1 #include <cstdio>  2 #include <cmath>  3 #include <cstring>  4 #include <algorithm>  5   6 const int maxn = 10;  7 const double eps = 1e-8;  8 const double PI = acos(-1.0);  9  10 int dcmp(double x) 11 { return (x > eps) - (x < -eps); } 12  13 struct Point 14 { 15     double x, y; 16     Point(double x=0, double y=0):x(x), y(y) {} 17     void read() { scanf("%lf%lf", &x, &y); } 18 }; 19 typedef Point Vector; 20 Point operator + (const Vector& a, const Vector& b) 21 { return Point(a.x+b.x, a.y+b.y); } 22 Point operator - (const Vector& a, const Vector& b) 23 { return Point(a.x-b.x, a.y-b.y); } 24 Vector operator * (const Vector& a, double p) 25 { return Point(a.x*p, a.y*p); } 26 Vector operator / (const Vector& a, double p) 27 { return Point(a.x/p, a.y/p); } 28 bool operator == (const Point& a, const Point& b) 29 { return dcmp(a.x-b.x) == 0 && dcmp(a.y-b.y) == 0; } 30  31 double Dot(const Vector& a, const Vector& b) 32 { return a.x*b.x + a.y*b.y; } 33 double Cross(const Vector& a, const Vector& b) 34 { return a.x*b.y - a.y*b.x; } 35 double Length(const Vector& a) 36 { return sqrt(Dot(a, a)); } 37 Vector unit(const Vector& a) 38 { return a / Length(a); } 39 Vector Normal(const Vector& a) 40 { 41     double l = Length(a); 42     return Vector(-a.y/l, a.x/l); 43 } 44 double Angle(const Vector& a) 45 { return atan2(a.y, a.x); } 46  47 Point Rotate(const Point& p, double angle, const Point& o = Point(0, 0)) 48 { 49     Vector t = p - o; 50     t = Vector(t.x*cos(angle)-t.y*sin(angle), t.x*sin(angle)+t.y*cos(angle)); 51     return t + o; 52 } 53  54 struct Region 55 { 56     double st, ed; 57     Region(double s=0, double e=0):st(s), ed(e) {} 58 }; 59  60 struct Circle 61 { 62     Point c; 63     double r; 64     Circle() {} 65     Circle(Point c, double r):c(c), r(r) {} 66      67     void read() { c.read(); scanf("%lf", &r); } 68      69     double area() const { return PI * r * r; } 70      71     bool contain(const Circle& rhs) const 72     { return dcmp(Length(c-rhs.c) + rhs.r - r) <= 0; } 73      74     bool contain(const Point& p) const 75     { return dcmp(Length(c-p) - r) <= 0; } 76      77     bool intersect(const Circle& rhs) const 78     { return dcmp(Length(c-rhs.c) - r - rhs.r) < 0; } 79      80     bool tangency(const Circle& rhs) const 81     { return dcmp(Length(c-rhs.c) - r - rhs.r) == 0; } 82      83     Point get_point(double ang) const 84     { return Point(c.x + r * cos(ang), c.y + r * sin(ang)); } 85 }; 86  87 void IntersectionPoint(const Circle& c1, const Circle& c2, Point& p1, Point& p2) 88 { 89     double d = Length(c1.c - c2.c); 90     double l = (c1.r*c1.r + d*d - c2.r*c2.r) / (2 * d); 91     double h = sqrt(c1.r*c1.r - l*l); 92     Point mid = c1.c + unit(c2.c-c1.c) * l; 93     Vector t = Normal(c2.c - c1.c) * h; 94     p1 = mid + t; 95     p2 = mid - t; 96 } 97  98 double IntersectionArea(const Circle& c1, const Circle& c2) 99 {100     double area = 0.0;101     const Circle& M = c1.r > c2.r ? c1 : c2;102     const Circle& N = c1.r > c2.r ? c2 : c1;103     double d = Length(c1.c-c2.c);104     105     if(d < M.r + N.r && d > M.r - N.r)106     {107         double Alpha = 2.0 * acos((M.r*M.r + d*d - N.r*N.r) / (2 * M.r * d));108         double Beta  = 2.0 * acos((N.r*N.r + d*d - M.r*M.r) / (2 * N.r * d));109         area = ( M.r*M.r*(Alpha - sin(Alpha)) + N.r*N.r*(Beta - sin(Beta)) ) / 2.0;110     }111     else if(d <= M.r - N.r) area = N.area();112     113     return area;114 }115 116 struct Region_vector117 {118     int n;119     Region v[5];120     void clear() { n = 0; }121     void add(const Region& r) { v[n++] = r; }122 } *last, *cur;123 124 Circle cir[maxn];125 bool del[maxn];126 double r;127 int n = 5;128 129 bool IsOnlyOnePoint()130 {131     bool flag = false;132     Point t;133     for(int i = 0; i < n; ++i)134     {135         for(int j = i + 1; j < n; ++j)136         {137             if(cir[i].tangency(cir[j]))138             {139                 t = (cir[i].c + cir[j].c) / 2;140                 flag = true;141                 break;142             }143         }144     }145     146     if(!flag) return false;147     for(int i = 0; i < n; ++i)148         if(!cir[i].contain(t)) return false;149     150     printf("Only the point (%.2f, %.2f) is for victory.