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ID | Problem | Submitter | Result | Time | Memory | Language | File size | Submit time | Judge time |
---|---|---|---|---|---|---|---|---|---|
#242046 | #7730. Convex Checker | invaded | WA | 29ms | 11568kb | C++17 | 13.1kb | 2023-11-06 21:31:42 | 2023-11-07 10:32:55 |
Judging History
你现在查看的是最新测评结果
- [2024-07-04 19:27:17]
- hack成功,自动添加数据
- (/hack/727)
- [2024-07-04 19:17:30]
- hack成功,自动添加数据
- (/hack/726)
- [2023-12-08 14:40:48]
- hack成功,自动添加数据
- (//qoj.ac/hack/493)
- [2023-11-07 10:32:52]
- hack成功,自动添加数据
- (//qoj.ac/hack/426)
- [2023-11-07 10:28:41]
- hack成功,自动添加数据
- (//qoj.ac/hack/425)
- [2023-11-06 21:31:42]
- 提交
answer
#include<bits/stdc++.h>
#ifndef xxx
#define dbg(...) ;
#endif
using namespace std;
template<class T> ostream &operator<<(ostream &o, const vector <T> &v) { bool f=false; for(T i:v) { f?o<<' ':o; o<<(i); f=true; } return o; }
template<class T> void sort(T &v) { std::sort(v.begin(), v.end()); }
template<class T, class C> void sort(T &v, C c) { std::sort(v.begin(), v.end(), c); }
template<class T> void reverse(T &v) { std::reverse(v.begin(), v.end()); }
template<class T> bool is_sorted(T &v) { return std::is_sorted(v.begin(), v.end()); }
template<class T> inline void _min(T &x, const T &y) { x>y?x=y:x; }
template<class T> inline void _max(T &x, const T &y) { x<y?x=y:x; }
istream &operator>>(istream &i, __int128_t &x) { x=0; short f=1; char c=0; while(!isdigit(c)) { if(c=='-')f=-1; c=i.get(); } while(isdigit(c))x=x*10+c-'0', c=i.get(); x*=f; return i; }
ostream &operator<<(ostream &o, __int128_t x) { if(x==0) { o<<0; return o; } bool f=false; string s; if(x<0)f=true, x=-x; while(x)s+=x%10+'0', x/=10; reverse(s); if(f)o<<'-'; o<<s; return o; }
mt19937 mt(time(0));
//typedef double db;
typedef long long ll;
typedef unsigned long long ull;
typedef pair<int, int> pii;
typedef pair<ll, ll> pll;
constexpr int maxn=2e5+5;
constexpr int mod=1e9+7;
constexpr int inf=0x3f3f3f3f;
constexpr ll INF=0x3f3f3f3f3f3f3f3fll;
constexpr double pi=acos(-1.0);
constexpr double eps=1e-9;
namespace geometry
{
//db toRadian(const db a) { return pi*a/180; }
/**
* a==b sgn(a-b)==0
* a!=b sgn(a-b)!=0
* a<b sgn(a-b)<0
* a<=b sgn(a-b)<=0
* a>b sgn(a-b)>0
* a>=b sgn(a-b)>=0
*/
int sgn(double x)
{
if(abs(x)<eps)return 0;
return x<0?-1:1;
}
using gtype=ll;
template <class T>
struct Point_t
{
using db=T;
using Point=Point_t;
db x, y;
Point_t() :x(0), y(0) {}
Point_t(db x, db y) :x(x), y(y) {}
// y<P.y x<P.x
bool operator<(const Point &P)const { return y==P.y?x<P.x:y<P.y; }
bool operator==(const Point &P)const { return x==P.x&&y==P.y; }
bool operator!=(const Point &P)const { return x!=P.x||y!=P.y; }
bool operator>(const Point &P)const { return operator!=(P)&&!operator<(P); }
/**
*@param rad radian rad<0: anticlockwise, rad>0: clockwise
*@note rotate first, translate second
*/
Point rotateOrigin(const db rad) { return Point(x*cos(rad)+y*sin(rad), y*cos(rad)-x*sin(rad)); }
/**
*@param rad radian rad<0: anticlockwise, rad>0: clockwise
*@param P Rotate around point P
*@note rotate first, translate second
*/
Point rotate(const Point &P, const db rad) { return Point((x-P.x)*cos(rad)+(y-P.y)*sin(rad)+P.x, (y-P.y)*cos(rad)-(x-P.x)*sin(rad)+P.y); }
/**
*@return new Point
*@note rotate first, translate second
*/
Point translateOrigin(const db dx, const db dy) { return Point(x-dx, y-dy); }
