1 #include<cstdio> 2 #include<cstring> 3 #include<cmath> 4 #define MAXM 20 5 #define MAXN 10000 6 #define EPS 1e-8 7 #define INF 0x7FFFFFFF 8 int L[MAXN], R[MAXN], U[MAXN], D[MAXN]; 9 int S[MAXN], H[MAXN], C[MAXN], B[MAXN]; 10 double dis[MAXM][MAXM]; 11 bool vis[MAXM]; 12 struct Point { 13 double x, y; 14 }; 15 Point p[MAXM], center[MAXN]; 16 int n, m, size; 17 inline int dbcmp(double x, double y) { 18 if (fabs(x - y) < EPS) 19 return 0; 20 return x > y ? 1 : -1; 21 } 22 inline double DIS(Point a, Point b) { 23 double x, y; 24 x = b.x - a.x; 25 y = b.y - a.y; 26 return x * x + y * y; 27 } 28 void Init() { 29 int i; 30 for (i = 0; i <= n; i++) { 31 R[i] = i + 1; 32 L[i + 1] = i; 33 U[i] = D[i] = i; 34 S[i] = 0; 35 } 36 R[n] = 0; 37 size = n + 1; 38 } 39 void Link(int r, int c) { 40 D[size] = D[c]; 41 U[size] = c; 42 U[D[c]] = size; 43 D[c] = size; 44 if (H[r] < 0) 45 H[r] = L[size] = R[size] = size; 46 else { 47 L[size] = H[r]; 48 R[size] = R[H[r]]; 49 L[R[H[r]]] = size; 50 R[H[r]] = size; 51 } 52 S[c]++; 53 C[size++] = c; 54 } 55 int A() { 56 int i, j, k, res; 57 memset(vis, false, sizeof(vis)); 58 for (res = 0, i = R[0]; i; i = R[i]) { 59 if (vis[i]) 60 continue; 61 res++; 62 for (j = D[i]; j != i; j = D[j]) { 63 for (k = R[j]; k != j; k = R[k]) 64 vis[C[k]] = true; 65 } 66 } 67 return res; 68 } 69 void Remove(int c) { 70 int i; 71 for (i = D[c]; i != c; i = D[i]) { 72 L[R[i]] = L[i]; 73 R[L[i]] = R[i]; 74 } 75 } 76 void Resume(int c) { 77 int i; 78 for (i = D[c]; i != c; i = D[i]) 79 L[R[i]] = R[L[i]] = i; 80 } 81 bool Dance(int now) { 82 if (now + A() > m) 83 return false; 84 if (R[0] == 0) 85 return true; 86 int i, j, temp, c; 87 for (temp = INF,i = R[0]; i; i = R[i]) { 88 if (temp > S[i]) { 89 temp = S[i]; 90 c = i; 91 } 92 } 93 for (i = D[c]; i != c; i = D[i]) { 94 Remove(i); 95 for (j = R[i]; j != i; j = R[j]) 96 Remove(j); 97 if (Dance(now + 1)) 98 return true; 99 for (j = L[i]; j != i; j = L[j]) 100 Resume(j); 101 Resume(i); 102 } 103 return false; 104 } 105 void Center(int i, int j, double r, int &cnt) { 106 double x0, y0, x1, y1, d; 107 if (dbcmp(dis[i][j], 0) == 0) 108 center[cnt++] = p[i]; 109 else if (dbcmp(dis[i][j], 2 * r) == 0) { 110 center[cnt].x = (p[i].x + p[j].x) / 2; 111 center[cnt++].y = (p[i].y + p[j].y) / 2; 112 } else if (dbcmp(dis[i][j], 2 * r) < 0) { 113 x0 = (p[i].x + p[j].x) / 2; 114 y0 = (p[i].y + p[j].y) / 2; 115 x1 = (p[i].x - p[j].x) / 2; 116 y1 = (p[i].y - p[j].y) / 2; 117 d = sqrt(r * r - x1 * x1 - y1 * y1) / dis[i][j]; 118 center[cnt].x = (p[j].y - p[i].y) * d + x0; 119 center[cnt++].y = (p[i].x - p[j].x) * d + y0; 120 center[cnt].x = (p[i].y - p[j].y) * d + x0; 121 center[cnt++].y = (p[j].x - p[i].x) * d + y0; 122 } 123 } 124 bool OK(double r) { 125 int i, j, k, cnt; 126 Init(); 127 for (cnt = 0, i = 1; i <= n; i++) { 128 for (j = i; j <= n; j++) 129 Center(i, j, r, cnt); 130 } 131 for (r *= r, i = 0; i < cnt; i++) { 132 H[i] = -1; 133 B[i] = 0; 134 for (j = 1; j <= n; j++) { 135 B[i] <<= 1; 136 if (dbcmp(DIS(center[i], p[j]), r) <= 0) 137 B[i] |= 1; 138 } 139 } 140 for (i = 0; i < cnt; i++) { 141 for (j = i + 1; j < cnt; j++) { 142 if ((B[i] | B[j]) == B[j]) 143 break; 144 } 145 if (j == cnt) { 146 for (k = 0; k < n; k++) { 147 if (B[i] & (1 << k)) 148 Link(i, k + 1); 149 } 150 } 151 } 152 return Dance(0); 153 } 154 int main() { 155 int T, i, j; 156 double low, high, mid; 157 scanf("%d", &T); 158 while (T--) { 159 scanf("%d%d", &n, &m); 160 for (i = 1; i <= n; i++) 161 scanf("%lf%lf", &p[i].x, &p[i].y); 162 for (i = 1; i <= n; i++) { 163 dis[i][i] = 0; 164 for (j = i + 1; j <= n; j++) 165 dis[i][j] = dis[j][i] = sqrt(DIS(p[i], p[j])); 166 } 167 for (low = 0, high = 15; dbcmp(low, high) < 0;) { 168 mid = (low + high) / 2; 169 if (OK(mid)) 170 high = mid; 171 else 172 low = mid; 173 } 174 printf("%lf\n", low); 175 } 176 return 0; 177 }
