=c+v/v.len()*d1,q=c+v/v.len()*d2;
return {1,{(p+q)/2,p.dis(q)/2},null_l};
}
};
// 多边形
template<typename T> struct polygon{
vector<point<T>> p;
// 以逆时针顺序存储
size_t nxt(const size_t i) const{
return i==p.size()-1?0:i+1;
}
size_t pre(const size_t i) const{
return i==0?p.size()-1:i-1;
}
// 回转数
// 返回值第一项表示点是否在多边形边上
// 对于狭义多边形,回转数为 0 表示点在多边形外,否则点在多边形内
pair<bool,int> winding(const point<T> &a) const{
int cnt=0;
for(size_t i=0;i<p.size();i++){
const point<T> u=p[i],v=p[nxt(i)];
if(abs((a-u)^(a-v))<=eps && (a-u)*(a-v)<=eps) return {true,0};
if(abs(u.y-v.y)<=eps) continue;
const Line uv={u,v-u};
if(u.y<v.y-eps&&uv.toleft(a)<=0) continue;if(u.y>v.y+eps&&uv.toleft(a)>=0) continue;
if(u.y<a.y-eps&&v.y>=a.y-eps) cnt++;
if(u.y>=a.y-eps&&v.y<a.y-eps) cnt--;
}
return {false,cnt};
}
// 多边形面积的两倍
// 可用于判断点的存储顺序是顺时针或逆时针
T area() const{
T sum=0;
for(size_t i=0;i<p.size();i++) sum+=p[i]^p[nxt(i)];
return sum;
}
// 多边形的周长
long double circ() const{
long double sum=0;
for(size_t i=0;i<p.size();i++) sum+=p[i].dis(p[nxt(i)]);
return sum;
}
};
using Polygon=polygon<point_t>;
//凸多边形
template<typename T> struct convex:polygon<T>{
// 闵可夫斯基和
convex operator+(const convex &c) const{
const auto &p=this->p;
vector<Segment> e1(p.size()),e2(c.p.size()),edge(p.size()+c.p.size());
vector<point<T>> res;
res.reserve(p.size()+c.p.size());
const auto cmp=[](const Segment &u,const Segment &v){
return argcmp()(u.b-u.a,v.b-v.a);
};
for(size_t i=0;i<p.size();i++) e1[i]={p[i],p[this->nxt(i)]};
for(size_t i=0;i<c.p.size();i++) e2[i]={c.p[i],c.p[c.nxt(i)]};
rotate(e1.begin(),min_element(e1.begin(),e1.end(),cmp),e1.end());
rotate(e2.begin(),min_element(e2.begin(),e2.end(),cmp),e2.end());
merge(e1.begin(),e1.end(),e2.begin(),e2.end(),edge.begin(),cmp);
const auto check=[](const vector<point<T>> &res,const point<T> &u){
const auto back1=res.back(),back2=*prev(res.end(),2);
return (back1-back2).toleft(u-back1)==0 && (back1-back2)*(u-back1)>=-eps;
};
auto u=e1[0].a+e2[0].a;
for(const auto &v:edge){
while(res.size()>1&&check(res,u)) res.pop_back();
res.push_back(u);
u=u+v.b-v.a;
}
if(res.size()>1&&check(res,res[0])) res.pop_back();
return {res};
}
// 旋转卡壳// 例:凸多边形的直径的平方
T rotcaliper() const{
const auto &p=this->p;
if(p.size()==1) return 0;
if(p.size()==2) return p[0].dis2(p[1]);
const auto area=[](const point<T> &u,const point<T> &v,const point<T> &w)
{return (w-u)^(w-v);};
T ans=0;
for(size_t i=0,j=1;i<p.size();i++){
const auto nxti=this->nxt(i);
ans=max({ans,p[j].dis2(p[i]),p[j].dis2(p[nxti])});
while (area(p[this->nxt(j)],p[i],p[nxti])>=area(p[j],p[i],p[nxti])){
j=this->nxt(j);
ans=max({ans,p[j].dis2(p[i]),p[j].dis2(p[nxti])});
}
}
return ans;
}
// 判断点是否在凸多边形内
// 复杂度 O(logn)
// -1 点在多边形边上 | 0 点在多边形外 | 1 点在多边形内
int is_in(const point<T> &a) const{
const auto &p=this->p;
if(p.size()==1) return a==p[0]?-1:0;
if(p.size()==2) return segment<T>{p[0],p[1]}.is_on(a)?-1:0;
if(a==p[0]) return -1;
if((p[1]-p[0]).toleft(a-p[0])==-1 || (p.back()-p[0]).toleft(a-p[0])==1)
return 0;
const auto cmp=[&](const point<T> &u,const point<T> &v){
return (u-p[0]).toleft(v-p[0])==1;
};
const size_t i=lower_bound(p.begin()+1,p.end(),a,cmp)-p.begin();
if(i==1) return segment<T>{p[0],p[i]}.is_on(a)?-1:0;
if(i==p.size()-1&&segment<T>{p[0],p[i]}.is_on(a)) return -1;
if(segment<T>{p[i-1],p[i]}.is_on(a)) return -1;
return (p[i]-p[i-1]).toleft(a-p[i-1])>0;
}
// 凸多边形关于某一方向的极点
// 复杂度 O(logn)
// 参考资料:https://codeforces.com/blog/entry/48868
template<typename F> size_t extreme(const F &dir) const{
const auto &p=this->p;
