? 书中第六章部分程序，加上自己补充的代码，包括 Graham 扫描生成凸包，计算最远点对
● Graham 扫描生成凸包
1 package package01;
2
3 import java.util.Arrays;
4 import edu.princeton.cs.algs4.StdIn;
5 import edu.princeton.cs.algs4.StdOut;
6 import edu.princeton.cs.algs4.Point2D;
7 import edu.princeton.cs.algs4.Stack;
8
9 public class class01
10 {
11 private Stack<Point2D> hull = new Stack<Point2D>();
12
13 public class01(Point2D[] points)
14 {
15 if (points == null || points.length == 0)
16 throw new IllegalArgumentException("argument is null");
17 int n = points.length;
18 Point2D[] a = new Point2D[n];
19 for (int i = 0; i < n; i++)
20 a[i] = points[i];
21
22 Arrays.sort(a); // Y 坐标升序排序，等值的按 X 坐标升序排序，保证 a[0] 为最下最左，a[1] 为
23 Arrays.sort(a, 1, n, a[0].polarOrder()); // 以 a[0] 为原点，幅角升序排序
24 hull.push(a[0]); // 第一个点
25 int k1; // 找到下一个相异点
26 for (k1 = 1; k1 < n; k1++)
27 {
28 if (!a[0].equals(a[k1]))
29 break;
30 }
31 if (k1 == n)
32 return;
33 int k2; // 找到下一个非共线点
34 for (k2 = k1 + 1; k2 < n; k2++)
35 {
36 if (Point2D.ccw(a[0], a[k1], a[k2]) != 0)
37 break;
38 }
39 hull.push(a[k2 - 1]); // a[k2-1] 是与 a[0]，a[k1] 共线的最后一个点（也可以先压 a[k1] 然后跳过 a[k2-1]）
40 for (int i = k2; i < n; i++)
41 {
42 Point2D top = hull.pop();
43 for (; Point2D.ccw(hull.peek(), top, a[i]) <= 0; top = hull.pop()); // 倒数第 2 点、倒数第 1 点和当前点计算三角形面积，逆时针方向为正
44 // 吐栈吐到这 3 点的面积为正为止，压入倒数第 2 点当前点
45 hull.push(top);
46 hull.push(a[i]);
47 }
48 assert isConvex();
49 }
50
51 public Iterable<Point2D> hull() // 得到凸包的迭代器
52 {
53 Stack<Point2D> s = new Stack<Point2D>();
54 for (Point2D p : hull)
55 s.push(p);
56 return s;
57 }
58
59 private boolean isConvex() // 检查凸性
60 {
61 int n = hull.size();
62 if (n <= 2) return true;
63
64 Point2D[] points = new Point2D[n];
65 int k = 0;
66 for (Point2D p : hull())
67 points[k++] = p;
68
69 for (int i = 0; i < n; i++)
70 {
71 if (Point2D.ccw(points[i], points[(i + 1) % n], points[(i + 2) % n]) <= 0)
72 return false;
73 }
74 return true;
75 }
76
77 public static void main(String[] args)
78 {
79 int n = StdIn.readInt();
80 Point2D[] points = new Point2D[n];
81 for (int i = 0; i < n; i++)
82 {
83 int x = StdIn.readInt(), y = StdIn.readInt();
84 points[i] = new Point2D(x, y);
85 }
86 class01 graham = new class01(points);
87 for (Point2D p : graham.hull())
88 StdOut.println(p);
89 }
90 }
● 计算最远点对
1 package package01;
2
3 import edu.princeton.cs.algs4.StdIn;
4 import edu.princeton.cs.algs4.StdOut;
5 import edu.princeton.cs.algs4.Point2D;
6 import edu.princeton.cs.algs4.GrahamScan;
7
8 public class class01
9 {
10 private Point2D best1, best2;
11 private double bestDistanceSquared = Double.NEGATIVE_INFINITY; // 当前最远点对距离的平方
12
13 public class01(Point2D[] points)
14 {
15 if (points == null || points.length <= 1)
16 throw new IllegalArgumentException("constructor argument is null");
17
18 GrahamScan graham = new GrahamScan(points);
19
20 int m = 0;// 凸包点数
21 for (Point2D p : graham.hull())
22 m++;
23 Point2D[] hull = new Point2D[m + 1]; // 凸包顶点放入 a[1] ~ a[m]
24 m = 1;
25 for (Point2D p : graham.hull())
26 hull[m++] = p;
27 m--; // m 等于凸包顶点数
28
29 if (m == 1) // 所有点都相同
30 return;
31 if (m == 2) // 所有点共线
32 {
33 best1 = hull[1];
34 best2 = hull[2];
35 bestDistanceSquared = best1.distanceSquaredTo(best2);
36 return;
37 }
38
39 int k = 2;
40 for (; Point2D.area2(hull[m], hull[1], hull[k + 1]) > Point2D.area2(hull[m], hull[1], hull[k]); k++); // a[k] 是距离直线 a[1]a[m] 最远的点
41
42 int j = k;
43 for (int i = 1; i <= k && j <= m; i++) // j 搜索后半部分，i 搜索前半部分
44 {
45 update(hull[i], hull[j]); // i 挪动一位，检查 a[i] 和 a[j] 距离是否更大
46 for (j++; (j <= m) && Point2D.area2(hull[i], hull[i + 1], hull[j]) > Point2D.area2(hull[i], hull[i + 1], hull[j - 1]); j++)
47 // j 挪动保持 a[j] 远离直线 a[i]a[i+1]
48 update(hull[i], hull[j]);
49 }
50 }
51
52 private void update(Point2D x, Point2D y)
53 {
54 double distanceSquared = x.distanceSquaredTo(y);
55 if (distanceSquared > bestDistanceSquared)
56 {
57 best1 = x;
58 best2 = y;
59 bestDistanceSquared = distanceSquared;
60 }
61 }
62
63 public Point2D either()
64 {
65 return best1;
66 }
67
68 public Point2D other()
69 {
70 return best2;
71 }
72
73 public double distance()
74 {
75 return Math.sqrt(bestDistanceSquared);
76 }
77
78 public static void main(String[] args)
79 {
80 int n = StdIn.readInt();
81 Point2D[] points = new Point2D[n];
82 for (int i = 0; i < n; i++)
83 {
84 int x = StdIn.readInt(), y = StdIn.readInt();
85 points[i] = new Point2D(x, y);
86 }
87 class01 farthest = new class01(points);
88 StdOut.println(farthest.distance() + " from " + farthest.either() + " to " + farthest.other());
89 }
90 }
原文地址：https://www.cnblogs.com/cuancuancuanhao/p/10115990.html
时间： 2024-11-13 03:59:50