C randomized pivot quicksort (improving the partition function)

Question

I\'m a computer science student (just started), I was working on writing from pseudocode a randomized pivot version of Quicksort. I\'ve written and tested it, and it all wor

Answer 1

This is the pseudo code of partition() from Introduction to Algorithms , which is called Lomuto's Partitioning Algorithm, and there's a good explanation below it in the book.

PARTITION(A, p, r)
1 x ← A[r]
2 i ← p - 1
3 for j ← p to r - 1
4   do if A[j] ≤ x
5       then i ←i + 1
6           exchange A[i] ↔ A[j]
7 exchange A[i + 1] ↔ A[r]
8 return i +1

You can implement a randomized partition implementation easily based on the pseudo code above. As the comment pointed out, move the srand() out of the partition.

// srand(time(NULL));
int partition(int* arr, int start, int end)
{
    int pivot_index = start + rand() % (end - start + 1);
    int pivot = arr[pivot_index ];

    swap(&arr[pivot_index ], &arr[end]); // swap random pivot to end.
    pivot_index = end;
    int i = start -1;

    for(int j = start; j <= end - 1; j++)
    {
        if(arr[j] <= pivot)
        {
            i++;
            swap(&arr[i], &arr[j]);
        }
    }
    swap(&arr[i + 1], &arr[pivot_index]); // place the pivot to right place

    return i + 1;
}

And there is another partition method mentioned in the book, which is called Hoare's Partitioning Algorithm, the pseudo code is as below:

Hoare-Partition(A, p, r)
x = A[p]
i = p - 1
j = r + 1
while true
    repeat
        j = j - 1
    until A[j] <= x
    repeat
        i = i + 1
    until A[i] >= x
    if i < j
        swap( A[i], A[j] )
    else
        return j

After the partition, every element in A[p...j] ≤ every element in A[j+1...r]. So the quicksort would be:

QUICKSORT (A, p, r)
if p < r then
 q = Hoare-Partition(A, p, r)
 QUICKSORT(A, p, q)
 QUICKSORT(A, q+1, r)