Quick Sort Algorithm in DSA Python - Interactive Practice

Practice - 5 Tasks

1fill in blank

easy

Complete the code to select the pivot element as the last element of the list.

DSA Python

def quick_sort(arr):
    if len(arr) <= 1:
        return arr
    pivot = arr[[1]]
    left = [x for x in arr[:-1] if x <= pivot]
    right = [x for x in arr[:-1] if x > pivot]
    return quick_sort(left) + [pivot] + quick_sort(right)

Drag options to blanks, or click blank then click option'

A0

B-1

Clen(arr)

D1

Attempts:

3 left

💡 Hint

Common Mistakes

Using 0 as pivot index selects the first element, not the last.

Using len(arr) causes an index error because it's out of range.

The pivot is chosen as the last element, which is at index -1 in Python lists.

2fill in blank

medium

Complete the code to partition the list into elements less than or equal to the pivot.

DSA Python

left = [x for x in arr[:-1] if x [1] pivot]

Drag options to blanks, or click blank then click option'

A<=

B<

C==

D>

Attempts:

3 left

💡 Hint

Common Mistakes

Using '>' puts larger elements on the left, which is incorrect.

Using '==' only selects elements equal to pivot, missing smaller ones.

We want elements less than or equal to the pivot on the left side.

3fill in blank

hard

Fix the error in the recursive call to quick_sort on the right partition.

DSA Python

return quick_sort(left) + [pivot] + quick_sort([1])

Drag options to blanks, or click blank then click option'

Aarr

Barr[1:]

Carr[:-1]

Dright

Attempts:

3 left

💡 Hint

Common Mistakes

Using arr[:-1] re-sorts the whole list except last element.

Using arr[1:] excludes the first element but not partitioned correctly.

The right partition is stored in the variable 'right', so we must call quick_sort(right).

4fill in blank

hard

Fill both blanks to complete the partitioning of the list into left and right parts.

DSA Python

left = [x for x in arr[:-1] if x [1] pivot]
right = [x for x in arr[:-1] if x [2] pivot]

Drag options to blanks, or click blank then click option'

A<=

B>

C<

D==

Attempts:

3 left

💡 Hint

Common Mistakes

Using '<' for left excludes elements equal to pivot.

Using '<=' for right includes elements that should be on left.

Left contains elements less than or equal to pivot; right contains elements greater than pivot.

5fill in blank

hard

Fill all three blanks to complete the quick sort function with pivot selection, partitioning, and recursive calls.

DSA Python

def quick_sort(arr):
    if len(arr) <= 1:
        return arr
    pivot = arr[[1]]
    left = [x for x in arr[:-1] if x [2] pivot]
    right = [x for x in arr[:-1] if x [3] pivot]
    return quick_sort(left) + [pivot] + quick_sort(right)

Drag options to blanks, or click blank then click option'

A-1

B<=

C>

D0

Attempts:

3 left

💡 Hint

Common Mistakes

Using 0 as pivot index selects first element, not last.

Mixing up comparison operators in partitioning.

Pivot is last element (index -1), left has elements <= pivot, right has elements > pivot.

Practice

1. What is the main idea behind the Quick Sort algorithm?

easy

A. Sort the list by inserting elements into their correct position one by one

B. Sort the list by repeatedly swapping adjacent elements

C. Divide the list into smaller parts using a pivot and sort them recursively

D. Sort the list by merging two sorted halves

Solution

1. Step 1: Understand Quick Sort approach

   Quick Sort picks a pivot element and divides the list into parts smaller and larger than the pivot.

2. Step 2: Recursive sorting

   It then sorts these parts recursively, combining them to get the sorted list.

3. Final Answer:

   Divide the list into smaller parts using a pivot and sort them recursively -> Option C

4. Quick Check:

   Quick Sort = Divide and conquer [OK]

Hint: Remember: pivot divides list, then sort parts recursively [OK]

Common Mistakes:

• Confusing Quick Sort with Bubble Sort
• Thinking Quick Sort merges sorted halves
• Assuming Quick Sort inserts elements one by one

2. Which of the following is the correct way to define the partition function header in Python for Quick Sort?

easy

A. def partition(arr, low, high):

B. def partition(arr):

C. def partition(low, high):

D. def partition(arr, pivot):

Solution

1. Step 1: Identify required parameters

   The partition function needs the array and the current low and high indices to work on a sublist.

2. Step 2: Match function signature

   Only def partition(arr, low, high): correctly includes all three parameters: arr, low, and high.

