QOJ.ac
QOJ
ID | Problem | Submitter | Result | Time | Memory | Language | File size | Submit time | Judge time |
---|---|---|---|---|---|---|---|---|---|
#721418 | #9520. Concave Hull | telgs | AC ✓ | 161ms | 18992kb | C++23 | 13.4kb | 2024-11-07 16:04:42 | 2024-11-07 16:04:44 |
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;
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>;
// 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;
vector<Point> vec1;
Point p;
for(int i=1;i<=n;i++){
cin>>p.x>>p.y;
vec1.push_back(p);
}
sort(vec1.begin(),vec1.end(),argcmp());
// for(auto x:vec1) cout<<x.x<<' '<<x.y<<'\n';
Convex cvx1=convexhull(vec1);
set<Point> q;
for(auto x:cvx1.p){
q.insert(x);
}
vector<Point> vec2;
for(auto x:vec1){
if(q.find(x)==q.end()){
vec2.push_back(x);
}
}
sort(vec2.begin(),vec2.end(),argcmp());
if(vec2.size()==0) return cout<<"-1\n",void();
Convex cvx2=convexhull(vec2);
if(cvx2.p.size()==0) cvx2.p.push_back(vec2[0]);
ll pos1=0,pos2=0;
ll cnt0=0;
ld ans=INF,sum=cvx1.area();
while(!cnt0){
Point p=cvx1.p[pos1],p1=cvx1.p[cvx1.nxt(pos1)];
ld dlt=(p1-p)^(cvx2.p[pos2]-p);
while(((p1-p)^(cvx2.p[cvx2.nxt(pos2)]-p))<dlt){
dlt=(p1-p)^(cvx2.p[cvx2.nxt(pos2)]-p);
pos2=cvx2.nxt(pos2);
}
pos1=cvx1.nxt(pos1);
if(!pos1) cnt0++;
// cout<<dlt<<'\n';
ans=min(ans,dlt);
}
cout<<(ll)(sum-ans)<<'\n';
}
int main(){
IOS;
int t=1;
cin>>t;
while(t--) solve();
return 0;
}
/*
2
6
-2 0
1 -2
5 2
0 4
1 2
3 1
4
0 0
1 0
0 1
1 1
7000000000000000000
6000000002000000000
*/
这程序好像有点Bug,我给组数据试试?
Details
Tip: Click on the bar to expand more detailed information
Test #1:
score: 100
Accepted
time: 0ms
memory: 3936kb
input:
2 6 -2 0 1 -2 5 2 0 4 1 2 3 1 4 0 0 1 0 0 1 1 1
output:
40 -1
result:
ok 2 lines
Test #2:
score: 0
Accepted
time: 1ms
memory: 3820kb
input:
10 243 -494423502 -591557038 -493438474 -648991734 -493289308 -656152126 -491185085 -661710614 -489063449 -666925265 -464265894 -709944049 -447472922 -737242534 -415977509 -773788538 -394263365 -797285016 -382728841 -807396819 -373481975 -814685302 -368242265 -818267002 -344482838 -833805545 -279398...
output:
2178418010787347715 1826413114144932145 1651687576234220014 1883871859778998985 2119126281997959892 894016174881844630 2271191316922158910 1998643358049669416 1740474221286618711 1168195646932543192
result:
ok 10 lines
Test #3:
score: 0
Accepted
time: 56ms
memory: 3876kb
input:
1000 125 64661186 -13143076 302828013 -185438065 -418713797 -191594241 430218126 -397441626 354327250 -836704374 149668812 -598584998 311305970 66790541 199720625 -592356787 468137 -584752683 258775829 96211747 -358669612 -134890109 -129221188 -998432368 -277309896 -140056561 356901185 420557649 -51...
output:
1986320445246155278 1900093336073022078 1612088392301142476 2012259136539173407 1819942017252118749 1772230185841892196 1164835025329039520 1527446155241140517 1807368432185303666 1236918659444944569 1306839249967484778 1984123720246784099 1868728080720036006 667458140583450322 2127932992585026491 4...
result:
ok 1000 lines
Test #4:
score: 0
Accepted
time: 81ms
memory: 3972kb
input:
10000 9 484630042 51929469 -40468396 -517784096 98214104 -103353239 629244333 -475172587 106398764 153884485 49211709 -44865749 1 10 166321833 -247717657 406208245 668933360 13 548702216 -631976459 37150086 -292461024 707804811 -486185860 239775286 -903166050 10096571 -541890068 686103484 558731937 ...
