Quicksort implementation in Python

Question

I have written an implementation of Quicksort in Python. I am new to Python. Any suggestions for improvement or criticism on my use of Python?

def partition(a, lo, hi):
    i, j, v = lo+1, hi, a[lo]
    while(True):
        while(a[i] < v):
            i += 1
            if (i == hi): break    
        while(a[j] > v):
            j -= 1
            if (j == lo): break    
        if (i >= j): break            
        a[i], a[j] = a[j], a[i]    
    a[lo], a[j] = a[j], a[lo]
    return j

def sort(a, lo, hi):
    if (hi <= lo):
        return
    q = partition(a, lo, hi)
    sort(a, lo, q-1)
    sort(a, q+1, hi)
    assert isSorted(a, lo, hi)

def quick_sort(a):
    shuffle(a)
    sort(a, 0, len(a)-1)
    assert isSortedArray(a)

def isSorted(a, lo, hi):
    for i in range(lo, hi):
        if a[i+1] < a[i]:
            return False
    return True

def isSortedArray(a):
    for i in range(0, len(a)-1):
        if a[i+1] < a[i]:
            return False
    return True

Answer 1

When describing quicksort partitioning, your v is typically called the "pivot". The code would be clearer if you named the variable according to that convention.

You always choose a[lo] as the pivot. However, that produces pathological performance when the input array is already sorted.

I would prefer to see

while(a[i] < v):
      i += 1
      if (i == hi): break

… written as

while i < hi and a[i] < pivot:
    i += 1

---

Array index bounds usually work better when specified as inclusive-exclusive ranges, such that sort(a, lo, hi) means "sort a where lo ≤ index < hi". This is a common convention — you can see it in Python's range() and slicings. Also, Java's Arrays.sort(a, fromIndex, toIndex) works with inclusive-exclusive ranges.

Some nice properties of inclusive-exclusive ranges are:

• hi - lo gives you the number of elements in the range.
• When creating a range for the entire array a, hi is just len(a). You save a "-1".
• When splitting [lo, hi) into two consecutive ranges, it becomes [lo, mid) and [mid, hi). You save a "-1".
• In Python, you can conveniently write for i in range(lo, hi) for the most common type of iteration. (Admittedly, iterating backwards is uglier, but it's less common.)