计算几何 半平面交

  1 #include<iostream>
  2 #include<cstring>
  3 #include<cstdio>
  4 #include<string>
  5 #include<algorithm>
  6 #include<queue>
  7 #include<cmath>
  8 #include<vector>
  9 
 10 using namespace std;
 11 
 12 #define mnx 50050
 13 #define LL long long
 14 #define mod 1000000007
 15 #define inf 0x3f3f3f3f
 16 #define eps 1e-8
 17 #define Pi acos(-1.0);
 18 #define lson l, m, rt << 1
 19 #define rson m+1, r, rt << 1 | 1
 20 
 21 int dcmp( double x ){
 22     if( fabs( x ) < eps ) return 0;
 23     return x < 0 ? -1 : 1;
 24 }
 25 struct point{
 26     double x, y;
 27     point( double x = 0, double y = 0 ) : x(x), y(y) {}
 28     point operator + ( const point &b ) const{
 29         return point( x + b.x, y + b.y );
 30     }
 31     point operator - ( const point &b ) const{
 32         return point( x - b.x, y - b.y );
 33     }
 34     point operator * ( const double &k ) const{
 35         return point( x * k, y * k );
 36     }
 37     point operator / ( const double &k ) const{
 38         return point( x / k, y / k );
 39     }
 40     bool operator < ( const point &b ) const{
 41         return dcmp( x - b.x ) < 0 || dcmp( x - b.x ) == 0 && dcmp( y - b.y ) < 0;
 42     }
 43     bool operator == ( const point &b ) const{
 44         return dcmp( x - b.x ) == 0 && dcmp( y - b.y ) == 0;
 45     }
 46     double len(){
 47         return sqrt( x * x + y * y );
 48     }
 49 };
 50 typedef point Vector;
 51 struct line{
 52     point p; 
 53     Vector v;
 54     double ang;
 55     line() {}
 56     line( point p, point v ) : p(p), v(v) {
 57         ang = atan2( v.y, v.x );
 58     }
 59     bool operator < ( const line &b ) const{
 60         return ang < b.ang;
 61     }
 62 };
 63 double dot( Vector a, Vector b ){
 64     return a.x * b.x + a.y * b.y;
 65 }
 66 double cross( Vector a, Vector b ){
 67     return a.x * b.y - a.y * b.x;
 68 }
 69 bool onleft( line l, point p ){
 70     return cross( l.v, p - l.p ) > 0;
 71 }
 72 point getintersection( line a, line b ){
 73     Vector u = a.p - b.p;
 74     double t = cross( b.v, u ) / cross( a.v, b.v );
 75     return a.p + a.v * t;
 76 }
 77 point pp[mnx];
 78 line q[mnx];
 79 int halfplaneintersection( line *L, int n, point *poly ){
 80     //sort( L, L + n );
 81     int first, last;
 82     q[first = last = 0] = L[0];
 83     for( int i = 1; i < n; i++ ){
 84         while( first < last && !onleft( L[i], pp[last-1] ) ) last--;
 85         while( first < last && !onleft( L[i], pp[first] ) ) first++;
 86         q[++last] = L[i];
 87         if( fabs( cross( q[last].v, q[last-1].v ) ) < eps ){
 88             last--;
 89             if( onleft( q[last], L[i].p ) ) q[last] = L[i];
 90         }
 91         if( first < last ) pp[last-1] = getintersection( q[last-1], q[last] );
 92     }
 93     while( first < last && !onleft( q[first], pp[last-1] ) ) last--;
 94     if( last - first <= 1 ) return 0;
 95     pp[last] = getintersection( q[last], q[first] );
 96     int m = 0;
 97     for( int i = first; i <= last; i++ ){
 98         poly[m++] = pp[i];
 99     }
100     return m;
101 }
102 point p[mnx], poly[mnx];
103 line l[mnx];
104 bool check( int n, int m ){
105     if( n - m <= 2 ) return 1;
106     for( int i = 0; i < n; i++ ){
107         l[i] = line( p[i], p[i] - p[(i+m+1)%n] );
108     }
109     int all = halfplaneintersection( l, n, poly );
110     if( !all ) return 1;
111     else return 0;
112 }
113 int main(){
114     int n, cas;
115     scanf( "%d", &cas );
116     while( cas-- ){
117         scanf( "%d", &n );
118         for( int i = 0; i < n; i++ ){
119             scanf( "%lf %lf", &p[i].x, &p[i].y );
120         }
121         if( n > 50000 ) continue;
122         int l = 0, r = n, ans;
123         while( l < r ){
124             int m = ( l + r ) >> 1;
125             if( check( n, m ) == 1 ){
126                 ans = m, r = m;
127             }
128             else l = m + 1;
129         }
130         printf( "%d\n", ans );
131     }
132     return 0;
133 }