Finding element of a given rank in an arbitrary array - algorithm

Question

What I am is doing is using a quicksort algorithm, so that my pivot element(which will always be the first element of the array gets positioned to its appropriate position in the sorted array and I am calling this method again until I do not position the element at a given rank. Is there a better solution?
Here is my code:
public static int arbitrary(int a[],int x,int y,int rank)//x and y are first and last indecies of the array
{
int j=y,temp;
if(x<y)
{
for(int i=y;i>x;i--)
{
if(a[i]>a[x])
{
temp=a[i];
a[i]=a[j];
a[j]=temp;
j--;
}
}
temp=a[x];
a[x]=a[j];
a[j]=temp;
//System.out.println("j is "+j);
if(j==rank)
return a[j];
else if(rank<j)
return arbitrary(a,x,j-1,rank);
else
return arbitrary(a,j+1,y,rank);
}
else
return 0;
}

Answer 1

The algorithm you have implemented is called Quickselect.
Just select a random pivot and to get rid of the worst case with O(n²) time complexity.
The expected runtime is now about 3.4n + o(n).
Quickselect is probably the best tradeoff between performance and simplicity.
An even more advanced pivot selection strategy results in 1.5n + o(n) expected time
(Floyd-Rivest Algorithm).
Fun Fact: With deterministic algorithms you can't go better than 2n. BFPRT for example needs about 2.95n to select the median.

Answer 2

Best way to find Rank element by using the QuickSort method:
In QuickSort, at every iteration you are able to get fixed one pivot element.
When the RankElement == PivotIndex, and break the condition and return the value.
public class FindRank {
public void find(int[] arr, int low, int high, int k) {
if (low < high) {
int pivot = partition(arr, low, high, k);
find(arr, low, pivot - 1, k);
find(arr, pivot + 1, high, k);
}
}
public int partition(int[] arr, int low, int high, int k) {
int pivotIndex = high;
while (low < high) {
while (low < high && arr[low] <= arr[pivotIndex]) {
low++;
}
while (low > high && arr[high] >= arr[pivotIndex]) {
high--;
}
if (low < high) {
swap(arr, low, high);
}
}
swap(arr, pivotIndex, high);
if (pivotIndex == k) {
System.out.println("Array Value:" + arr[k] + " index:" + k);
return k;
}
return high;
}
private void swap(int[] arr, int low, int high) {
int temp = arr[low];
arr[low] = arr[high];
arr[high] = temp;
}
}