Quick Sort - On log n complexity time

Quicksort is one of the advanced algorithms. It features a time complexity of O(n log n) and applies a divide & conquer strategy. This combination results in advanced algorithmic performance. Quicksort first divides a large array into two smaller sub-arrays: the low elements and the high elements. Quicksort can then recursively sort the sub-arrays.

The steps are:

1. Pick an element, called a pivot, from the array.
2. Reorder the array so that all elements with values less than the pivot come before the pivot, while all elements with values greater than the pivot come after it (equal values can go either way). After this partitioning, the pivot is in its final position. This is called the partition operation.
3. Recursively apply the above steps to the sub-array of elements with smaller values and separately to the sub-array of elements with greater values.

mutating func quickSort() -> Array<Element> {

func qSort(start startIndex: Int, _ pivot: Int) {
    
    if (startIndex < pivot) {
        let iPivot = qPartition(start: startIndex, pivot)
        qSort(start: startIndex, iPivot - 1)
        qSort(start: iPivot + 1, pivot)
    }
}
qSort(start: 0, self.endIndex - 1)
return self

}

mutating func qPartition(start startIndex: Int, _ pivot: Int) -> Int {

var wallIndex: Int = startIndex

//compare range with pivot
for currentIndex in wallIndex..<pivot {
    
    if self[currentIndex] <= self[pivot] {
        if wallIndex != currentIndex {
            swap(&self[currentIndex], &self[wallIndex])
        }
        
        //advance wall
        wallIndex += 1
    }
}

//move pivot to final position
if wallIndex != pivot {
    swap(&self[wallIndex], &self[pivot])
}
return wallIndex
}