db dis2(const Point &p)const { return (x-p.x)*(x-p.x)+(y-p.y)*(y-p.y); }
db dis(const Point &p)const { return sqrt(dis2(p)); }
friend istream &operator>>(istream &i, Point &P) { i>>P.x>>P.y; return i; }
friend ostream &operator<<(ostream &o, const Point &p) { o<<"("<<p.x<<", "<<p.y<<")"; return o; }
};
typedef Point_t<gtype> Point;
template<class T>
struct Vect_t
{
using db=T;
using Vect=Vect_t;
db x, y;
Vect_t() {}
Vect_t(const Point &p) :x(p.x), y(p.y) {}
Vect_t(db x, db y) :x(x), y(y) {}
Vect_t(const Point &st, const Point &ed) :x(ed.x-st.x), y(ed.y-st.y) {}
Vect operator+(const Vect &V)const { return Vect(x+V.x, y+V.y); }
Vect operator-(const Vect &V)const { return Vect(x-V.x, y-V.y); }
Vect operator*(db k)const { return Vect(x*k, y*k); }
Vect operator/(db k)const { return Vect(x/k, y/k); }
friend Vect operator*(const db &k, const Vect &V) { return V.operator*(k); }
friend Vect operator/(const db &k, const Vect &V) { return V.operator/(k); }
db dot(const Vect &V)const { return x*V.x+y*V.y; }
db cross(const Vect &V)const { return x*V.y-y*V.x; }
/**
* @brief to-left test
* @return res: V is on the left of *this if res>0;
* V is parallel with *this if res=0;
* V is on the right of *this if res<0
*/
int toLeft(const Vect &V)const { db t=cross(V); return (t>0)-(t<0); }
/**
* @brief angle of rotation
* @param V rotate from *this to V
* @return `r`(in radians): By rotating *this `r` radians, we can obtain the vector V
*/
db getRotationAngle(const Vect &V) { return acos(dot(V)/(V.len()*len()))*(toLeft(V)>0?-1:1); }
bool is_parallel(const Vect &V)const { return cross(V)==0; }
bool is_vertical(const Vect &V)const { return dot(V)==0; }
db len2()const { return x*x+y*y; }
db len()const { return sqrt(len2()); }
/**
* normal().dot(*this)=0
* @return normal vector
*/
Vect normal()
{
db length=len();
if(length==0)return Vect(0, 0);
return Vect(-y/length, x/length);
}
/**
*@param rad radian rad<0: anticlockwise, rad>0: clockwise
*@note use it when the origin rorates
*/
Point rotateOrigin(const db &rad) { return Point(x*cos(rad)+y*sin(rad), y*cos(rad)-x*sin(rad)); }
friend ostream &operator<<(ostream &o, const Vect &V) { o<<"("<<V.x<<", "<<V.y<<")"; return o; }
};
typedef Vect_t<gtype> Vect;
Vect operator-(const Point &a, const Point &b) { return Vect(a.x-b.x, a.y-b.y); }
template<class T>
struct Segment_t
{
using db=T;
using Segment=Segment_t;
Point st, ed;
Segment_t() {}
Segment_t(const Point &st, const Point &ed) :st(st), ed(ed) {}
bool is_on(const Point &P)const { return Vect(st, P).cross(Vect(ed, P))==0&&Vect(st, P).dot(Vect(ed, P))<=0; }
db dis(const Point &P)const
{
if((P-st).dot(ed-st)<0)return (P-st).len();
if((P-ed).dot(st-ed)<0)return (P-ed).len();
return abs((st-P).cross(ed-P)/len());
}
db len2()const { db x=ed.x-st.x, y=ed.y-st.y; return x*x+y*y; }
db len()const { return sqrt(len2()); }
Point mid()const { return Point((st.x+ed.x)/2, (st.y+ed.y)/2); }
friend ostream &operator<<(ostream &o, const Segment &s) { o<<"[ "<<s.st<<' '<<s.ed<<" ]"; return o; }
};
typedef Segment_t<gtype> Segment;
//v: st.y<ed.y or (st.y=ed.y and st.x<ed.x)
template<class T>
struct Line_t
{
using db=T;
using Line=Line_t;
Point p;
// @note v.y>0 or (v.y=0 and v.x>0)
Vect v;
Line_t() {}
Line_t(const Point &p, const Vect &v) :p(p), v(v) {}
Line_t(Point p1, Point p2)
{
// to ensure that p1.y<p2.y or (p1.y=p2.y and p1.x<p2.x)
if(p1.y>p2.y)swap(p1, p2);
if(p1.y==p2.y&&p1.x>p2.x)swap(p1, p2);
