UVa 11437 - Triangle Fun
我是求出来所有点的坐标用叉积算的面积……
据说可以证明出来S△PQR = S△ABC/7
1 #include <cstdio> 2 #include <cmath> 3 4 struct Point 5 { 6 double x, y; 7 Point( double x = 0, double y = 0 ):x(x), y(y) { } 8 }; 9 10 Point operator+( Point A, Point B ) 11 { 12 return Point( A.x + B.x, A.y + B.y ); 13 } 14 15 Point operator-( Point A, Point B ) 16 { 17 return Point( A.x - B.x, A.y - B.y ); 18 } 19 20 Point operator*( Point A, double p ) 21 { 22 return Point( A.x * p, A.y * p ); 23 } 24 25 Point operator/( Point A, double p ) 26 { 27 return Point( A.x / p, A.y / p ); 28 } 29 30 bool operator<( const Point& A, const Point& B ) 31 { 32 return A.x < B.x || ( A.x == B.x && A.y < B.y ); 33 } 34 35 Point Rotate( Point A, double rad ) 36 { 37 return Point( A.x * cos(rad) - A.y * sin(rad), A.x * sin(rad) + A.y * cos(rad) ); 38 } 39 40 double Cross( Point A, Point B ) 41 { 42 return A.x * B.y - A.y * B.x; 43 } 44 45 Point GetLineIntersection( Point P, Point v, Point Q, Point w ) 46 { 47 Point u = P - Q; 48 double t = Cross( w, u ) / Cross( v, w ); 49 return P + v * t; 50 } 51 52 double Dot( Point A, Point B ) 53 { 54 return A.x * B.x + A.y * B.y; 55 } 56 57 double Length( Point A ) 58 { 59 return sqrt( Dot( A, A ) ); 60 } 61 62 double Angle( Point A, Point B ) 63 { 64 return acos( Dot(A, B) / Length(A) / Length(B) ); 65 } 66 67 Point read_Point() 68 { 69 double x, y; 70 scanf( "%lf%lf", &x, &y ); 71 return Point( x, y ); 72 } 73 74 Point GetD( Point B, Point C ) 75 { 76 return ( C - B ) / 3.0 + B; 77 } 78 79 int main() 80 { 81 Point A, B, C, D, E, F; 82 Point P, Q, R; 83 int T; 84 scanf( "%d", &T ); 85 while ( T-- ) 86 { 87 A = read_Point(); 88 B = read_Point(); 89 C = read_Point(); 90 D = GetD( B, C ); 91 E = GetD( C, A ); 92 F = GetD( A, B ); 93 Point AD = D - A; 94 Point BE = E - B; 95 Point CF = F - C; 96 P = GetLineIntersection( B, BE, A, AD ); 97 Q = GetLineIntersection( C, CF, B, BE ); 98 R = GetLineIntersection( A, AD, C, CF ); 99 100 printf( "%.0f\n", Cross( Q - P, R - P ) / 2.0 ); 101 } 102 return 0; 103 }
