I’ve been trying to understand quick sort by implementing it myself in Python using the left and right pointer method. I can’t seem to get it to work and looking at visualizations online, I’m failing to understand how quicksort works when operating on a list of length 2. According to most sources I’ve read, you should select a pivot and your left and right pointers should not include that pivot value when moving left/right. When a list is of length 2, you select a pivot and are left with a list of length 1 and left/right immediately meet. How would quicksort ever sort the input [5,4]?

Here is the Python code I have written:

def quicksort(arr, low, high):
  if low < high:
    pivot_index = partition(arr, low, high)
    quicksort(arr, low, pivot_index-1)
    quicksort(arr, pivot_index+1, high)

  return arr

def partition(arr, low, high):
  # select last element as pivot
  pivot_index = high
  pivot = arr[high]
  left_wall = low
  # exclude pivot from left/right searching
  right_wall = high-1

  # keep searching until next swap point found
  while left_wall < right_wall:
    # if left wall value is not greater than pivot, keep searching
    while arr[left_wall] <= pivot:
      left_wall += 1
    # if right wall value is not less than pivot, keep searching
    while arr[right_wall] >= pivot:
      right_wall -= 1
    if left_wall < right_wall:
      # perform swap
      temp_left_wall = arr[left_wall]
      arr[left_wall] = arr[right_wall]
      arr[right_wall] = temp_left_wall

  # swap pivot with right wall
  arr[pivot_index] = arr[right_wall]
  arr[right_wall] = pivot
  return right_wall


quicksort([5,4,3,2],0,3)

Can someone help me understand what I am not understanding about the quicksort process?