Optimizing quick sort - algorithm

Question

I am implementing quick sort algorithm in java and here is the code :
public class quickSort {
private int array[];
private int length;
public void sort(int[] inputArr) {
if (inputArr == null || inputArr.length == 0) {
return;
}
this.array = inputArr;
length = inputArr.length;
quickSorter(0, length - 1);
}
private void quickSorter(int lowerIndex, int higherIndex) {
int i = lowerIndex;
int j = higherIndex;
// calculate pivot number, I am taking pivot as middle index number
int pivot = array[lowerIndex+(higherIndex-lowerIndex)/2];
// Divide into two arrays
while (i <= j) {
while (array[i] < pivot) {
i++;
}
while (array[j] > pivot) {
j--;
}
if (i <= j) {
exchangeNumbers(i, j);
//move index to next position on both sides
i++;
j--;
}
}
// call quickSort() method recursively
if (lowerIndex < j)
quickSorter(lowerIndex, j);
if (i < higherIndex)
quickSorter(i, higherIndex);
}
private void exchangeNumbers(int i, int j) {
int temp = array[i];
array[i] = array[j];
array[j] = temp;
}
}
Then I implement it with (median of three)
public class quickSort {
private int array[];
private int length;
public void sort(int[] inputArr) {
if (inputArr == null || inputArr.length == 0) {
return;
}
this.array = inputArr;
length = inputArr.length;
quickSorter(0, length - 1);
}
private void quickSorter(int lowerIndex, int higherIndex) {
int i = lowerIndex;
int j = higherIndex;
int mid = lowerIndex+(higherIndex-lowerIndex)/2;
if (array[i]>array[mid]){
exchangeNumbers( i, mid);
}
if (array[i]>array[j]){
exchangeNumbers( i, j);
}
if (array[j]<array[mid]){
exchangeNumbers( j, mid);
}
int pivot = array[mid];
// Divide into two arrays
while (i <= j) {
while (array[i] < pivot) {
i++;
}
while (array[j] > pivot) {
j--;
}
if (i <= j) {
exchangeNumbers(i, j);
//move index to next position on both sides
i++;
j--;
}
}
// call quickSort() method recursively
if (lowerIndex < j)
quickSorter(lowerIndex, j);
if (i < higherIndex)
quickSorter(i, higherIndex);
}
private void exchangeNumbers(int i, int j) {
int temp = array[i];
array[i] = array[j];
array[j] = temp;
}
}
and the testing main :
public static void main(String[] args) {
File number = new File ("f.txt");
final int size = 10000000;
try{
quickSortOptimize opti = new quickSortOptimize();
quickSort s = new quickSort();
PrintWriter printWriter = new PrintWriter(number);
for (int i=0;i<size;i++){
printWriter.println((int)(Math.random()*100000));
}
printWriter.close();
Scanner in = new Scanner (number);
int [] arr1 = new int [size];
for (int i=0;i<size;i++){
arr1[i]=Integer.parseInt(in.nextLine());
}
long a=System.currentTimeMillis();
opti.sort(arr1);
long b=System.currentTimeMillis();
System.out.println("Optimaized quicksort: "+(double)(b-a)/1000);
in.close();
int [] arr2 = new int [size];
Scanner in2= new Scanner(number);
for (int i=0;i<size;i++){
arr2[i]=Integer.parseInt(in2.nextLine());
}
long c=System.currentTimeMillis();
s.sort(arr2);
long d=System.currentTimeMillis();
System.out.println("normal Quicksort: "+(double)(d-c)/1000);
}catch (Exception ex){ex.printStackTrace();}
}
The problem is that this method of optimization should improve performance by 5%
but, what happens actually is that I have done this test many times and almost always getting better result on normal quicksort that optimized one
so what is wrong with the second implementation

Answer 1

A median of three (or more) will usually be slower for input that's randomly ordered.
A median of three is intended to help prevent a really bad case from being quite as horrible. There are ways of making it pretty bad anyway, but at least avoids the problem for a few common orderings--e.g., selecting the first element as the pivot can produce terrible results if/when (most of) the input is already ordered.