随机化快速排序(Java实现)

Randomized quicksort(随机化快速排序)

• running time is independent of input ordering.
• no assumption about the input distribution.(无需对输入序列分布做任何假设)
• no specific input elicit the worst-case behavior.(没有特定输入引起最差的运行效率)
• worst-case determined only by a random -number generator.(最差的情况由随机数产生器决定)
• pivot a random element.(随机选择一个主元)

根据《算法导论》中快速排序的随机化样本中的伪代码如下：

数组的划分：

1 RANDOMIZED-PARTITION(A, p, r)
2 i = RANDOM(p, r)
3 exchange A[r] with A[i]
4 return PARTITION(A, p ,r)

其中PARTITION(A, p, r)参考快速排序（Java实现）

1 RANDOMIZED-QUICKSORT(A, p, r)
2     if p < r
3         q = RANDOMIZED-PARTITION(A, p, r)
4         RANDOMIZED-QUICKSORT(A, p, q-1)
5         RANDOMIZED-QUICKSORT(A, q+1, r)

随机快速排序，随机选择一个主元和数组划分：RandomQuickSort.java

 1 package quicksort;
 2
 3 import java.util.Random;
 4
 5 public class RandomQuickSort {
 6
 7     public void Sort(int[] a, int p, int r) {
 8         if (p < r) {
 9             int q = Partition(a, p, r);
10             Sort(a, p, q-1);
11             Sort(a,q+1, r);
12         }
13     }
14
15     private int Partition(int[] A, int p, int r) {
16         /*随机选取主元元素*/
17         Random random = new Random();
18         int random_index = random.nextInt(r-p+1)+p;
19         System.out.println("random_index="+random_index);
20         int temp = A[random_index];
21         A[random_index] = A[r];
22         A[r] = temp;
23
24         int x = A[r];  //pivot = A[p]
25         int i = p-1;
26         for (int j = p; j < r; j++) {
27             if (A[j] <= x) {  //与pivot作比较
28                 i++;
29                 int tmp = A[j];
30                 A[j] = A[i];
31                 A[i] = tmp;
32             }
33         }
34
35         int tmp = A[r];
36         A[r] = A[i+1];
37         A[i+1] = tmp;
38
39         return i+1;
40
41     }
42
43 }

测试随机化快速排序：RandomQuickSortTest.java

 1 package quicksort;
 2
 3 public class RandomQuickSortTest {
 4
 5 //    static int[] a ={2, 8, 7, 1, 3, 5, 6, 4};
 6     static int[] a ={13, 19, 9, 5, 12, 8, 7, 4, 21, 2, 6, 11};
 7     public static void main(String[] args) {
 8         RandomQuickSort randomQuickSort = new RandomQuickSort();
 9         randomQuickSort.Sort(a, 0, a.length-1);
10
11         for (int i = 0; i < a.length; i++) {
12             System.out.print(a[i]+" ");
13         }
14     }
15 }

测试结果：

random_index=2
random_index=2
random_index=0
random_index=0
random_index=8
random_index=10
random_index=7
random_index=7
2 4 5 6 7 8 9 11 12 13 19 21