Quick Sort Algorithm in DSA Python - Build from Scratch

Quick Sort Algorithm

📖 Scenario: You are helping a librarian organize a list of book IDs in ascending order. The librarian wants to use a fast method called Quick Sort to sort the list efficiently.

🎯 Goal: Build a program that sorts a list of numbers using the Quick Sort algorithm step-by-step.

📋 What You'll Learn

Create a list of integers called book_ids with exact values

Create a variable called pivot to select the pivot element

Write the core Quick Sort logic using recursion and list comprehensions

Print the sorted list of book_ids

💡 Why This Matters

🌍 Real World

Quick Sort is used in many software systems to sort data quickly, such as organizing files, searching databases, or arranging items in apps.

💼 Career

Understanding Quick Sort helps in coding interviews and building efficient programs that handle large amounts of data.

1

Create the list of book IDs

Create a list called book_ids with these exact integers in this order: 34, 7, 23, 32, 5, 62

DSA Python

# Create the list of book IDs
# Your code here

Hint

Use square brackets [] to create a list and separate numbers with commas.

2

Select the pivot element

Create a variable called pivot and set it to the middle element of book_ids using the index len(book_ids) // 2

DSA Python

book_ids = [34, 7, 23, 32, 5, 62]
# Select the pivot element
# Your code here

Hint

Use len(book_ids) // 2 to find the middle index and assign the element at that index to pivot.

3

Write the Quick Sort function

Define a function called quick_sort that takes a list arr and returns the sorted list using recursion and list comprehensions. Use pivot = arr[len(arr) // 2], then create left, middle, and right lists by comparing elements to pivot. Return quick_sort(left) + middle + quick_sort(right). If arr has length less than or equal to 1, return arr.

DSA Python

book_ids = [34, 7, 23, 32, 5, 62]
pivot = book_ids[len(book_ids) // 2]
# Define the quick_sort function
# Your code here

Hint

Use recursion to sort the left and right parts, and combine them with the middle.

4

Print the sorted list

Call the quick_sort function with book_ids and print the result.

DSA Python

book_ids = [34, 7, 23, 32, 5, 62]
pivot = book_ids[len(book_ids) // 2]

def quick_sort(arr):
    if len(arr)  pivot]
    return quick_sort(left) + middle + quick_sort(right)

# Print the sorted list
# Your code here

Hint

Use print(quick_sort(book_ids)) to show the sorted list.

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