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