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：

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

其中PARTITION(A, p, r)参考快速排序（Java实现）

RANDOMIZED-QUICKSORT(A, p, r)
    if p < r
        q = RANDOMIZED-PARTITION(A, p, r)
        RANDOMIZED-QUICKSORT(A, p, q-1)
        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

package quicksort;

import java.util.Random;

public class RandomQuickSort {

    public void Sort(int[] a, int p, int r) {
        if (p < r) {
            int q = Partition(a, p, r);
            Sort(a, p, q-1);
            Sort(a,q+1, r);            
        }
    }
    
    private int Partition(int[] A, int p, int r) {
        /*随机选取主元元素*/
        Random random = new Random();
        int random_index = random.nextInt(r-p+1)+p;
        System.out.println("random_index="+random_index);
        int temp = A[random_index];
        A[random_index] = A[r];
        A[r] = temp;
        
        int x = A[r];  //pivot = A[p]
        int i = p-1;
        for (int j = p; j < r; j++) {
            if (A[j] <= x) {  //与pivot作比较
                i++;
                int tmp = A[j];
                A[j] = A[i];
                A[i] = tmp;
            }
        }
        
        int tmp = A[r];
        A[r] = A[i+1];
        A[i+1] = tmp;
        
        return i+1;
        
    }
    
}

 测试随机化快速排序：RandomQuickSortTest.java

package quicksort;

public class RandomQuickSortTest {

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

 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