p=p1;
v=p2-p1;
}
Line_t(const Segment &S)
{
auto p1=S.st;
auto p2=S.ed;
// to ensure that p1.y<p2.y or (p1.y=p2.y and p1.x<p2.x)
if(p1.y>p2.y)swap(p1, p2);
if(p1.y==p2.y&&p1.x>p2.x)swap(p1, p2);
p=p1;
v=p2-p1;
}
//int toLeft(const Vect &V)const { return v.toLeft(V); }
int toLeft(const Point &P)const { return v.toLeft(Vect(p, P)); }
bool is_parallel(const Line &L)const { return v.y*L.v.x==v.x*L.v.y; }
bool is_vertical(const Line &L)const { return v.is_vertical(L.v); }
bool is_intersect(const Segment &S)const
{
return v.toLeft(p-S.st)*v.toLeft(p-S.ed)<=0;
}
bool is_on(const Segment &S)const { return !toLeft(S.st)&&!toLeft(S.ed); }
bool is_on(const Point &A)const { return !toLeft(A); }
pair<bool, Point>get_intersect(const Line &L)const
{
if(is_parallel(L))return make_pair(false, Point());
Vect OQ=Vect(p)+(v*(L.v.cross(Vect(L.p, p))))/(v.cross(L.v));
return make_pair(true, Point(OQ.x, OQ.y));
}
pair<bool, Point>get_intersect(const Segment &S)const
{
if(!is_intersect(S))return make_pair(false, Point());
return get_intersect(Line(S));
}
db dis(const Point &P) const { return abs(v.cross(Vect(P, p)))/v.len(); }
Point project(const Point &A) const
{
Vect Q=Vect(p)+v*((v.dot(A-p))/v.len2());
return Point(Q.x, Q.y);
}
friend ostream &operator<<(ostream &o, const Line &L) { o<<"[ p="<<L.p<<" v="<<L.v<<" ]"; return o; }
};
typedef Line_t<gtype> Line;
/**
* @note store points in anticlockwise order
*/
struct Polygon :vector<Point>
{
using db=gtype;
Polygon() {}
Polygon(int n) :vector<Point>(n) {}
Polygon(const vector<Point> &vec) :vector<Point>(vec) {}
Polygon(const initializer_list<Point> &l) :vector<Point>(l) {}
int nex(const int index)const { return index+1==size()?0:index+1; }
int pre(const int index)const { return index==0?size()-1:index-1; }
Point nextPoint(const int index)const { return at(nex(index)); }
Point prevPoint(const int index)const { return at(pre(index)); }
/**
* @return pair<int,int> [flag, winding number]
* @note flag=1: in, flag=0: on, flag=-1: out
*/
pii is_in(const Point &P)const
{
int cnt=0;
for(int i=0; i<size(); i++)
{
const Point &st=at(i);
const Point &ed=at(nex(i));
if(Segment(st, ed).is_on(P))return make_pair(0, 0);
if(st.y==ed.y)continue;
auto k=(ed-st).cross(P-st);
auto d1=st.y-P.y;
auto d2=ed.y-P.y;
if(k>0&&d1<=0&&d2>0)++cnt;
if(k<0&&d2<=0&&d1>0)--cnt;
}
return make_pair(cnt?1:-1, cnt);
}
/**
* @brief whether P is in *this(*this is a convex)
*
* @param P
* @return true - P is in or on *this; false - P is out
*/
bool isInConvex(const Point &P)const
{
for(int i=0; i<size(); i++)
{
Vect vec(at(i), at(nex(i)));
if(vec.toLeft(P-at(i))<0)
{
return false;
}
}
return true;
}
bool is_convex()const
{
auto xmul=[&](const Point &p1, const Point &p2, const Point &p0)->db
{
return (p1.x-p0.x)*(p2.y-p0.y)-(p2.x-p0.x)*(p1.y-p0.y);
};
auto sgn=[&](const db &x)->int
{
if(x>0)return 1;
return x<0?2:0;
};
vector<bool>s(3, true);
for(int i=0; i<size()&&(s[1]|s[2]); i++)
{
int u=i;
int v=nex(u);
int w=nex(v);
s[sgn(xmul(at(v), at(w), at(u)))]=false;
}
return s[0]&&s[1]|s[2]; //不允许共线
// 允许共线
return s[1]|s[2];
}
db area()const
{
db ans=0;
for(int i=0; i<size(); i++)
ans+=Vect(at(i)).cross(Vect(at(nex(i))));
return abs(ans/2);
}
db perimeter()const
{
db ans=0;
for(int i=0; i<size(); i++)
ans+=at(i).dis(nextPoint(i));
return ans;
}
};
struct Convex :Polygon
{
using db=gtype;
Convex() :Polygon() {}
Convex(int n) :Polygon(n) {}
