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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 |
---|---|---|---|---|---|---|---|---|---|
#352084 | #7730. Convex Checker | _Sheepsheep | WA | 0ms | 3928kb | C++17 | 6.9kb | 2024-03-12 20:32:26 | 2024-03-12 20:32:27 |
Judging History
answer
#include<bits/stdc++.h>
using namespace std ;
#define ll long long
const int inf = 1e8 ;
const int N = 3e6+9 ;
typedef long double LD ;
const LD eps = 1e-7 ;
const LD box = 1e7 ;
int sgn( LD x )
{
return x > eps ? 1 : ( x < -eps ? -1 : 0 ) ;
}
struct point
{
LD x , y , polar_angle;
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 LD &a) const
{
return{ x*a , y*a } ;
}
point operator / (const LD &a) const
{
return{ x/a , y/a } ;
}
friend bool operator == ( const point &a , const point &b )
{
return sgn(a.x-b.x) == 0 && sgn(a.y-b.y) == 0 ;
}
friend ostream & operator << ( ostream &out , point &a )
{
out << "(" << a.x << "," << a.y << ")" ;
return out ;
}
friend istream & operator >> ( istream &in , point &a )
{
in >> a.x >> a.y ;
return in ;
}
int idx , hull_rank ;
};
struct line
{
point s , t ;
friend bool operator == ( const line &a , const line &b )
{
return (a.s==b.s&&a.t==b.t)||(a.s==b.t&&a.t==b.s) ;
}
};
LD sqr( LD x )
{
return x*x ;
}
LD mo( point x )
{
return sqrtl( sqr(x.x) + sqr(x.y) ) ;
}
LD dis( const point &a , const point &b )
{
return sqrtl( sqr(a.x-b.x) + sqr(a.y-b.y) ) ;
}
LD dot( const point &a , const point &b )
{
return a.x*b.x+a.y*b.y;
}
LD det( const point &a , const point &b )
{
// + : b ? a ??????
return a.x*b.y-b.x*a.y ;
}
bool point_on_segment( const point &a , const line &l )
{
if( l.s == l.t )
{
return a == l.s ;
}
return sgn( det(l.s-a,a-l.t) ) == 0 && sgn( dot(l.s-a,l.t-a) ) <= 0 ;
}
bool two_side( const point &a , const point &b , const line &c )
{
// ???????
return sgn( det(a-c.s,c.t-c.s) ) * sgn( det(b-c.s,c.t-c.s) ) < 0 ;
}
bool segment_inter_judge( const line &a , const line &b )
{
bool ok = 0 ;
ok |= point_on_segment( b.s , a ) ;
ok |= point_on_segment( b.t , a ) ;
ok |= point_on_segment( a.s , b ) ;
ok |= point_on_segment( a.t , b ) ;
ok |= ( two_side(a.s,a.t,b)&&two_side(b.s,b.t,a) ) ;
return ok ;
}
bool ray_inter_judge( const line &a , const line &b )
{
//??????????
return sgn( det( a.t-a.s , b.t-b.s ) ) == 0 ? 0 : 1 ;
}
LD point_to_line( const point &p , const line &l )
{
return fabs( det(l.t-l.s,p-l.s) )/dis(l.s,l.t) ;
}
LD point_to_segment( const point &p , const line &l )
{
if( l.s == l.t ) return dis( p , l.s ) ;
if( sgn( dot(l.s-p,l.t-l.s) )*sgn( dot(l.t-p,l.t-l.s) ) <= 0 ) return point_to_line(p,l) ;
else return min( dis(p,l.s) , dis(p,l.t) ) ;
}
LD arg( const line &a , const line &b )
{
LD res = dot( a.t-a.s , b.t-b.s ) ;
res /= mo( a.t-a.s ) ;
res /= mo( b.t-b.s ) ;
return acos( res ) ;
}
point line_intersect( const line &a , const line &b )
{
LD u = det( a.t-a.s,b.s-a.s ) ;
LD v = det( a.t-a.s , b.t-a.s ) ;
return ( b.s*v - b.t*u )/(v-u) ;
}
bool turn_left( const point &a , const point &b , const point &c )
{
// a ???????ac????ab??????????
return sgn( det( b-a , c-a ) ) > 0 ;
}
bool turn_left( const line &a , const line &b , const line &c )
{
// bc?????????a???