const auto check=[&](const size_t i){
return dir(p[i]).toleft(p[this->nxt(i)]-p[i])>=0;
};
const auto dir0=dir(p[0]);
const auto check0=check(0);
if(!check0&&check(p.size()-1)) return 0;
const auto cmp=[&](const point<T> &v){
const size_t vi=&v-p.data();
if (vi==0) return 1;
const auto checkv=check(vi);
const auto t=dir0.toleft(v-p[0]);
if (vi==1 && checkv==check0 && t==0) return 1;
return checkv^(checkv==check0&&t<=0);
};
return partition_point(p.begin(),p.end(),cmp)-p.begin();
}
// 过凸多边形外一点求凸多边形的切线,返回切点下标
// 复杂度 O(logn)
// 必须保证点在多边形外
pair<size_t,size_t> tangent(const point<T> &a) const{
const size_t i=extreme([&](const point<T> &u){return u-a;});
const size_t j=extreme([&](const point<T> &u){return a-u;});
return {i,j};
}
// 求平行于给定直线的凸多边形的切线,返回切点下标
// 复杂度 O(logn)
pair<size_t,size_t> tangent(const line<T> &a) const{
const size_t i=extreme([&](...){return a.v;});
const size_t j=extreme([&](...){return -a.v;});
return {i,j};
}
};
using Convex=convex<point_t>;
// 点集的凸包
// Andrew 算法,复杂度 O(nlogn)
Convex convexhull(vector<Point> p){
vector<Point> st;
if (p.empty()) return Convex{st};sort(p.begin(),p.end());
const auto check=[](const vector<Point> &st,const Point &u){
const auto back1=st.back(),back2=*prev(st.end(),2);
return (back1-back2).toleft(u-back1)<=0;
};
for (const Point &u:p){
while (st.size()>1 && check(st,u)) st.pop_back();
st.push_back(u);
}
size_t k=st.size();
p.pop_back();
reverse(p.begin(),p.end());
for (const Point &u:p){
while (st.size()>k && check(st,u)) st.pop_back();
st.push_back(u);
}
st.pop_back();
return Convex{st};
}
void solve(){
cin>>n;
Point p;
ld r;
cin>>p.x>>p.y>>r;
Circle cir={p,r};
vector<Point> vec(n*2+10);
for(int i=1;i<=n;i++){
cin>>vec[i].x>>vec[i].y;
vec[i+n]=vec[i];
}
queue<Point> q;
Point last;
ld res=0,ans=0;
for(int i=1;i<=2*n;i++){
while(q.size()<2) q.push(vec[i]),last=vec[i++];
while(!q.empty()&&cir.relation({q.front(),vec[i]-q.front()})){
auto t1=q.front();
q.pop();
auto t2=q.front();
res-=((last-t2)^(t1-t2));
}
if(q.size()>=2){
res+=((q.front()-vec[i])^(last-vec[i]));
}
q.push(vec[i]);
last=vec[i];
ans=max(ans,res);
}
cout<<ans<<'\n';
}
int main(){
IOS;
int t=1;
cin>>t;
while(t--) solve();
return 0;
}
/*
3
5
1 1 1
0 0
1 0
5 0
3 3
0 5
6
2 4 1
2 0
4 0
6 3
4 6
2 6
0 3
4
3 3 1
3 0
6 3
3 6
0 3
5
24
0
*/
详细
Test #1:
score: 100
Accepted
time: 0ms
memory: 3736kb
input:
3 5 1 1 1 0 0 1 0 5 0 3 3 0 5 6 2 4 1 2 0 4 0 6 3 4 6 2 6 0 3 4 3 3 1 3 0 6 3 3 6 0 3
output:
5 24 0
result:
ok 3 number(s): "5 24 0"
Test #2:
score: 0
Accepted
time: 0ms
memory: 3736kb
input:
1 6 0 0 499999993 197878055 -535013568 696616963 -535013568 696616963 40162440 696616963 499999993 -499999993 499999993 -499999993 -535013568
output:
0
result:
ok 1 number(s): "0"
Test #3:
score: -100
Wrong Answer
time: 38ms
memory: 3800kb
input:
6666 19 -142 -128 26 -172 -74 -188 -86 -199 -157 -200 -172 -199 -186 -195 -200 -175 -197 -161 -188 -144 -177 -127 -162 -107 -144 -90 -126 -87 -116 -86 -104 -89 -97 -108 -86 -125 -80 -142 -74 -162 -72 16 -161 -161 17 -165 -190 -157 -196 -154 -197 -144 -200 -132 -200 -128 -191 -120 -172 -123 -163 -138...
output:
5093 2862 2539 668 3535 7421 4883 10757 13089 1034 4974 3920 4372 2044 4996 5070 2251 4382 4175 1489 1154 3231 12364 1631 5086 25218 1692 6066 2381 1512 4849 5456 2757 14238 8557 18465 1877 11759 17426 12398 11813 4480 2303 2728 1739 2187 3385 4266 12406 909 4334 1518 948 13832 1449 2376 3180 4810 1...
result:
wrong answer 2nd numbers differ - expected: '3086', found: '2862'