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QOJ
ID | Problem | Submitter | Result | Time | Memory | Language | File size | Submit time | Judge time |
---|---|---|---|---|---|---|---|---|---|
#313753 | #7730. Convex Checker | OMoonStars | WA | 35ms | 13060kb | C++17 | 2.6kb | 2024-01-24 23:01:08 | 2024-07-04 19:17:55 |
Judging History
answer
#include<algorithm>
#include<array>
#include<bitset>
#include<cmath>
#include<cstdio>
#include<cstring>
#include<iomanip>
#include<iostream>
#include<map>
#include<numeric>
#include<queue>
#include<set>
#include<unordered_map>
#define fi first
#define se second
#define pb push_back
#define mp make_pair
#define endl '\n'
using namespace std;
using ll=long long;
using db=double;
using pii=pair<int,int>;
const int inf=0x3f3f3f3f;
const int mod=998244353;
const db eps=1e-8;
const db PI=acos(-1);
const int N=2e5+10,M=1e3+10;
//?????????????,????????
//???????:?????????(n-2)*PI;?????,??????cos,????-1~1,??acos????
bool sgn(db x){
return x>eps?1:(x<-eps?-1:0);
}
inline int cmp(db a,db b){return sgn(a-b);}//a=b??0,a>b??1,a<b??-1
struct point{
db x,y;
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 db a)const{
return {x*a,y*a};
}
bool operator<(point p)const{//?????,??????
int c=cmp(x,p.x);
if(c)return c==-1;
return cmp(y,p.y)==-1;
}
db abs(){return sqrt(abs2());}
db abs2(){return x*x+y*y;}
db distTo(point p){return (*this-p).abs();}
};
double dot(const point &a,const point &b){
return a.x*b.x+a.y*b.y;
}
double det(const point &a,const point &b){
return a.x*b.y-a.y*b.x;
}
bool turn_left(const point &a,const point &b,const point &c){
return sgn(det(b-a,c-a))>0;
}
bool convex_hull(vector<point> a)
{
sort(a.begin(), a.end()); // ? ? ?: less <pair >
vector<point> ret;
for (int i = 0; i < (int)a.size(); i++)
{
while (ret.size() > 1 && !turn_left(ret[ret.size() - 2], ret[ret.size() - 1], a[i]))
return false;
ret.push_back(a[i]);
}
int fixed = (int)ret.size();
for (int i = (int)a.size() - 2; i >= 0; --i)
{
while (ret.size() > fixed && !turn_left(ret[ret.size() - 2], ret[ret.size() - 1], a[i]))
return false;
ret.push_back(a[i]);
}
ret.pop_back();
return true;
}
int main()
{
ios::sync_with_stdio(false);
cin.tie(nullptr);
int n;
cin >> n;
vector<point>p(n);
for(auto &[x,y]:p)
cin >> x >> y;
if(convex_hull(p))
{
db sum=0;
for(int i=0;i<n;i++)
{
point p1=p[i],p2=p[(i+1)%n],p3=p[(i+2)%n];
db cost=dot(p2-p1,p2-p3)/p1.distTo(p2)/p2.distTo(p3);
db theta=acos(cost);
sum+=theta;
}
if(cmp(sum,(n-2)*PI))cout << "No" << endl;
else cout << "Yes" << endl;
}
else cout << "No" << endl;
return 0;
}
Details
Tip: Click on the bar to expand more detailed information
Test #1:
score: 100
Accepted
time: 0ms
memory: 4232kb
input:
3 0 0 1 0 0 1
output:
Yes
result:
ok answer is YES
Test #2:
score: 0
Accepted
time: 0ms
memory: 4160kb
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: 4032kb
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: 4004kb
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: 3744kb
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: 3720kb
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: 4080kb
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: 35ms
memory: 11952kb
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: -100
Wrong Answer
time: 34ms
memory: 13060kb
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:
No
result:
wrong answer expected YES, found NO