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

Challenge - 5 Problems

❓ Predict Output

intermediate

Output of Radix Sort on a small array

What is the output of the following C# code after applying Radix Sort on the array?

DSA C#

using System;

class Program {
    static void RadixSort(int[] arr) {
        int max = arr[0];
        foreach (int num in arr) {
            if (num > max) max = num;
        }

        for (int exp = 1; max / exp > 0; exp *= 10) {
            CountSort(arr, exp);
        }
    }

    static void CountSort(int[] arr, int exp) {
        int n = arr.Length;
        int[] output = new int[n];
        int[] count = new int[10];

        for (int i = 0; i < n; i++) {
            count[(arr[i] / exp) % 10]++;
        }

        for (int i = 1; i < 10; i++) {
            count[i] += count[i - 1];
        }

        for (int i = n - 1; i >= 0; i--) {
            int index = (arr[i] / exp) % 10;
            output[count[index] - 1] = arr[i];
            count[index]--;
        }

        for (int i = 0; i < n; i++) {
            arr[i] = output[i];
        }
    }

    static void Main() {
        int[] arr = {170, 45, 75, 90, 802, 24, 2, 66};
        RadixSort(arr);
        foreach (int num in arr) {
            Console.Write(num + " ");
        }
    }
}

A 2 24 45 75 66 90 170 802

B 2 24 45 66 75 90 170 802

C 802 170 90 75 66 45 24 2

D 24 2 45 66 75 90 170 802

💡 Hint

Radix sort sorts numbers digit by digit starting from the least significant digit.

Radix sort processes digits from right to left. After sorting by each digit, the array becomes more sorted. The final sorted array is ascending: 2 24 45 66 75 90 170 802.

🧠 Conceptual

intermediate

Understanding Radix Sort Stability

Why is stability important in Radix Sort when sorting numbers digit by digit?

A Because stability makes the algorithm faster by skipping some digits.

B Because unstable sorting uses less memory and is preferred for Radix Sort.

C Because stable sorting preserves the relative order of equal elements, ensuring correct final order after sorting all digits.

D Because stability allows sorting negative numbers directly without extra steps.

💡 Hint

Think about what happens when sorting by each digit and how previous order affects the final result.

Radix sort sorts digits from least significant to most significant. If sorting by a digit is unstable, the order of numbers with the same digit can change, breaking the correct final order. Stability preserves order of equal elements, so the final sorted array is correct.

🔧 Debug

advanced

Identify the error in this Radix Sort implementation

What error will this code produce when running Radix Sort on the array?

DSA C#

void CountSort(int[] arr, int exp) {
    int n = arr.Length;
    int[] output = new int[n];
    int[] count = new int[9];

    for (int i = 0; i < n; i++) {
        count[(arr[i] / exp) % 10]++;
    }

    for (int i = 1; i < 9; i++) {
        count[i] += count[i - 1];
    }

    for (int i = n - 1; i >= 0; i--) {
        int index = (arr[i] / exp) % 10;
        output[count[index] - 1] = arr[i];
        count[index]--;
    }

    for (int i = 0; i < n; i++) {
        arr[i] = output[i];
    }
}

A IndexOutOfRangeException because count array size is too small

B NullReferenceException because output array is not initialized

C No error, code runs correctly

D DivideByZeroException when exp is zero

💡 Hint

Check the size of the count array and the indexing used.

The count array is initialized with size 9 but digits range from 0 to 9, so index 9 access causes IndexOutOfRangeException.

🚀 Application

advanced

Radix Sort on Strings of Equal Length

Given an array of strings all of length 3 containing only lowercase letters, which approach correctly sorts them lexicographically using Radix Sort?

A Sort strings from rightmost character to leftmost using a stable counting sort on each character.

B Sort strings from leftmost character to rightmost using any sorting algorithm.

C Sort strings from rightmost character to leftmost using an unstable sort on each character.

D Sort strings once by the first character only using counting sort.

💡 Hint

Radix sort processes digits/characters from least significant to most significant with stable sorting.

Radix sort for strings works by sorting characters from right to left using a stable sort. This preserves order of previous characters and results in lexicographical order.

🧠 Conceptual

expert

Time Complexity of Radix Sort with Different Bases

If Radix Sort is implemented with base b (digits 0 to b-1) to sort n numbers with d digits each, what is the time complexity?

A O(n * d * log b)

B O(n * log_b n)

C O(n * d * b)

D O(d * (n + b))

💡 Hint

Consider that each digit is sorted using counting sort which takes O(n + b) time.

Radix sort runs counting sort d times. Counting sort takes O(n + b) time. So total is O(d * (n + b)).

Practice

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

easy

A. Sort numbers digit by digit starting from the least significant digit

B. Sort numbers by comparing each pair directly

C. Sort numbers by dividing them into two halves recursively

D. Sort numbers by swapping adjacent elements repeatedly

Solution

1. Step 1: Understand Radix Sort approach

   Radix Sort sorts numbers by processing each digit separately, starting from the least significant digit (rightmost).

2. Step 2: Compare with other sorting methods

   Unlike comparison-based sorts, Radix Sort uses digit positions to sort without direct comparisons between whole numbers.

