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++

void countingSort(int arr[], int n, int exp) {
    int output[n];
    int count[10] = {0};
    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--) {
        output[count[(arr[i] / exp) % 10] - 1] = arr[i];
        count[(arr[i] / exp) % 10]--;
    }
    for (int i = 0; i < n; i++)
        arr[i] = output[i];
}

void radixSort(int arr[], int n) {
    int maxVal = arr[0];
    for (int i = 1; i < n; i++)
        if (arr[i] > maxVal) maxVal = arr[i];
    for (int exp = 1; maxVal / exp > 0; exp *= 10)
        countingSort(arr, n, exp);
}

int main() {
    int arr[] = {170, 45, 75, 90, 802, 24, 2, 66};
    int n = sizeof(arr) / sizeof(arr[0]);
    radixSort(arr, n);
    for (int i = 0; i < n; i++)
        std::cout << arr[i] << " ";
    return 0;
}

A 802 170 90 75 66 45 24 2

B 2 24 45 66 75 90 170 802

C 2 24 45 66 75 170 90 802

D 170 45 75 90 802 24 2 66

💡 Hint

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

Radix sort uses counting sort on each digit starting from the least significant digit. After sorting all digits, the array becomes sorted in ascending order.

❓ Predict Output

intermediate

Radix Sort output with numbers having different digit lengths

What will be the output of the following code after applying Radix Sort on the array?

DSA C++

int arr[] = {3, 300, 34, 5, 9};
int n = sizeof(arr) / sizeof(arr[0]);
radixSort(arr, n);
for (int i = 0; i < n; i++)
    std::cout << arr[i] << " ";

A 3 5 9 34 300

B 300 34 9 5 3

C 3 34 5 9 300

D 5 3 9 34 300

💡 Hint

Radix sort handles numbers with different digit lengths by sorting from least significant digit.

Radix sort sorts numbers digit by digit. Smaller numbers with fewer digits come before larger numbers when sorted correctly.

🧠 Conceptual

advanced

Why Radix Sort is not comparison-based?

Which statement best explains why Radix Sort is not a comparison-based sorting algorithm?

A It sorts numbers by grouping digits and using counting sort without direct element comparisons.

B It sorts numbers by comparing each pair of elements multiple times.

C It uses quicksort internally to sort digits of numbers.

D It compares elements only once and then sorts them using a heap.

💡 Hint

Think about how Radix Sort processes digits instead of comparing whole numbers.

Radix Sort processes digits of numbers and uses counting sort on each digit, which does not involve comparing elements directly.

🔧 Debug

advanced

Identify the bug in this Radix Sort counting sort implementation

What error will this code cause when running countingSort in Radix Sort?

DSA C++

void countingSort(int arr[], int n, int exp) {
    int output[n];
    int count[10] = {0};
    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--) {
        output[count[(arr[i] / exp) % 10] - 1] = arr[i];
        count[(arr[i] / exp) % 10]--;
    }
    for (int i = 0; i < n; i++)
        arr[i] = output[i];
}

A Logical error causing reversed sorted array

B No error, code runs correctly

C Compilation error due to missing semicolon

D Array index out of bounds error due to incorrect loop limit in count array update

💡 Hint

Check the loop that updates the count array prefix sums.

The loop runs from i=1 to i<=10, but count array has size 10 (indices 0 to 9). Accessing count[10] causes out of bounds error.

🚀 Application

expert

Radix Sort on strings of digits

Given an array of strings representing numbers with equal length digits, which approach correctly sorts them using Radix Sort?

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

B Sort strings lexicographically using built-in sort only

C Sort strings from rightmost character to leftmost using counting sort on each character

D Convert strings to integers and apply quicksort

💡 Hint

Radix Sort processes digits starting from least significant digit.

Radix Sort on strings representing numbers sorts from rightmost character (least significant digit) to leftmost using counting sort at each step.

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. Compare each element with every other element and swap if needed

C. Divide the array into halves and sort each half recursively

D. Use a pivot element to partition the array and sort partitions

Solution

1. Step 1: Understand Radix Sort approach

   Radix Sort sorts numbers by processing individual digits starting from the least significant digit (rightmost) to the most significant digit (leftmost).

2. Step 2: Compare with other sorting methods

   Other options describe Bubble Sort, Merge Sort, and Quick Sort, which are different algorithms.

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:

• Confusing Radix Sort with comparison-based sorts
• Thinking it sorts from most significant digit first
• Assuming it uses swapping of elements

2. Which of the following is the correct way to extract the digit at position pos (starting from 0 for least significant digit) from an integer num in C++?

easy

A. (num / (10 * pos)) % 10

B. ((num / (int)pow(10, pos)) % 10)

C. (num % (10 * pos)) / 10

D. (num % pow(10, pos)) / 10

Solution

1. Step 1: Understand digit extraction formula

   To get the digit at position pos, divide num by 10^pos and then take modulo 10.

2. Step 2: Check each option

   ((num / (int)pow(10, pos)) % 10 correctly uses pow(10, pos) for exponentiation and modulo 10 to get the digit.

3. Final Answer:

   ((num / (int)pow(10, pos)) % 10) -> Option B

4. Quick Check:

   Digit extraction = (num / 10^pos) % 10 [OK]

Hint: Divide by 10^pos then mod 10 to get digit [OK]

Common Mistakes:

• Using multiplication instead of exponentiation
• Incorrect order of operations
• Using modulo before division

3. What will be the output of the following C++ code snippet using Radix Sort on array arr = {170, 45, 75, 90, 802, 24, 2, 66}?

void countingSort(int arr[], int n, int exp) {
    int output[n];
    int count[10] = {0};
    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--) {
        output[count[(arr[i] / exp) % 10] - 1] = arr[i];
        count[(arr[i] / exp) % 10]--;
    }
    for (int i = 0; i < n; i++)
        arr[i] = output[i];
}

void radixSort(int arr[], int n) {
    int maxVal = *max_element(arr, arr + n);
    for (int exp = 1; maxVal / exp > 0; exp *= 10)
        countingSort(arr, n, exp);
}

int main() {
    int arr[] = {170, 45, 75, 90, 802, 24, 2, 66};
    int n = sizeof(arr) / sizeof(arr[0]);
    radixSort(arr, n);
    for (int i = 0; i < n; i++)
        cout << arr[i] << " ";
    return 0;
}

medium

A. 24 2 45 66 75 90 170 802

B. 802 170 90 75 66 45 24 2

C. 2 24 45 66 75 90 170 802

D. 2 24 45 75 66 90 170 802

Solution

1. Step 1: Understand Radix Sort steps on given array

   Radix Sort sorts by digits: first units, then tens, then hundreds. After full sorting, array becomes sorted ascending.

2. Step 2: Trace final sorted array

   Sorted array is: 2 24 45 66 75 90 170 802.

3. Final Answer:

   2 24 45 66 75 90 170 802 -> Option C

4. Quick Check:

   Radix Sort final output = sorted array ascending [OK]

Hint: Radix Sort outputs fully sorted array ascending [OK]

Common Mistakes:

• Confusing intermediate steps with final output
• Misordering numbers with same digits
• Ignoring stable sorting in countingSort

4. Identify the bug in the following Radix Sort counting sort implementation and select the correct fix:

void countingSort(int arr[], int n, int exp) {
    int output[n];
    int count[10] = {0};
    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 = 0; i < n; i++) {
        output[count[(arr[i] / exp) % 10] - 1] = arr[i];
        count[(arr[i] / exp) % 10]--;
    }
    for (int i = 0; i < n; i++)
        arr[i] = output[i];
}

medium

A. Change the last for loop to iterate from n-1 down to 0 for stable sorting

B. Initialize count array with -1 instead of 0

C. Remove the cumulative sum loop for count array

D. Replace output array with a vector for dynamic sizing

Solution

1. Step 1: Identify stable sorting requirement in counting sort

   Counting sort must process elements from right to left to maintain stability.

2. Step 2: Check the for loop direction

   Current loop goes from 0 to n-1, which breaks stability. Changing it to n-1 down to 0 fixes this.

3. Final Answer:

   Change the last for loop to iterate from n-1 down to 0 for stable sorting -> Option A

4. Quick Check:

   Stable counting sort = reverse iteration [OK]

Hint: Counting sort must iterate backward for stability [OK]

Common Mistakes:

• Iterating forward breaks stable sorting
• Misunderstanding count array initialization
• Ignoring cumulative sum step

5. Given an array of strings representing numbers with leading zeros, e.g., {"002", "010", "001", "100"}, how can you adapt Radix Sort to correctly sort them as numbers?

hard

A. Use counting sort only on the first character of each string

B. Sort strings lexicographically using Radix Sort on characters

C. Ignore leading zeros and sort strings as-is with Radix Sort

D. Convert strings to integers first, then apply Radix Sort on integers

Solution

1. Step 1: Understand sorting numeric strings with leading zeros

   Sorting strings lexicographically will not sort numbers correctly if leading zeros exist.

2. Step 2: Convert strings to integers for numeric sorting

   Convert strings to integers to remove leading zeros, then apply Radix Sort on integers for correct numeric order.

3. Final Answer:

   Convert strings to integers first, then apply Radix Sort on integers -> Option D

4. Quick Check:

   Numeric string sorting = convert to int then Radix Sort [OK]

Hint: Convert strings to int before Radix Sort for numeric order [OK]

Common Mistakes:

• Sorting strings lexicographically causes wrong order
• Ignoring leading zeros impact
• Using only first character for sorting