Convex(const vector<Point> &vec) :Polygon(vec) {}
Convex(const initializer_list<Point> &l) :Polygon(l) {}
/**
* @brief check whether Point is in *this convex in O(logn)
*
* @param a the Point
* @return int 1:in 0:on -1:out
*/
int is_in(const Point &a) const
{
const auto &p=*this;
if(p.size()==1) return a==p[0]?0:-1;
if(p.size()==2) return Segment{p[0], p[1]}.is_on(a)?0:-1;
if(a==p[0]) return 0;
if((p[1]-p[0]).toLeft(a-p[0])==-1||(p.back()-p[0]).toLeft(a-p[0])==1) return -1;
const auto cmp=[&](const Point &u, const Point &v)->bool
{
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{p[0], p[i]}.is_on(a)?0:-1;
if(i==p.size()-1&&Segment{p[0], p[i]}.is_on(a)) return 0;
if(Segment{p[i-1], p[i]}.is_on(a)) return 0;
return (p[i]-p[i-1]).toLeft(a-p[i-1])>0?1:-1;
}
/**
* @brief Andrew O(nlogn)
*
* @param p
* @return Convex Hull
*/
static 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);
}
};
/**
* @brief sort Points by arg (i.e. atan) in anticlockwise
* @note 1: y<0
* @note 2: (x=0, y=0)
* @note 3: (x>0, y=0)
* @note 4: y>0
* @note 5: (x<0, y=0)
* @note Points with the same arg can be ordered arbitrarily
*/
struct argcmp
{
bool operator()(const Point &a, const Point &b)const
{
auto quad=[&](const Point &p)->int
{
if(p.y<0)return 1;
if(p.y>0)return 4;
if(p.x>0)return 3;
if(p.x<0)return 5;
return 2;
};
int qa=quad(a), qb=quad(b);
if(qa!=qb)return qa<qb;
auto t=Vect(a).cross(b);
return t>0;
}
};
}
using namespace geometry;
int main()//MARK: main
{
#ifndef xxx
ios::sync_with_stdio(false), cin.tie(nullptr), cout.tie(nullptr);
#endif
cout<<fixed<<setprecision(10);
int n;
cin>>n;
Polygon poly(n);
for(auto &p:poly)
{
cin>>p;
}
auto checkSame=[&]()->bool
{
map<Point, bool>mp;
for(auto p:poly)
{
if(mp.count(p))
{
return true;
}
mp[p]=true;
}
return false;
};
Convex conv=Convex::convexHull(poly);
cout<<(poly.is_convex()&&poly.area()==conv.area()?"Yes":"No")<<'\n';
return 0;
}
Details
Tip: Click on the bar to expand more detailed information
Test #1:
score: 100
Accepted
time: 0ms
memory: 3880kb
input:
3 0 0 1 0 0 1
output:
Yes
result:
ok answer is YES
Test #2:
score: 0
Accepted
time: 0ms
memory: 3664kb
input:
4 0 0 0 1 1 1 1 0
output:
Yes
result:
ok answer is YES
Test #3:
score: 0
Accepted
time: 0ms
memory: 3688kb
input:
4 0 0 0 3 1 2 1 1
output:
Yes
result:
ok answer is YES
Test #4:
score: 0
Accepted
time: 0ms
memory: 3912kb
input:
3 0 0 0 0 0 0
output:
No
result:
ok answer is NO
Test #5:
score: 0
Accepted
time: 0ms
memory: 3616kb
input:
5 1 0 4 1 0 1 2 0 3 2
output:
No
result:
ok answer is NO
Test #6:
score: 0
Accepted
time: 0ms
memory: 3880kb
input:
5 0 0 1000000000 0 1000000000 500000000 1000000000 1000000000 0 1000000000
output:
No
result:
ok answer is NO
Test #7:
score: 0
Accepted
time: 0ms
memory: 3684kb
input:
5 0 0 1000000000 0 1000000000 499999999 1000000000 1000000000 0 1000000000
output:
No
result:
ok answer is NO
Test #8:
score: 0
Accepted
time: 0ms
memory: 3684kb
input:
5 0 0 999999999 0 1000000000 50000000 999999999 1000000000 0 1000000000
output:
Yes
result:
ok answer is YES
Test #9:
score: 0
Accepted
time: 29ms
memory: 11432kb
input:
128312 5578014 410408218 5585076 410404717 5588011 410403262 5588473 410403033 5589740 410402405 5593295 410400643 5593751 410400417 5597248 410398684 5598935 410397848 5600618 410397014 5605185 410394751 5610514 410392111 5614281 410390245 5617263 410388768 5621142 410386847 5630840 410382045 56310...
