Question

对于带有第一个元素枢轴的快速排序，我得到了奇怪的计时结果。我的代码首先使用未排序的非随机整数列表运行快速排序。然后它对先前排序的列表进行排序。通过我选择的数据透视表，我预计快速排序可以使用排序列表而不是未排序列表运行最差。我已通过以下结果验证了这一点：

Quicksort 1st run (unsorted, non-randomized)
# of calls to exch(): 14
# of calls to sort(): 17
# of calls to partition():8
# of calls to less(): 47
Sorted?: true
Time to sort input: 0.004212 secs

Quicksort 2nd run (sorted)
# of calls to exch(): 25
# of calls to sort(): 40
# of calls to partition(): 19
# of calls to less(): 138
Sorted?: true
Time to sort input: 0.000535 secs

注意时间没有意义。 Quicksort 2nd run应该比Quicksort 1st run慢。

Timing code:
start();
Quick.sort(a);
stop();

private static void start(){
   start = System.nanoTime();       
}

private static void stop(){
   elapsed = (System.nanoTime() - start)/1E9;
}

快速排序算法是正确的。因此，我实现计时器的方式一定存在问题。

完整代码：

public class Quick {

static int exchCount; //DEBUG
static int sortCount; //DEBUG
static int partitionCount; //DEBUG
static int compareCount; //DEBUG

public static void sort(Comparable[]a){
    //StdRandom.shuffle(a);
    exchCount=0; //DEBUG
    sortCount=0; //DEBUG
    partitionCount=0; //DEBUG
    compareCount=0; //DEBUG
    sort(a, 0, a.length-1);
    System.out.printf("# of calls to exch(): %d%n", exchCount); //DEBUG
    System.out.printf("# of calls to sort(): %d%n", sortCount); // DEBUG
    System.out.printf("# of calls to partition(): %d%n", partitionCount); // DEBUG
    System.out.printf("# of calls to less(): %d%n", compareCount); // DEBUG
    return;

}

private static void sort(Comparable a[], int lo, int hi){
    sortCount++; // DEBUG

    if (hi<=lo) return; // base case    
    int p = partition(a, lo, hi); // select partition
    sort(a, lo, p-1); // recursively sort left side of partition
    sort(a, p+1, hi); // recursively sort right side of partition

    return; 
}


private static int partition(Comparable[]a, int lo, int hi){    
    partitionCount++; //DEBUG
    int i = lo, j = hi+1; // set pointers i (left) & j (right)

    Comparable p = a[lo]; // select a partition point we'll use lo as default

    while (true){

        // continue walking right if values are < p
        // captures any value < p
        while (less(a[++i], p)) if(i==hi)break;

        // continue walking left if values are > p
        while (less(p, a[--j]));

        if(i>=j) break; // has i crossed j?

        exch(a, i, j);

    }

    exch(a, lo, j); 
    return j;
}


private static boolean less(Comparable a, Comparable b){
    compareCount++; //DEBUG
    return a.compareTo(b)<0;

}

private static void exch(Comparable[] a, int i, int j){
    exchCount++; //DEBUG
    Comparable tmp = a[i];
    a[i] = a[j];
    a[j] = tmp; 

}

}


public class SortClient {

static double start=0, elapsed=0;
public static void main(String[] args) {

    for(int i=0; i<10; i++){

        //Comparable[] a={"K","R","A","T","E","L","E","P","U","I"
        //  ,"M","Q","C","X","O","S"};
        //Comparable[] a = DataReader.readInt("http://algs4.cs.princeton.edu/14analysis/8Kints.txt");
        Comparable[] a={8,4,45,23,13,1,65,44,9,8,3,33,21};

        start();
        Quick.sort(a);
        stop();
        System.out.printf("Quicksort#1%n");
        System.out.printf("Sorted?: %b%n",isSorted(a));
        System.out.printf("Time to sort input: %f secs%n%n%n",elapsed);

        start();
        Quick.sort(a);
        stop();
        System.out.printf("Quicksort#2%n");
        System.out.printf("Sorted?: %b%n",isSorted(a));
        System.out.printf("Time to sort input: %f secs%n%n%n",elapsed);

    }
}

private static void start(){

    start = System.nanoTime();

}

private static void stop(){

    elapsed = (System.nanoTime() - start)/1E9;


}

private static boolean isSorted(Comparable[]a){

    for(int i=0; i<a.length-2; i++)
       if(a[i].compareTo(a[i+1])>0)
           return false;
    return true;

}

}

Java的nanoTime（）调用有什么怪癖我不知道吗？有什么想法吗？

Answer 1

“我们都知道快速排序运行最糟糕的是排序列表而不是未排序列表”：这是一个大胆的声明。

Quicksort的效率取决于枢轴的正确选择：良好的枢轴是这样的，它们将区域分开以便以平衡的方式进行分类，因此该过程仍然是二分的，这导致O(N.Lg(N))行为。相反，导致最大不平衡的糟糕选择可能导致二次O(N²)退化，因为该过程仍然是递增的。

Naïve枢轴选择策略，例如“第一元素”确实会导致最坏情况出现在排序序列上。但更明智的实施，例如“三个中位数（第一个，中间和最后一个）”将表现最佳。

Answer 2

正如@AbhisekBansal指出的那样，快速排序按预期在大型阵列上运行，即> 1000项。在4K整数列表上运行快速排序后，快速排序在所有迭代中按预期执行（即，T * unsorted *＆lt; T * sorted *）：

输出（前4次迭代）：

Quicksort#1(unsorted)
calls to exch(): 11466
calls to sort(): 5329
calls to partition(): 2664
calls to less(): 60092
Sorted?: true
Time to sort input: 0.006784 secs

Quicksort#2(presorted)
calls to exch(): 3999
calls to sort(): 7999
calls to partition(): 3999
calls to less(): 8005998
Sorted?: true
Time to sort input: 0.079226 secs

Quicksort#1(unsorted)
calls to exch(): 11466
calls to sort(): 5329
calls to partition(): 2664
calls to less(): 60092
Sorted?: true
Time to sort input: 0.001649 secs

Quicksort#2(presorted)
calls to exch(): 3999
calls to sort(): 7999
calls to partition(): 3999
calls to less(): 8005998
Sorted?: true
Time to sort input: 0.079353 secs

Quicksort#1(unsorted)
calls to exch(): 11466
calls to sort(): 5329
calls to partition(): 2664
calls to less(): 60092
Sorted?: true
Time to sort input: 0.001680 secs

Quicksort#2(presorted)
calls to exch(): 3999
calls to sort(): 7999
calls to partition(): 3999
calls to less(): 8005998
Sorted?: true
Time to sort input: 0.079331 secs

Quicksort#1(unsorted)
calls to exch(): 11466
calls to sort(): 5329
calls to partition(): 2664
calls to less(): 60092
Sorted?: true
Time to sort input: 0.001625 secs

Quicksort#2(presorted)
calls to exch(): 3999
calls to sort(): 7999
calls to partition(): 3999
calls to less(): 8005998
Sorted?: true
Time to sort input: 0.079593 secs

Quicksort未排序列表比排序列表运行得更快

2 个答案: