Quicksort incorrect results - c++

Question

I have this quicksort code which I want to troubleshoot. There is this code that I have changed in the partition. Have tried selected the pivot element as the median of the array. But still it does not give me the correct output. Here I have different four types of arrays that I have created dynamically and trying to sort them. There are quicksort applied four times.
int counter=0, comparison=0;
void QUICKSORT(int *,int,int);
int PARTITION(int * ,int,int);
int values(float l);
int main(){
int i,n,q;
cout<<"Enter number of elements:";
cin>>n;
int* a = new int[ n ];
for(int p=1;p<=n;p++)
{
q = rand() % (n*100) ;
a[p]=q;
}
cout<<"\nThe elements od the original array are:\n\n";
for(i=1;i<=n;i++)
cout<<a[i]<<" ";
clock_t tStart = clock();
QUICKSORT(a,1,n);
cout<<"\nThe elements of the sorted array are:\n\n";
for(i=1;i<=n;i++)
cout<<a[i]<<" ";
}
// function for the generation of random poisson values. This function is called as many times
// as the array size decided by the user
int values(float l)
{
for (int i=0;i<1000;i++)
{
float L=exp(-l);
float k=0;
float p=1;
//begin while
do{
k=k+1;
double u = rand() / (double)RAND_MAX;
p=p*u;
} while (p>L);
return k-1;
}
}
//}
void QUICKSORT(int *a,int p,int r){
int q;
if(p<r){
q=PARTITION(a,p,r);
QUICKSORT(a,p,q-1);
QUICKSORT(a,q+1,r);
}
}
int PARTITION(int *a,int p,int r){
counter++;
// cout<<" first a " <<a[p]<<endl;
// cout<<" second a : "<<a[r-1]<<endl;
int x=(a[r]+a[p])/2;
//int x=a[r];
int i = p-1,temp,j;
for(j=p;j<=r-1;j++){
if(a[j]<=x){
i=i+1;
temp=a[i];
a[i]=a[j];
a[j]=temp;
}
}
temp=a[i+1];
a[i+1]=a[r];
a[r]=temp;
return(i+1);
}

Answer 1

At a glance..
QUICKSORT(a,p,q-1);
QUICKSORT(a,q+1,r);
That looks like it should be either:
QUICKSORT(a,p,q);
QUICKSORT(a,q+1,r);
or:
QUICKSORT(a,p,q-1);
QUICKSORT(a,q,r);
But also that partition method looks very questionable. Even if it successfully finds the median I doubt it's worth the effort. The point of quicksort is to sort with as few comparisons as possible, so looping through each entire subarray to find the median kind of defeats that purpose, and is overkill. I would suggest picking three items: first, middle, last, and just using the median of those.