3. Final Answer:

   def partition(arr, low, high): -> Option A

4. Quick Check:

   Partition needs array and index bounds [OK]

Hint: Partition needs array plus low and high indexes [OK]

Common Mistakes:

• Omitting low and high parameters
• Using pivot as parameter instead of indices
• Defining partition with only one parameter

3. What will be the output of the following code snippet?

def quick_sort(arr, low, high):
    if low < high:
        pi = partition(arr, low, high)
        quick_sort(arr, low, pi - 1)
        quick_sort(arr, pi + 1, high)

def partition(arr, low, high):
    pivot = arr[high]
    i = low - 1
    for j in range(low, high):
        if arr[j] <= pivot:
            i += 1
            arr[i], arr[j] = arr[j], arr[i]
    arr[i + 1], arr[high] = arr[high], arr[i + 1]
    return i + 1

arr = [3, 6, 8, 10, 1, 2, 1]
quick_sort(arr, 0, len(arr) - 1)
print(arr)

medium

A. [1, 1, 2, 3, 6, 8, 10]

B. [10, 8, 6, 3, 2, 1, 1]

C. [3, 6, 8, 10, 1, 2, 1]

D. [1, 2, 1, 3, 6, 8, 10]

Solution

1. Step 1: Understand partition and recursive calls

   The partition function places the pivot in correct position and divides array into smaller and larger parts. Quick sort recursively sorts these parts.

2. Step 2: Trace sorting of given array

   Starting with [3,6,8,10,1,2,1], after full recursion, the array becomes sorted ascending: [1,1,2,3,6,8,10].

3. Final Answer:

   [1, 1, 2, 3, 6, 8, 10] -> Option A

4. Quick Check:

   Quick Sort output = sorted array ascending [OK]

Hint: Quick Sort outputs sorted array ascending by default [OK]

Common Mistakes:

• Thinking Quick Sort sorts descending by default
• Confusing original array with sorted output
• Ignoring pivot placement effect

4. Identify the error in this Quick Sort partition function:

def partition(arr, low, high):
    pivot = arr[low]
    i = low + 1
    for j in range(low + 1, high):
        if arr[j] < pivot:
            arr[i], arr[j] = arr[j], arr[i]
            i += 1
    arr[low], arr[i-1] = arr[i-1], arr[low]
    return i-1

medium

A. Swapping inside the loop is incorrect

B. Pivot should be arr[high] instead of arr[low]

C. Return statement should return 'i' instead of 'i-1'

D. The for loop should include 'high' index by using range(low + 1, high + 1)

Solution

1. Step 1: Check loop range for partitioning

   The for loop uses range(low + 1, high), which excludes the 'high' index element. It should include 'high' to consider the pivot's correct position.

2. Step 2: Correct loop range

   Changing to range(low + 1, high + 1) includes the last element, ensuring all elements are compared to pivot.

3. Final Answer:

   The for loop should include 'high' index by using range(low + 1, high + 1) -> Option D

4. Quick Check:

   Loop must cover full sublist including high index [OK]

Hint: Loop must include high index to compare all elements [OK]

Common Mistakes:

• Forgetting to include last element in loop
• Changing pivot position unnecessarily
• Returning wrong index after partition

5. You want to sort a list of strings by their length using Quick Sort. Which modification to the partition function is correct?

def partition(arr, low, high):
    pivot = arr[high]
    i = low - 1
    for j in range(low, high):
        if ???:
            i += 1
            arr[i], arr[j] = arr[j], arr[i]
    arr[i + 1], arr[high] = arr[high], arr[i + 1]
    return i + 1

What should replace ??? to sort by string length?

hard

A. arr[j].startswith(pivot)

B. len(arr[j]) <= len(pivot)

C. len(arr[j]) >= len(pivot)

D. arr[j] <= pivot

Solution

1. Step 1: Understand sorting by string length

   To sort strings by length, compare lengths of elements, not the strings themselves.

2. Step 2: Replace condition with length comparison

   Using len(arr[j]) <= len(pivot) ensures elements with length less or equal to pivot's length go left.

3. Final Answer:

   len(arr[j]) <= len(pivot) -> Option B

4. Quick Check:

   Compare lengths to sort strings by length [OK]

Hint: Compare lengths, not strings, to sort by length [OK]

Common Mistakes:

• Comparing strings lexicographically instead of length
• Using >= instead of <= causing reverse order
• Using unrelated string methods like startswith