3. Final Answer:

   Sort numbers digit by digit starting from the least significant digit -> Option A

4. Quick Check:

   Radix Sort = Digit by digit sorting [OK]

Hint: Radix Sort processes digits from right to left [OK]

Common Mistakes:

• Thinking Radix Sort compares whole numbers directly
• Confusing Radix Sort with quicksort or mergesort
• Assuming it sorts from most significant digit first

2. Which of the following is the correct way to initialize a queue in C# for use in Radix Sort?

easy

A. Queue<int> buckets = new Queue<int>[10];

B. Queue<int> buckets = new Queue<int>(10);

C. Queue buckets = new Queue<int>(10);

D. Queue<int>[] buckets = new Queue<int>[10];

Solution

1. Step 1: Understand array of queues declaration

   We need an array of 10 queues, so the correct syntax is an array of Queue<int>: Queue<int>[] buckets = new Queue<int>[10];

2. Step 2: Check other options

   Queue<int> buckets = new Queue<int>[10]; tries to assign an array to a single Queue<int> variable, which is invalid. Queue buckets = new Queue<int>(10); uses non-generic Queue incorrectly. Queue<int> buckets = new Queue<int>(10); creates a single Queue with capacity 10, not an array.

3. Final Answer:

   Queue<int>[] buckets = new Queue<int>[10]; -> Option D

4. Quick Check:

   Array of queues = Queue<int>[] [OK]

Hint: Use [] to declare array of queues in C# [OK]

Common Mistakes:

• Declaring a single queue instead of an array
• Using non-generic Queue instead of Queue<int>
• Confusing array initialization syntax

3. What will be the output of the following C# code snippet using Radix Sort on the array [170, 45, 75, 90, 802, 24, 2, 66]?

int[] arr = {170, 45, 75, 90, 802, 24, 2, 66};
RadixSort(arr);
Console.WriteLine(string.Join(", ", arr));

medium

A. [170, 45, 75, 90, 802, 24, 2, 66]

B. [2, 24, 45, 66, 75, 90, 170, 802]

C. [802, 170, 90, 75, 66, 45, 24, 2]

D. [24, 2, 45, 66, 75, 90, 170, 802]

Solution

1. Step 1: Apply Radix Sort on given array

   Radix Sort sorts numbers by digits from least significant to most significant. After sorting, the array becomes sorted in ascending order: 2, 24, 45, 66, 75, 90, 170, 802.

2. Step 2: Verify output matches sorted array

   [2, 24, 45, 66, 75, 90, 170, 802] matches the sorted array. [170, 45, 75, 90, 802, 24, 2, 66] is original unsorted. [802, 170, 90, 75, 66, 45, 24, 2] is descending order. [24, 2, 45, 66, 75, 90, 170, 802] is incorrect order.

3. Final Answer:

   [2, 24, 45, 66, 75, 90, 170, 802] -> Option B

4. Quick Check:

   Radix Sort output = Sorted array ascending [OK]

Hint: Radix Sort outputs sorted array ascending [OK]

Common Mistakes:

• Confusing original and sorted array
• Assuming Radix Sort sorts descending
• Mixing digit order in sorting

4. Identify the error in this Radix Sort code snippet in C#:

for (int i = 0; i < maxDigit; i++)
{
    Queue<int>[] buckets = new Queue<int>[10];
    for (int j = 0; j < 10; j++)
        buckets[j] = new Queue<int>();

    foreach (int num in arr)
    {
        int digit = (num / (int)Math.Pow(10, i)) % 10;
        buckets[digit].Enqueue(num);
    }

    int index = 0;
    foreach (var bucket in buckets)
    {
        while (bucket.Count > 0)
            arr[index++] = bucket.Dequeue();
    }
}

medium

A. The inner foreach loop should use a for loop instead

B. The digit calculation is incorrect; it should use modulus 100

C. There is no error in the code snippet

D. The buckets array is reinitialized inside the outer loop, causing loss of data

Solution

1. Step 1: Analyze the code structure

   The code correctly creates fresh buckets for each digit position, distributes all elements by the current digit using stable queues, and reconstructs the array in place. This is proper LSD Radix Sort implementation.

2. Step 2: Evaluate options

   A: foreach loops are fine for iterating arr and buckets. B: (num / pow(10,i)) % 10 correctly extracts the i-th digit from LSD. C: Reinitializing buckets each pass prevents carry-over from previous passes and does not lose data since all elements are re-enqueued from arr every iteration.

3. Final Answer:

   There is no error in the code snippet -> Option C

4. Quick Check:

   Buckets reinitialized each pass = Correct [OK]

Hint: Buckets reset each digit pass is required, not an error [OK]

Common Mistakes:

• Thinking buckets reinitialization causes data loss
• Misunderstanding digit extraction formula
• Resetting index inside wrong loop

5. You want to adapt Radix Sort to sort an array of strings representing numbers with varying lengths (e.g., ["170", "45", "9", "802", "24"]). Which approach is best to handle different string lengths correctly?

hard

A. Pad shorter strings with leading zeros to match the longest length before sorting

B. Sort strings as they are without padding, digit by digit from left to right

C. Convert strings to integers and apply normal Radix Sort

D. Sort strings by length first, then apply Radix Sort on digits

Solution

1. Step 1: Understand problem with varying string lengths

   Radix Sort requires uniform digit positions. Strings of different lengths cause misalignment when sorting digit by digit.

2. Step 2: Choose padding strategy

   Padding shorter strings with leading zeros makes all strings equal length, allowing digit-by-digit sorting from right to left correctly.

3. Step 3: Evaluate other options

   Sort strings as they are without padding, digit by digit from left to right sorts left to right which breaks Radix Sort logic. Convert strings to integers and apply normal Radix Sort loses string format and may cause overflow. Sort strings by length first, then apply Radix Sort on digits sorting by length first does not solve digit alignment.

4. Final Answer:

   Pad shorter strings with leading zeros to match the longest length before sorting -> Option A

5. Quick Check:

   Pad strings to equal length = Correct approach [OK]

Hint: Pad strings with zeros to equal length before sorting [OK]

Common Mistakes:

• Sorting strings without padding causes wrong order
• Sorting digits left to right breaks Radix Sort
• Converting strings to int may cause errors with large numbers