Algs4-2.2.23-3根据经验给出应该在何时为子数组切换到插入排序

2.2.23改进。用实验评估正文中所提到的归并排序的三项改进(请见练习2.2.11)的效果，并比较正文中实现的归并和练习2.2.10所实现的归并之间的性能。根据经验给出应该在何时为子数组切换到插入排序。
3)根据经验给出应该在何时为子数组切换到插入排序。

依据下图的试验结果，得出子数组长度在16至18时适合切换到插入排序。

public class E2d2d23d3
{
    public static double time (Double[] a,int subArrayLenTrunONInsertionSort)
    {
        Stopwatch timer =new Stopwatch();
        E2d2d11d3.sort(a,subArrayLenTrunONInsertionSort);
        return timer.elapsedTime();
    }
   
    public static double timeRandomInput(int N,int T,int subArrayLenTrunONInsertionSort)
    {
        double total =0.0;
        Double[] a=new Double[N];
        for (int t=0;t<T;t++)
        {
            for (int i=0;i<N;i++)
                a[i]=StdRandom.uniform();
            total+=time(a,subArrayLenTrunONInsertionSort);
        }
        return total/T;
    }//end timeRandomInput

   
    public static void main(String[] args)
    {
        int N=Integer.parseInt(args[0]);
        int T=Integer.parseInt(args[1]);
        int maxInsertLen=Integer.parseInt(args[2]);
       
        StdOut.printf("For %d random Doubles %d times sort ",N,T);

       for (int i=1;i<=maxInsertLen;i++)
       {
        double t=timeRandomInput(N,T,i);
        StdOut.printf("subArrayLenTrunONInsertionSort=%d  spend time=%.2f ",i,t);
       }
    }
}


public class E2d2d11d3
{
    public static void sort(Comparable[] a,int subArrayLenTrunONInsertionSort)
    {
        int len=a.length;
        Comparable[] aux=new Comparable[len];
        for(int i=0;i<len;i++)
            aux[i]=a[i];
        sort(a,aux,0,a.length-1,subArrayLenTrunONInsertionSort);
   }
    private static void sort(Comparable[] a,Comparable[] aux,int lo,int hi,int subArrayLenTrunONInsertionSort)
    {
        if ((hi-lo+1)<=subArrayLenTrunONInsertionSort)
        {
          insertionSort(a,lo,hi);
        }
        else
        {
          int mid=lo+(hi-lo)/2;
          sort(aux,a,lo,mid,subArrayLenTrunONInsertionSort);
          sort(aux,a,mid+1,hi,subArrayLenTrunONInsertionSort);
       
          if(!less(aux[mid+1],aux[mid]))
          {
              for(int i=lo;i<=hi;i++)
                  a[i]=aux[i];
              return;
          }
         
          merge(aux,a,lo,mid,hi);
        }
    }

   
    private static void merge(Comparable[] a,Comparable[] aux,int lo,int mid,int hi)
    {
      int i=lo;
      int j=mid+1;
      for(int k=lo;k<=hi;k++)
      {
           if (i>mid) aux[k]=a[j++];
           else if (j>hi) aux[k]=a[i++];
           else if (less(a[j],a[i])) aux[k]=a[j++];
           else                           aux[k]=a[i++];
      }
      }
    private static boolean less(Comparable v,Comparable w)
    { return v.compareTo(w)<0;}
   
    private static void exch(Comparable[] a,int i,int j)
    {
      Comparable t=a[i];
      a[i]=a[j];
      a[j]=t;
    }
   
    private static void insertionSort(Comparable[] a,int lo,int hi)
    {
      for (int i=lo+1;i<=hi;i++)
        for (int j=i;j>lo && less(a[j],a[j-1]);j--)
            exch(a,j,j-1);
    }
   
 public static boolean isSorted(Comparable[] a)
    {
      for(int i=1;i<a.length;i++)
        if(less(a[i],a[i-1])) return false;
      return true;
    }

}