快速排序未排序列表运行速度快于已排序列表

Question

我得到奇怪的计时结果与第一个元素枢轴快速排序。我的代码首先对一个未排序的、非随机化的整数列表运行快速排序。然后对之前排序过的列表进行排序。对于我所选择的枢轴，我期望快速排序在排序列表中比在未排序列表中运行得最差。我用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。快速排序第二次运行应该比快速排序第一次运行慢。

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。我实现计时器的方式肯定有问题。

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;
}
}

是否有一个怪癖与Java的nanoTime()调用我不知道?什么好主意吗?

Answer 1

"我们都知道快速排序在排序列表中比在未排序列表中运行得更糟糕":这是一个大胆的声明。

快速排序的效率取决于正确的枢轴选择:好的枢轴是这样的，它们以平衡的方式分割要排序的区域，因此过程保持二分类，这导致O(N.Lg(N))行为。相反，由于过程保持增量，导致最大不平衡的不良选择可能导致二次O(N²)退化。

Naïve枢轴选择策略，例如"第一个元素"，确实会导致在排序序列上出现最坏的情况。但更明智的实现，如"三个(第一，中间和最后)的中位数"将执行最佳。

Answer 2

正如@AbhisekBansal指出的那样，快速排序在大型数组(即>1000个条目)上按预期运行。在对4K整数列表运行快速排序后，快速排序在所有迭代中都按预期执行(即T*unsorted*

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