HDU 4720 Naive and Silly Muggles(几何)

题目链接：http://acm.hdu.edu.cn/showproblem.php?pid=4720

用几何模板，求外接圆，再判断点在不在圆内

#include <stdio.h>
#include <string.h>
#include <math.h>
const double esp = 1e-9;

//点
struct Point {
double x, y;
Point() {}
Point(double x, double y) {
this->x = x;
this->y = y;
}
void read() {
scanf("%lf%lf", &x, &y);
}
};

//线段
struct Line {
Point p[2];
double A, B, C;
Line() {}
Line(Point a, Point b) {
this->p[0] = a;
this->p[1] = b;
A = p[0].y - p[1].y;
B = p[1].x - p[0].x;
C = -(A * p[0].x + B * p[0].y);
}
};

//圆
struct Circle {
Point center;
double r;
Circle() {}
Circle(Point center, double r) {
this->center = center;
this->r = r;
}
};

//三角形
struct Tra {
Point p[3];
Tra() {}
Tra(Point a, Point b, Point c) {
this->p[0] = a;
this->p[1] = b;
this->p[2] = c;
}
};

//点点距离
double dis(Point a, Point b) {
double dx = a.x - b.x;
double dy = a.y - b.y;
return sqrt(dx * dx + dy * dy);
}

//点线对称点
Point P_dc(Line l, Point p) {
Point ans;
ans.x = p.x - (2 * l.A * (l.A * p.x + l.B * p.y + l.C)) / (l.A * l.A + l.B * l.B);
ans.y = p.y - (2 * l.B * (l.A * p.x + l.B * p.y + l.C)) / (l.A * l.A + l.B * l.B);
return ans;
}

//三角形面积
double Tra_Area(Tra t) {
return fabs((t.p[1].x - t.p[0].x) * (t.p[2].y - t.p[0].y) - (t.p[2].x - t.p[0].x) * (t.p[1].y - t.p[0].y)) / 2.0;
}

//求三角形外接圆
Circle Tra_Cir(Tra t) {
Circle ans;
double a = dis(t.p[0], t.p[1]);
double b = dis(t.p[1], t.p[2]);
double c = dis(t.p[2], t.p[0]);
ans.r = (a * b * c) / (Tra_Area(t) * 4.0);
double xA = t.p[0].x;
double yA = t.p[0].y;
double xB = t.p[1].x;
double yB = t.p[1].y;
double xC = t.p[2].x;
double yC = t.p[2].y;
double c1 = (xA*xA+yA*yA - xB*xB-yB*yB) / 2;
double c2 = (xA*xA+yA*yA - xC*xC-yC*yC) / 2;
ans.center.x = (c1*(yA - yC)-c2*(yA - yB)) / ((xA - xB)*(yA - yC)-(xA - xC)*(yA - yB));
ans.center.y = (c1*(xA - xC)-c2*(xA - xB)) / ((yA - yB)*(xA - xC)-(yA - yC)*(xA - xB));
return ans;
}

//判断点在圆内（含边界)
bool In_Cir(Circle c, Point p) {
double d = dis(p, c.center);
if (d - c.r > esp) return false;
return true;
}

int t;
Point p[4];

bool judge(Circle pc) {
if (!In_Cir(pc, p[3])) return true;
Circle pc1 = Circle(P_dc(Line(p[0], p[1]), p[3]), pc.r);
if (In_Cir(pc1, p[2]) && !In_Cir(pc1, p[3])) return true;
pc1 = Circle(P_dc(Line(p[1], p[2]), p[3]), pc.r);
if (In_Cir(pc1, p[0]) && !In_Cir(pc1, p[3])) return true;
pc1 = Circle(P_dc(Line(p[0], p[2]), p[3]), pc.r);
if (In_Cir(pc1, p[1]) && !In_Cir(pc1, p[3])) return true;
return false;
}

int main() {
int cas = 0;
scanf("%d", &t);
while (t--) {
for (int i = 0; i < 4; i++)
p[i].read();
Tra pt = Tra(p[0], p[1], p[2]);
Circle pc = Tra_Cir(pt);
printf("Case #%d: ", ++cas);
if (judge(pc))
printf("Safe\n");
else
printf("Danger\n");
}
return 0;
}