QuickSort : C++

i was having a re look at quick sort.

Here is the code in c++ :

template< class T >
int partition(T a[], int p, int r){
 T x = a[r];
 int i = p - 1;
 for(int j = p;j < r;j++){
  if(a[j] <= x){
   i++;
   swap(a[i],a[j]);
  }
 }
 swap(a[i+1] , a[r]);
 return i + 1;
}


template< class T >
void quickSort(T a[], int p, int r){
 if(p < r){
  int q = partition(a, p , r);
  quickSort(a, p , q-1);
  quickSort(a, q+1 , r);
 }
}

The idea of quicksort is to take an array and divide it into partitions .
First a key is chosen . That is called the pivot . Here 'x' is the pivot .
Based on the value of 'x' other values in an array are put in 2 partitions .
One partition that contains values less than 'x' and other partition contains values greater than x .

Here i and j are used to mark the extent of these 2 partitions .

The beauty of the algorithm lies in the fact , how integers are used to manipulate partitions . 'i' is initially set to value that precedes a real boundary . 'j' is set to the first location in the array . Now as values are compared with 'x' ( the key)
if value is less than 'x' the partition extent marked by 'i' are increased , else the partition extent marked by 'j' is increased . In the first case where values of 'i' is less than 'x' and since 'i' now occupies what 'j' occupied the values at those indices are swapped .

the partition method does in place sorting of the array and the quickSort method is responsible for choosing partitons .