#include #include #include #include #include #include #include #include #include #include #include #define MID(x,y) ( ( x + y ) >> 1 ) #define L(x) ( x << 1 ) #define R(x) ( x << 1 | 1 ) #define FOR(i,s,t) for(int i=(s); i<(t); i++) #define BUG puts("here!!!") #define STOP system("pause") #define file_r(x) freopen(x, "r", stdin) #define file_w(x) freopen(x, "w", stdout) using namespace std; const int MAX = 1000; const double eps = 1e-6; const double inf = 1e50; struct point{ double x, y; void get() { scanf("%lf%lf", &x, &y); } }; bool dy(double x,double y) { return x > y + eps;} bool xy(double x,double y) { return x < y - eps;} bool dyd(double x,double y) { return x > y - eps;} bool xyd(double x,double y) { return x < y + eps;} bool dd(double x,double y) { return fabs( x - y ) < eps;} double disp2p(point a,point b) { return sqrt( ( a.x - b.x ) * ( a.x - b.x ) + ( a.y - b.y ) * ( a.y - b.y ) ); } bool operator==(point a, point b) { return dd(a.x, b.x) && dd(a.y, b.y); } typedef struct NODE{ int to; double len; NODE *next; }NODE; NODE *p[MAX],node[MAX*MAX]; struct circle{ point c; double r; }; circle c[MAX]; int cou; void init() { cou = 0; memset(p, 0, sizeof(p)); } void Add(int from,int to,double len) { node[cou].next = p[from]; node[cou].to = to; node[cou].len = len; p[from] = &node[cou++]; } queue q; double SPFA_List(int from,int to,int n) { while( !q.empty() ) q.pop(); double dis[MAX]; bool inq[MAX]; for(int i=0; ito; double len = head->len; if( dy(dis[v], dis[now] + len) ) { dis[v] = dis[now] + len; if( !inq[v] ) { inq[v] = true; q.push(v); } } head = head->next; } } if( dd(dis[to], inf) ) return -1; return dis[to]; } point l2l_inst_p(point u1,point u2,point v1,point v2) { point ans = u1; double t = ((u1.x - v1.x)*(v1.y - v2.y) - (u1.y - v1.y)*(v1.x - v2.x))/ ((u1.x - u2.x)*(v1.y - v2.y) - (u1.y - u2.y)*(v1.x - v2.x)); ans.x += (u2.x - u1.x)*t; ans.y += (u2.y - u1.y)*t; return ans; } void l2c_inst_p(point c,double r,point l1,point l2,point &p1,point &p2) { point p = c; double t; p.x += l1.y - l2.y; p.y += l2.x - l1.x; p = l2l_inst_p(p,c,l1,l2); t = sqrt(r*r - disp2p(p,c)*disp2p(p,c))/disp2p(l1,l2); p1.x = p.x + (l2.x - l1.x)*t; p1.y = p.y + (l2.y - l1.y)*t; p2.x = p.x - (l2.x - l1.x)*t; p2.y = p.y - (l2.y - l1.y)*t; } void c2c_inst_p(point c1,double r1,point c2,double r2,point &p1,point &p2) { point u,v; double t; t = (1 + (r1*r1 - r2*r2)/disp2p(c1,c2)/disp2p(c1,c2))/2; u.x = c1.x + (c2.x - c1.x)*t; u.y = c1.y + (c2.y - c1.y)*t; v.x = u.x + c1.y - c2.y; v.y = u.y - c1.x + c2.x; l2c_inst_p(c1,r1,u,v,p1,p2); } bool c2c_tangent(point a,double r1,point b,double