Python中快速排序算法的解释

Question

I am following the lines of code for quicksort algorithm lesson, with these lines of codes:

def quicksort(array):
    if len(array) < 2:
        return array
    else:
        pivot = array[0] #Recursive case
        less = [i for i in array[1:] if i <= pivot] #Sub-array of all elements < pivot
        greater = [i for i in array[1:] if i > pivot] #sub array of all elements > pivot
        return quicksort(less) + [pivot] + quicksort(greater)

print(quicksort([1,15,7,3,9]))

I run the code successfully if the pivot is set on array[0] , but fails when I change to other number, say, 2,3. The error message is list index out of range .

Now I am confused how can it be out of range if there is 5 instances in the list? And why is the code not working if I change the pivot to other array positions instead of [0]? I thought that the pivot can be set to any other element position to speed up the process? Thanks!

Answer 1

The code will be called recursively, using smaller subsets of the array. The smaller subsets can have 2 elements, in which case, accessing to array[2] will lead to index out of range .

For example, in the above test, if you use array[2] as pivot, the code pivot by at array[2]=7 and recursively call quicksort([7,3]) and quicksort([15,9]) . If you use array[2] as pivot for both of these subarray, definitely it will be out of range. (see the code and output below).

Apart from the list index out of range error. I would like to raise 2 comments on your implementation:

• If using pivot other than array[0] , make sure to adjust the set array[1:] accordingly (it should be array[:p] + array[p+1:] )
• One advantage of quicksort over other sorting algorithm (eg mergesort) is that it can be implemented in-place and require O(log N) extra memory. The use of less and greater kind of defeat this advantage.

Code example:

def quicksort(array):
    print(array)
    if len(array) < 2:
        return array
    else:
        pivot = array[2] #Recursive case
        less = [i for i in array[1:] if i <= pivot] #Sub-array of all elements < pivot
        greater = [i for i in array[1:] if i > pivot] #sub array of all elements > pivot
        return quicksort(less) + [pivot] + quicksort(greater)

print(quicksort([1,15,7,3,9]))

Output:

[1, 15, 7, 3, 9]
[7, 3]
IndexError: list index out of range