Counting Sort Algorithm in DSA C# - Practice Problems & Challenges

Challenge - 5 Problems

❓ Predict Output

intermediate

Output of Counting Sort on a small array

What is the output of the following C# code that uses counting sort on the array [4, 2, 2, 8, 3, 3, 1]?

DSA C#

using System;

class Program {
    static void CountingSort(int[] arr) {
        int max = arr[0];
        for (int i = 1; i < arr.Length; i++) {
            if (arr[i] > max) max = arr[i];
        }
        int[] count = new int[max + 1];
        for (int i = 0; i < arr.Length; i++) {
            count[arr[i]]++;
        }
        int index = 0;
        for (int i = 0; i < count.Length; i++) {
            while (count[i] > 0) {
                arr[index++] = i;
                count[i]--;
            }
        }
    }

    static void Main() {
        int[] arr = {4, 2, 2, 8, 3, 3, 1};
        CountingSort(arr);
        foreach (int num in arr) {
            Console.Write(num + " ");
        }
    }
}

A 1 2 2 3 3 4 8

B 8 4 3 3 2 2 1

C 1 2 3 4 8

D 1 2 2 3 3 4

💡 Hint

Counting sort arranges numbers from smallest to largest by counting occurrences.

The counting sort counts how many times each number appears, then writes them back in order. The array is sorted ascending: 1 2 2 3 3 4 8.

🧠 Conceptual

intermediate

Counting Sort Stability Property

Which statement best describes the stability property of counting sort?

A Counting sort always reverses the order of equal elements.

B Counting sort maintains the relative order of equal elements.

C Counting sort does not guarantee any order for equal elements.

D Counting sort sorts elements only by their index positions.

💡 Hint

Stability means equal elements keep their original order after sorting.

Counting sort is stable because it places elements in output array in the order they appear in input when counts are processed.

🔧 Debug

advanced

Identify the error in this counting sort implementation

What error will this C# counting sort code produce when run on array [3, 1, 2]?

DSA C#

void CountingSort(int[] arr) {
    int max = arr[0];
    for (int i = 1; i < arr.Length; i++) {
        if (arr[i] > max) max = arr[i];
    }
    int[] count = new int[max + 1];
    for (int i = 0; i < arr.Length; i++) {
        count[arr[i]]++;
    }
    int index = 0;
    for (int i = 0; i < count.Length; i++) {
        while (count[i] > 0) {
            arr[index++] = i;
            count[i]--;
        }
    }
}

A IndexOutOfRangeException

B No error, sorts correctly

C NullReferenceException

D DivideByZeroException

💡 Hint

Check the size of the count array and the maximum value used as index.

The count array size is max, but max is the largest value in arr. Since arrays are zero-indexed, count[max] is out of range causing IndexOutOfRangeException.

❓ Predict Output

advanced

Counting Sort Output with Negative Numbers

What happens when you run counting sort on array [-1, 2, 0, -1] with the standard counting sort code that assumes only non-negative integers?

DSA C#

int[] arr = {-1, 2, 0, -1};
CountingSort(arr); // standard counting sort code without handling negatives

A Throws NullReferenceException

B Sorts correctly as -1 0 2 -1

C Throws IndexOutOfRangeException

D Sorts correctly as -1 -1 0 2

💡 Hint

Counting sort uses array indices for counts, negative indices are invalid.

Negative numbers cause indexing errors because array indices cannot be negative, so it throws IndexOutOfRangeException.

🚀 Application

expert

Counting Sort Time Complexity Analysis

Given an input array of size n with maximum value k, what is the time complexity of counting sort?

A O(n log n)

B O(k log n)

C O(n * k)

D O(n + k)

💡 Hint

Counting sort counts occurrences and then writes output based on counts.

Counting sort runs in O(n + k) time because it counts each element once and iterates over the count array of size k.

Practice

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

easy

A. Count the occurrences of each element and use counts to place elements in order

B. Compare each element with every other element to sort

C. Divide the array into halves and sort recursively

D. Swap adjacent elements if they are in wrong order repeatedly

Solution

1. Step 1: Understand Counting Sort principle

   Counting sort counts how many times each value appears in the input.

2. Step 2: Use counts to place elements

   These counts help to directly place elements in the sorted output without comparisons.