\n", t.x, t.y);151     return true;152 }153 154 bool solve()155 {156     if(IsOnlyOnePoint()) return true;157     memset(del, false, sizeof(del));158     159     for(int i = 0; i < n; ++i)160         for(int j = 0; j < n; ++j)161         {162             if(del[j] || i == j) continue;163             if(cir[i].contain(cir[j]))164             {165                 del[i] = true;166                 break;167             }168         }169         170     double ans = 0.0;171     for(int i = 0; i < n; ++i)172     {173         if(del[i]) continue;174         last->clear();175         Point p1, p2;176         for(int j = 0; j < n; ++j)177         {178             if(del[j] || i == j) continue;179             if(!cir[i].intersect(cir[j])) return false;180             cur->clear();181             IntersectionPoint(cir[i], cir[j], p1, p2);182             double rs = Angle(p2 - cir[i].c);183             double rt = Angle(p1 - cir[i].c);184             if(dcmp(rs) < 0) rs += 2 * PI;185             if(dcmp(rt) < 0) rt += 2 * PI;186             if(last->n == 0)187             {188                 if(dcmp(rt - rs) < 0)189                 {190                     cur->add(Region(rs, 2*PI));191                     cur->add(Region(0,  rt));192                 }193                 else cur->add(Region(rs, rt));194             }195             else196             {197                 for(int k = 0; k < last->n; ++k)198                 {199                     if(dcmp(rt - rs) < 0)200                     {201                         if(dcmp(last->v[k].st-rt) >= 0 && dcmp(last->v[k].ed-rs) <= 0) continue;202                         if(dcmp(last->v[k].st-rt) < 0) cur->add(Region(last->v[k].st, std::min(last->v[k].ed, rt)));203                         if(dcmp(last->v[k].ed-rs) > 0) cur->add(Region(std::max(last->v[k].st, rs), last->v[k].ed));204                     }205                     else206                     {207                         if(dcmp(rt-last->v[k].st <= 0 || dcmp(rs-last->v[k].ed) >= 0)) continue;208                         cur->add(Region(std::max(rs, last->v[k].st), std::min(rt, last->v[k].ed)));209                     }210                 }211             }212             std::swap(cur, last);213             if(last->n == 0) break;214         }215         for(int j = 0; j < last->n; ++j)216         {217             p1 = cir[i].get_point(last->v[j].st);218             p2 = cir[i].get_point(last->v[j].ed);219             ans += Cross(p1, p2) / 2;220             double ang = last->v[j].ed - last->v[j].st;221             ans += cir[i].r * cir[i].r * (ang - sin(ang)) / 2;222         }223     }224     225     if(dcmp(ans) == 0) return false;226     printf("The total possible area is %.2f.\n", ans);227     return true;228 }229 230 int main(void)231 {232     //freopen("3467in.txt", "r", stdin);233     last = new Region_vector;234     cur =  new Region_vector;235     while(scanf("%lf", &r) == 1)236     {237         Point t;238         for(int i = 0; i < n; ++i)239         {240             t.read();241             cir[i] = Circle(t, r);242         }243         if(!solve())244             puts("Poor iSea, maybe 2012 is coming!");245     }246     247     return 0;248 }