r2) { if( dd(disp2p(a,b),r1+r2) || dd(disp2p(a,b),fabs(r1-r2)) ) return true; return false; } point c2c_tangent_p(point a,double r1,point b,double r2) { point t; if( dd(disp2p(a,b),r1 + r2) ) { t.x = (r1*b.x + r2*a.x)/(r1 + r2); t.y = (r1*b.y + r2*a.y)/(r1 + r2); return t; } t.x = (r1*b.x - r2*a.x)/(r1 - r2); t.y = (r1*b.y - r2*a.y)/(r1 - r2); return t; } point g[MAX]; bool f[MAX][MAX]; double crossProduct(point a,point b,point c) { return (c.x - a.x)*(b.y - a.y) - (b.x - a.x)*(c.y - a.y); } double disp2l(point a,point l1,point l2) { return fabs( crossProduct(a,l1,l2) )/disp2p(l1,l2); } bool onSegment(point a, point b, point c) { if( dd(crossProduct(a,b,c),0.0) && dyd(c.x,min(a.x,b.x)) && xyd(c.x,max(a.x,b.x)) && dyd(c.y,min(a.y,b.y)) && xyd(c.y,max(a.y,b.y)) ) return true; return false; } bool cmp(point a, point b) { if( dd(a.x, b.x) ) return xy(a.y, b.y); return xy(a.x, b.x); } point tp[MAX]; bool check(int cnt, int n) { FOR(i, 1, cnt) { point tt; tt.x = (tp[i].x + tp[i-1].x)/2; tt.y = (tp[i].y + tp[i-1].y)/2; bool f = false; FOR(k, 0, n) if( xyd(disp2p(c[k].c, tt), c[k].r) ) { f = true; break; } if( !f ) return false; } return true; } double solve(int n) { int l = 0; int s = 0, t = n-1; FOR(i, 0, n) g[l++] = c[i].c; FOR(i, 0, n) { FOR(k, i+1, n) { if( dy(disp2p(c[i].c, c[k].c), c[i].r + c[k].r) || c[i].c == c[k].c ) continue; if( c2c_tangent(c[i].c, c[i].r, c[k].c, c[k].r) ) { point tt = c2c_tangent_p(c[i].c, c[i].r, c[k].c, c[k].r); g[l++] = tt; continue; } point t1, t2; c2c_inst_p(c[i].c, c[i].r, c[k].c, c[k].r, t1, t2); g[l++] = t1; g[l++] = t2; } } memset(f, false, sizeof(f)); int tmp[MAX]; FOR(i, 0, n) { int cnt = 0; FOR(k, 0, l) if( xyd(disp2p(c[i].c, g[k]), c[i].r) ) tmp[cnt++] = k; FOR(k, 0, cnt) FOR(j, k+1, cnt) { int x = tmp[k], y = tmp[j]; if( f[x][y] ) continue; double dis = disp2p(g[x], g[y]); Add(x, y, dis); Add(y, x, dis); f[x][y] = f[y][x] = true; } } FOR(i, 0, l) FOR(k, i+1, l) { if( f[i][k] ) continue; int cnt = 0; tp[cnt++] = g[i]; tp[cnt++] = g[k]; FOR(j, 0, n) if( xyd(disp2l(c[j].c, g[i], g[k]),c[j].r) ) { point t1, t2; l2c_inst_p(c[j].c, c[j].r, g[i], g[k], t1, t2); if( onSegment(g[i], g[k], t1) ) tp[cnt++] = t1; if( onSegment(g[i], g[k], t2) ) tp[cnt++] = t2; } sort(tp, tp+cnt, cmp); if( check(cnt, n) ) { Add(i, k, disp2p(g[i], g[k])); Add(k, i, disp2p(g[k], g[i])); } } return SPFA_List(s, t, l); } int main() { int ncases, n, ind = 1; scanf("%d", &ncases); while( ncases-- ) { scanf("%d", &n); init(); FOR(i, 0, n) { c[i].c.get(); scanf("%lf", &c[i].r); } double ans = solve(n); printf("Case %d: ",ind++); if( ans < -eps ) puts("No such path."); else printf("%.4lf\n", ans); } return 0; }