return turn_left( a.s , a.t , line_intersect(b,c) ) ;
}
int point_quadrant( const point &a )
{
if( sgn( a.x ) >= 0 && sgn( a.y ) >= 0 ) return 1 ;
else if( sgn(a.x) < 0 && sgn( a.y ) >= 0 ) return 2 ;
else if( sgn(a.x) < 0 && sgn( a.y ) < 0 ) return 3 ;
else return 4 ;
}
vector<point> convex_hull( vector<point> a )
{
vector<point>ret ;
int a_size = a.size() , ret_size = 0 ;
if( a_size <= 2 ) return a ;
sort( a.begin() , a.end() , []( point x , point y ){ return x.x == y.x ? x.y < y.y : x.x < y.x ; } ) ;
for( int i = 0 ; i < a_size ; i ++ )
{
while( ret_size > 1 && !turn_left( ret[ret_size-2] , ret[ret_size-1] , a[i] ) )
{
ret.pop_back() ; ret_size -- ;
}
ret.push_back( a[i] ) ; ret_size ++ ;
}
int fix = ret_size ;
for( int i = a_size-2 ; i >= 0 ; i -- )
{
while( ret_size > fix && !turn_left( ret[ret_size-2] , ret[ret_size-1] , a[i] ) )
{
ret.pop_back() ; ret_size -- ;
}
ret.push_back( a[i] ) ; ret_size ++ ;
}
ret.pop_back() ; ret_size -- ;
return ret ;
}
int half( const point &a ) //???????
{
return a.y > 0 || ( a.y == 0 && a.x > 0 ? 1 : 0 );
}
bool is_para( const line &a , const line &b ) //?????
{
return sgn( det(a.t-a.s,b.t-b.s) ) == 0 ;
}
bool cmp( const line &a , const line &b )
{
// (0,0) is org
int sign = half( a.t-a.s ) - half( b.t-b.s ) ; //????????
int dir = sgn( det(a.t-a.s,b.t-b.s) ) ; //????
if( sign == 0 && dir == 0 ) return sgn( det(a.t-a.s , b.t-a.s) ) < 0 ; //??????
else return sign ? sign > 0 : dir > 0 ;
//???????????
//??????????
}
vector<point> hpi( vector<line> A , LD DX , LD DY )
{
int siz_a = A.size() ;
vector<line>h ;
for( int i = 0 ; i < siz_a ; i ++ ) h.push_back( A[i] ) ;
h.push_back( {{DX,DY} , {0,DY}} ) ;
h.push_back( {{0,DY} , {0,0}} ) ;
h.push_back( {{0,0} , {DX,0}} ) ;
h.push_back( {{DX,0} , {DX,DY}} ) ;
sort( h.begin() , h.end() , cmp ) ;
vector<line> q( h.size()+10 ) ;
int l = 0 , r = -1 ;
for( auto &i : h )
{
while( l<r && !turn_left(i,q[r-1],q[r]) ) --r ;
while( l<r && !turn_left(i,q[l],q[l+1]) ) ++l ;
if( l <= r && is_para(i,q[r]) ) continue ;
q[++r] = i ;
}
while( r-l>1 && !turn_left(q[l],q[r-1],q[r]) ) --r ;
while( r-l>1 && !turn_left(q[r],q[l],q[l+1]) ) ++l ;
if( r-l < 2 ) return {} ;
vector<point> ret(r-l+1) ;
for( int i = l ; i <= r ; i ++ )
ret[i-l] = line_intersect( q[i] , q[i==r?l:i+1] ) ;
return ret ;
}
bool on_box( point a )
{
if( sgn(a.x-box) == 0 || sgn(a.y-box) == 0 ) return 1 ;
return 0;
}
bool is_open( vector<point>ret )
{
if( ret.size() <= 2 )
for( auto &u : ret ) if( on_box(u) ) return 1 ;
return 0 ;
}
void solve()
{
int n ; cin >> n ;
vector<point>a(n) ;
for( int i = 0 ; i < n ; i ++ )
{
cin >> a[i] ;
if( a[i].x == a[0].x )
{
if( a[i].y < a[0].y ) swap( a[i] , a[0] ) ;
}
else if( a[i].x < a[0].x ) swap( a[i] , a[0] ) ;
}
//???(a^b)??b??
sort( a.begin()+1 , a.end() , [&]( point x , point y ){
if( sgn(x.y-a[0].y) != sgn(y.y-a[0].y) ) return x.y < y.y ;
return sgn(det( x-a[0] , y-a[0] )) > 0 ;
} );
bool ok = 1 ;
for( int i = 1 ; i < n ; i ++ )
{
if( !turn_left( a[i-1] , a[i] , a[(i+1)%n] ) ) ok = 0 ;
}
if( ok ) cout << "Yes\n" ;
else cout << "No\n" ;
}
int main()
{
ios::sync_with_stdio(false);cin.tie(0);cout.tie(0);
int tt = 1 ; //cin >> tt ;
while( tt-- ) solve() ;
return 0 ;
}
/*
5 4.321
-2 -1 3 -2
1 6 3 -2
1 6 -2 -1
-3 4 3 3
-2 1 5 4
*/
詳細信息
Test #1:
score: 100
Accepted
time: 0ms
memory: 3816kb
input:
3 0 0 1 0 0 1
output:
Yes
result:
ok answer is YES
Test #2:
score: 0
Accepted
time: 0ms
memory: 3920kb
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: 3760kb
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: 3928kb
input:
3 0 0 0 0 0 0
output:
No
result:
ok answer is NO
Test #5:
score: -100
Wrong Answer
time: 0ms
memory: 3924kb
input:
5 1 0 4 1 0 1 2 0 3 2
output:
Yes
result:
wrong answer expected NO, found YES