Counting Sort Algorithm in DSA Python - Build from Scratch

Counting Sort Algorithm

📖 Scenario: You work in a warehouse where boxes are labeled with numbers from 0 to 9. You want to sort these boxes quickly by their labels using a simple counting method.

🎯 Goal: Build a program that sorts a list of box labels using the counting sort algorithm. You will count how many times each label appears, then use that to create a sorted list.

📋 What You'll Learn

Create a list called boxes with the exact values: [4, 2, 2, 8, 3, 3, 1]

Create a list called count with 10 zeros to count labels from 0 to 9

Use a for loop with variable label to count each label in boxes

Create a sorted list called sorted_boxes using the counts

Print the sorted_boxes list as the final output

💡 Why This Matters

🌍 Real World

Counting sort is useful in situations like sorting labeled boxes, grades, or small-range numbers quickly and simply.

💼 Career

Understanding counting sort helps in jobs involving data processing, inventory management, and optimizing sorting tasks.

1

Create the list of box labels

Create a list called boxes with these exact values: [4, 2, 2, 8, 3, 3, 1]

DSA Python

# Create the list of box labels called boxes
# Your code here

Hint

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

2

Create the count list for labels 0 to 9

Create a list called count with 10 zeros to count labels from 0 to 9

DSA Python

boxes = [4, 2, 2, 8, 3, 3, 1]
# Create a list called count with 10 zeros
# Your code here

Hint

Use [0] * 10 to create a list of ten zeros.

3

Count each label in the boxes list

Use a for loop with variable label to count each label in boxes. Increase count[label] by 1 for each label.

DSA Python

boxes = [4, 2, 2, 8, 3, 3, 1]
count = [0] * 10
# Count each label in boxes
# Your code here

Hint

Loop over each label in boxes and add 1 to the corresponding index in count.

4

Create the sorted list and print it

Create a list called sorted_boxes. Use a for loop with variable number from 0 to 9. For each number, add it to sorted_boxes count[number] times. Then print sorted_boxes.

DSA Python

boxes = [4, 2, 2, 8, 3, 3, 1]
count = [0] * 10
for label in boxes:
    count[label] += 1
# Create sorted_boxes list and fill it using count
# Print sorted_boxes
# Your code here

Hint

Use extend to add multiple copies of number to sorted_boxes. Then print the final sorted list.

Practice

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

easy

A. Swapping adjacent elements if they are in wrong order

B. Comparing each element with every other element to sort

C. Dividing the list into halves and sorting recursively

D. Counting the occurrences of each element and using that to place elements in order

Solution

1. Step 1: Understand Counting Sort principle

   Counting Sort counts how many times each value appears in the list.

2. Step 2: Use counts to place elements

   It then uses these counts to place elements directly in the sorted order without comparisons.

3. Final Answer:

   Counting the occurrences of each element and using that to place elements in order -> Option D

4. Quick Check:

   Counting occurrences = A [OK]

Hint: Counting Sort uses counts, not comparisons, to sort [OK]

Common Mistakes:

• Thinking Counting Sort compares elements
• Confusing Counting Sort with comparison-based sorts
• Assuming Counting Sort works on all data types

2. Which of the following is the correct way to initialize the count array for Counting Sort in Python for input values ranging from 0 to 5?

easy

A. count = [0] * 6

B. count = [0] * 5

C. count = [null] * 6

D. count = []

Solution

1. Step 1: Determine count array size

   For values 0 to 5 inclusive, we need 6 slots (0,1,2,3,4,5).

2. Step 2: Initialize count array with zeros

   Using [0] * 6 creates a list of six zeros to count occurrences.

3. Final Answer:

   count = [0] * 6 -> Option A

4. Quick Check:

   Length 6 with zeros = D [OK]

Hint: Count array size = max value + 1 [OK]

Common Mistakes:

• Using wrong size for count array
• Initializing with null instead of 0
• Leaving count array empty

3. What will be the output of the following Python code using Counting Sort on the list [4, 2, 2, 8, 3, 3, 1]?

def counting_sort(arr):
    max_val = max(arr)
    count = [0] * (max_val + 1)
    for num in arr:
        count[num] += 1
    sorted_arr = []
    for i in range(len(count)):
        sorted_arr.extend([i] * count[i])
    return sorted_arr

print(counting_sort([4, 2, 2, 8, 3, 3, 1]))

medium

A. [1, 2, 2, 3, 3, 4, 8]

B. [8, 4, 3, 3, 2, 2, 1]

C. [1, 2, 3, 4, 8]

D. [0, 1, 2, 2, 3, 3, 4, 8]

Solution

1. Step 1: Count occurrences of each number

   Count array for max_val=8: counts for 1=1, 2=2, 3=2, 4=1, 8=1, others=0.

2. Step 2: Build sorted list using counts

   Extend sorted_arr with each number repeated by its count: [1, 2, 2, 3, 3, 4, 8].

3. Final Answer:

   [1, 2, 2, 3, 3, 4, 8] -> Option A

4. Quick Check:

   Sorted list matches counting sort output = B [OK]

Hint: Counting Sort output is sorted list with duplicates in order [OK]

Common Mistakes:

• Forgetting to repeat elements by their count
• Returning unsorted or reversed list
• Including zeros for missing elements

4. The following code attempts to implement Counting Sort but has a bug. What is the error?

def counting_sort_bug(arr):
    max_val = max(arr)
    count = [0] * max_val
    for num in arr:
        count[num] += 1
    sorted_arr = []
    for i in range(len(count)):
        sorted_arr.extend([i] * count[i])
    return sorted_arr

print(counting_sort_bug([3, 1, 2, 3]))

medium

A. Count array initialized with zeros incorrectly

B. Loop to build sorted_arr uses wrong range

C. Count array size is too small, missing last element count

D. Function does not return anything

Solution

1. Step 1: Check count array size

   Count array size is max_val, but should be max_val + 1 to include max element index.

2. Step 2: Understand impact on counting

   Missing last index causes error when counting max element (3), leading to IndexError or wrong counts.

3. Final Answer:

   Count array size is too small, missing last element count -> Option C

4. Quick Check:

   Count array size = max_val + 1 [OK]

Hint: Count array size must be max value + 1 [OK]

Common Mistakes:

• Using max_val instead of max_val + 1 for count array size
• Ignoring IndexError from out-of-range access
• Not initializing count array properly

5. You have a list of exam scores ranging from 0 to 100, but some scores are missing. How can you modify Counting Sort to efficiently sort this list and also find how many students scored exactly 75?

hard

A. Use a comparison sort and count 75s during sorting

B. Use Counting Sort normally, then check count[75] for number of students scoring 75

C. Sort with Counting Sort and then scan sorted list to count 75s

D. Use Counting Sort but ignore counts for missing scores

Solution

1. Step 1: Apply Counting Sort on scores 0-100

   Create count array of size 101, count occurrences of each score.

2. Step 2: Use count array to find number of 75 scores

   Count at index 75 directly gives number of students scoring 75 without scanning sorted list.

3. Final Answer:

   Use Counting Sort normally, then check count[75] for number of students scoring 75 -> Option B

4. Quick Check:

   Counting array index = score count, access directly [OK]

Hint: Counting array index = score count, access directly [OK]

Common Mistakes:

• Scanning sorted list instead of using count array
• Ignoring missing scores in count array
• Using slower comparison sorts unnecessarily