3. Final Answer:

   Count the occurrences of each element and use counts to place elements in order -> Option A

4. Quick Check:

   Counting occurrences = A [OK]

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

Common Mistakes:

• Thinking counting sort compares elements
• Confusing counting sort with merge sort
• Assuming counting sort works on all data types

2. Which of the following is the correct way to declare the count array for counting sort in C# if the input range is from 0 to 9?

easy

A. int[] count = new int[0];

B. int[] count = new int[10];

C. int[] count = new int[11];

D. int count = new int[9];

Solution

1. Step 1: Determine size of count array

   For range 0 to 9, we need 10 slots to count each number.

2. Step 2: Correct C# syntax for array declaration

   Use int[] count = new int[10]; to create an array of size 10.

3. Final Answer:

   int[] count = new int[10]; -> Option B

4. Quick Check:

   Array size = max value + 1 = 10 [OK]

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

Common Mistakes:

• Using size less than max value + 1
• Declaring count as single int instead of array
• Using incorrect array size causing index errors

3. What will be the output of the following C# code snippet using counting sort on array int[] arr = {4, 2, 2, 8, 3, 3, 1}?

int max = 8;
int[] count = new int[max + 1];
int[] output = new int[arr.Length];

// Count occurrences
foreach (int num in arr) count[num]++;

// Modify count array
for (int i = 1; i <= max; i++) count[i] += count[i - 1];

// Build output
for (int i = arr.Length - 1; i >= 0; i--) {
    output[count[arr[i]] - 1] = arr[i];
    count[arr[i]]--;
}

// Print output
foreach (int num in output) Console.Write(num + " ");

medium

A. 1 2 2 3 3 4 8

B. 8 4 3 3 2 2 1

C. 1 3 2 2 3 4 8

D. 2 2 3 3 4 8 1

Solution

1. Step 1: Count occurrences of each number

   Count array after counting: [0,1,2,2,1,0,0,0,1]

2. Step 2: Modify count array to cumulative counts

   Cumulative count: [0,1,3,5,6,6,6,6,7]

3. Step 3: Place elements in output using counts

   Placing elements from right to left gives sorted array: 1 2 2 3 3 4 8

4. Final Answer:

   1 2 2 3 3 4 8 -> Option A

5. Quick Check:

   Sorted array = 1 2 2 3 3 4 8 [OK]

Hint: Use cumulative counts to place elements from right [OK]

Common Mistakes:

• Not using cumulative counts before placing elements
• Placing elements from left to right causing wrong order
• Off-by-one errors in indexing output

4. Identify the error in this counting sort code snippet and choose the correct fix:

int max = 5;
int[] count = new int[max];
int[] arr = {1, 4, 3, 2, 5};

foreach (int num in arr) {
    count[num]++;
}

medium

A. Initialize count array with zeros explicitly

B. Change foreach loop to for loop

C. Change count array size to max + 1 to avoid index out of range

D. No error, code is correct

Solution

1. Step 1: Analyze count array size

   Count array size is 5, but max value is 5, so index 5 is out of range.

2. Step 2: Fix by increasing count array size

   Count array should be size max + 1 = 6 to include index 5 safely.

3. Final Answer:

   Change count array size to max + 1 to avoid index out of range -> Option C

4. Quick Check:

   Array size = max + 1 to cover all indices [OK]

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

Common Mistakes:

• Using count array size equal to max value only
• Ignoring index out of range exceptions
• Assuming default array size is enough

5. You have an array int[] arr = {5, 3, 0, 2, 3, 5, 1, 4} and want to sort it using counting sort. However, the array may contain negative numbers in future. How should you modify the counting sort algorithm to handle negative numbers correctly?

hard

A. Sort negative and positive numbers separately and then merge

B. Ignore negative numbers as counting sort only works for positive numbers

C. Use a dictionary instead of an array for counts

D. Shift all numbers by adding the absolute value of the minimum negative number before counting

Solution

1. Step 1: Identify problem with negative numbers

   Counting sort uses array indices as counts, negative indices are invalid.

2. Step 2: Shift numbers to non-negative range

   Add absolute value of minimum negative number to all elements to make them non-negative.

3. Step 3: Apply counting sort on shifted values

   Sort shifted values, then shift back to original values after sorting.

4. Final Answer:

   Shift all numbers by adding the absolute value of the minimum negative number before counting -> Option D

5. Quick Check:

   Shift negatives to zero or above before counting [OK]

Hint: Shift negatives to zero or above before counting [OK]

Common Mistakes:

• Trying to use negative indices in count array
• Ignoring negative values in input
• Using dictionary without sorting logic