已知平面上若干个点的坐标。需要求出在所有的组合中，4个点间平均距离的最小值（四舍五入，保留2位小数）。

/* *已知平面上若干个点的坐标。需要求出在所有的组合中，4个点间平均距离的最小值（四舍五入，保留2位小数）。比如有4个点：a,b,c,d,则平均距离是指：ab, ac, ad, bc, bd, cd 这6个距离的平均值。每个点的坐标表示为：横坐标,纵坐标坐标的取值范围是：1~1000所有点的坐标记录在in.txt中，请读入该文件，然后计算。注意：我们测试您的程序的时候，in.txt 可能会很大，比如包含上万条记录。举例：如果，in.txt 内的值为：10,1020,2080,5010,2020,10则程序应该输出：11.38 */import java.io.BufferedReader;import java.io.FileInputStream;import java.io.InputStreamReader;import java.util.List;import java.util.Vector;// 代表一个点class PP {public int x;public int y;public String toString() {return x + "," + y;}public PP(int x, int y) {this.x = x;this.y = y;}}class RR {double x1;double y1;double x2;double y2;public RR() {}public RR(double x1, double y1, double x2, double y2) {this.x1 = x1;this.y1 = y1;this.x2 = x2;this.y2 = y2;}boolean isIn(PP p) {return (x1 < p.x && p.x < x2 && y1 < p.y && p.y < y2);}}public class T07 {public static double f(List<PP> lst, RR r) {// lst：当前要处理的点，r:当前区域if (lst.size() < 4)return 10000; // 代表很远if (lst.size() < 13) {// 测试中所有13中选4的组合double min = 10000;for (int i = 0; i < lst.size(); i++)for (int j = i + 1; j < lst.size(); j++)for (int k = j + 1; k < lst.size(); k++)for (int m = k + 1; m < lst.size(); m++) {double d = distance(lst.get(i), lst.get(j),lst.get(k), lst.get(m));if (d < min)min = d;}return min;}// 缩小边界double x1a = r.x2;double x2a = r.x1;double y1a = r.y2;double y2a = r.y1;for (int i = 0; i < lst.size(); i++) {PP p = lst.get(i);if (p.x < x1a)x1a = p.x;if (p.x > x2a)x2a = p.x;if (p.y < y1a)y1a = p.y;if (p.y > y2a)y2a = p.y;}r.x1 = x1a;r.x2 = x2a;r.y1 = y1a;r.y2 = y2a;// 拆分lst 为4块,重叠4个区域RR r1 = new RR();RR r2 = new RR();RR r3 = new RR();RR r4 = new RR();r1.x1 = r.x1;r1.y1 = r.y1;r1.x2 = r.x1 * 0.25 + r.x2 * 0.75; // 0.75*(x2-x1) + x1r1.y2 = r.y1 * 0.25 + r.y2 * 0.75;r2.x1 = r.x1 * 0.75 + r.x2 * 0.25; // 0.25*(x2-x1) + x1r2.y1 = r.y1 * 0.75 + r.y2 * 0.25;r2.x2 = r.x2;r2.y2 = r.y2;r3.x1 = r.x1;r3.y1 = r.y1 * 0.75 + r.y2 * 0.25;r3.x2 = r.x1 * 0.25 + r.x2 * 0.75;r3.y2 = r.y2;r4.x1 = r.x1 * 0.75 + r.x2 * 0.25;r4.y1 = r.y1;r4.x2 = r.x2;r4.y2 = r.y1 * 0.25 + r.y2 * 0.75;List<PP> t1 = new Vector<PP>();List<PP> t2 = new Vector<PP>();List<PP> t3 = new Vector<PP>();List<PP> t4 = new Vector<PP>();// isIn(p)判断是否在该矩形中for (int i = 0; i < lst.size(); i++) {PP p = lst.get(i);if (r1.isIn(p))t1.add(p);if (r2.isIn(p))t2.add(p);if (r3.isIn(p))t3.add(p);if (r4.isIn(p))t4.add(p);}// 递归double d1 = f(t1, r1);double d2 = f(t2, r2);double d3 = f(t3, r3);double d4 = f(t4, r4);double d = d1;if (d2 < d)d = d2;if (d3 < d)d = d3;if (d4 < d)d = d4;return d;}// 计算 4个点间平均距离public static double distance(PP a,PP b,PP c,PP d){double dis = (distance(a,b) + distance(a,c) + distance(a,d) +distance(b,c) + distance(b,d) + distance(c,d)) / 6.0;return dis;}// 求两个点的距离public static double distance(PP a, PP b){double dx = a.x - b.x;double dy = a.y - b.y;return Math.sqrt(dx*dx + dy*dy);}// 读入文件，填入List中public static List<PP> readPoints(String fname)throws Exception{BufferedReader br = new BufferedReader(new InputStreamReader(new FileInputStream(fname)));List<PP> lst = new Vector<PP>();for(;;){String s = br.readLine();if(s==null) break;String[] ss = s.split(",");PP a = new PP(0,0);a.x = Integer.parseInt(ss[0]);a.y = Integer.parseInt(ss[1]);lst.add(a);}br.close();return lst;}public static void main(String[] args) throws Exception {List<PP> lst = readPoints("in.txt");double x = f(lst, new RR(0, 0, 1000, 1000));System.out.printf("%.2f",x);}}

运行结果：

11.38