output:
Yes
result:
ok answer is YES
Test #10:
score: 0
Accepted
time: 29ms
memory: 11488kb
input:
128086 149550602 509469827 149551059 509465022 149551336 509462107 149551964 509455497 149552572 509449094 149553350 509440895 149553656 509437667 149554161 509432339 149554254 509431357 149554545 509428284 149555017 509423299 149555366 509419611 149555842 509414580 149556382 509408867 149556564 509...
output:
Yes
result:
ok answer is YES
Test #11:
score: 0
Accepted
time: 29ms
memory: 11368kb
input:
128369 146452483 526399214 146453715 526394712 146454820 526390674 146456370 526385008 146457099 526382343 146457964 526379180 146458751 526376302 146460091 526371401 146460722 526369093 146461114 526367659 146462323 526363236 146463053 526360565 146464791 526354204 146465863 526350280 146467488 526...
output:
Yes
result:
ok answer is YES
Test #12:
score: 0
Accepted
time: 28ms
memory: 11568kb
input:
128629 -49533670 490353833 -49532992 490346840 -49532611 490342912 -49531898 490335566 -49531313 490329543 -49531185 490328226 -49530713 490323370 -49530074 490316799 -49529672 490312668 -49528947 490305222 -49528647 490302143 -49528203 490297587 -49527568 490291076 -49527548 490290871 -49527039 490...
output:
Yes
result:
ok answer is YES
Test #13:
score: 0
Accepted
time: 28ms
memory: 11488kb
input:
128259 75790065 403382855 75793744 403383837 75801054 403385789 75805360 403386939 75810275 403388252 75813681 403389162 75820264 403390921 75830809 403393740 75832118 403394090 75837226 403395456 75840000 403396198 75844837 403397492 75849584 403398762 75852835 403399632 75860658 403401726 75865562...
output:
Yes
result:
ok answer is YES
Test #14:
score: 0
Accepted
time: 29ms
memory: 11408kb
input:
128166 46176199 599926866 46170746 599926657 46165737 599926465 46159641 599926231 46152002 599925937 46147638 599925769 46143595 599925613 46138544 599925418 46131124 599925131 46125834 599924926 46120627 599924724 46118799 599924653 46115505 599924525 46110055 599924313 46109413 599924288 46107744...
output:
No
result:
ok answer is NO
Test #15:
score: 0
Accepted
time: 23ms
memory: 11484kb
input:
128507 149999857 500169091 149999867 500163069 149999868 500162459 149999880 500154866 149999887 500150300 149999898 500142815 149999902 500139971 149999913 500131887 149999918 500128019 149999923 500124046 149999926 500121605 149999929 500119099 149999933 500115702 149999941 500108613 149999946 500...
output:
No
result:
ok answer is NO
Test #16:
score: 0
Accepted
time: 21ms
memory: 11528kb
input:
128133 140873382 458262385 140873715 458263110 140876530 458269240 140878601 458273750 140879764 458276283 140880913 458278786 140884549 458286707 140886668 458291324 140890730 458300177 140893254 458305679 140895530 458310641 140897744 458315468 140900237 458320905 140902076 458324916 140904176 458...
output:
No
result:
ok answer is NO
Test #17:
score: 0
Accepted
time: 28ms
memory: 11540kb
input:
128319 18407912 594878554 18403065 594876940 18399018 594875592 18391672 594873145 18389499 594872421 18386714 594871493 18383857 594870541 18370816 594866194 18363997 594863920 18356279 594861346 18349086 594858946 18343059 594856935 18338283 594855341 18334712 594854149 18329890 594852539 18326410...
output:
No
result:
ok answer is NO
Test #18:
score: 0
Accepted
time: 27ms
memory: 11540kb
input:
128502 10448094 591845777 10450502 591846814 10453758 591848216 10459200 591850559 10461337 591851479 10463544 591852429 10473696 591856798 10479318 591859217 10480608 591859772 10483502 591861017 10487533 591862751 10490644 591864089 10494176 591865608 10495627 591866232 10505163 591870332 10509490...
output:
No
result:
ok answer is NO
Extra Test:
score: -3
Extra Test Failed : Wrong Answer on 6
time: 0ms
memory: 3820kb
input:
8 0 0 1 0 1 1 0 1 -1 -1 2 -1 2 2 -1 2
output:
Yes
result:
wrong answer expected NO, found YES