output:
950319193795831919 1661025342421008544 1285164852091455548 1159924751776806668 1206071151805176722 794021230296144371 699991678992587791 1133990718508584290 1486311831172661605 984875884297072200 1327767982175057345 758247019006396699 1355381234262206155 1139262078529131471 1613462877860621700 12392...
result:
ok 10000 lines
Test #5:
score: 0
Accepted
time: 142ms
memory: 5068kb
input:
100 439 471536154 -312612104 155692036 -937312180 -461624056 -357636609 236656684 -911414873 -288656914 -74788431 -465779694 -381475149 -334197401 -903065737 491513067 -447615916 337664889 -852236281 -281689379 -53519178 -159101704 -920779200 -326159514 -95396204 21868593 -994282736 488425383 -41046...
output:
1973162724053130487 2054612790507830954 1726805687754843724 1699420177872986528 2129388571309147631 2198295137903288810 1697185883164440272 1219697450095721478 2027023581922285255 1674691247127206655 1673105966817209954 2179188692918747442 2146544318743443141 2230356305133660648 1676850321902993764 ...
result:
ok 100 lines
Test #6:
score: 0
Accepted
time: 125ms
memory: 4952kb
input:
100 1362 -467257672 -466669 -467054869 -478108 -466973270 -481776 -466556983 -499770 -466329414 -508693 -466248017 -511805 -466158865 -513786 -466101273 -515035 -465927700 -518748 -465717624 -522106 -465303448 -528127 -465124548 -530726 -464649746 -536693 -464554872 -537799 -464478196 -538680 -46416...
output:
1666097696993497 1791366071767866 1806187278469532 1683419854733713 1685891971828916 1730190225081651 1787048201197565 1850308098208660 1710694884375502 1826363113637639 1816375352374659 2047431269497691 1549806516003854 1829438662895747 1678707854135065 1687423392883819 2121960009997761 16687219538...
result:
ok 100 lines
Test #7:
score: 0
Accepted
time: 68ms
memory: 11840kb
input:
2 62666 -486101704 -505730259 -486101698 -506082699 -486101689 -506111362 -486101682 -506126031 -486101528 -506293759 -486101259 -506556385 -486101196 -506613483 -486101154 -506648604 -486100935 -506831392 -486100631 -507083675 -486100470 -507199151 -486100233 -507368923 -486100193 -507397039 -48609...
output:
2178736946152219010 1825181940245096152
result:
ok 2 lines
Test #8:
score: 0
Accepted
time: 157ms
memory: 18992kb
input:
2 100000 301945097 76373292 467957663 -286424714 8245445 -597212507 -474204621 -708828667 184159460 105942538 443435905 -429212625 490658771 -382198656 82512047 -612522436 -228221388 -965890088 394789011 -145801151 -106120174 -528202395 428939626 -194437311 497429477 -527407728 365739746 -114818962 ...
output:
2502889432701099511 2267250485735988121
result:
ok 2 lines
Test #9:
score: 0
Accepted
time: 161ms
memory: 17484kb
input:
2 100000 221128057 -975244780 -618765360 -785575858 422567455 -906331476 -988680318 -150037424 -929870145 367887908 -757813541 -652471177 291995621 -956419655 -785381507 619012026 468864522 -883270094 -588416522 808557973 859345881 511394814 988105866 153775152 216931298 -976186873 467050734 8842305...
output:
6283183114882825575 6283183188903854361
result:
ok 2 lines
Test #10:
score: 0
Accepted
time: 0ms
memory: 3776kb
input:
7 5 -1000000000 -1000000000 1000000000 -1000000000 1000000000 1000000000 1 0 -1 0 5 1000000000 1000000000 -1000000000 -1000000000 -2 0 -1 0 1 -1 6 1000000000 1000000000 -1000000000 -1000000000 -3 0 -1 0 0 -1 1 -1 4 -1000000000 -1000000000 1000000000 -1000000000 1000000000 1000000000 -1000000000 1000...
output:
4000000000000000000 7000000000 9000000001 -1 6000000002000000000 7999999998000000000 -1
result:
ok 7 lines
Extra Test:
score: 0
Extra Test Passed