Radix Sort Algorithm in DSA C - Cheat Sheet & Quick Revision

Recall & Review

beginner

What is Radix Sort?

Radix Sort is a sorting method that sorts numbers digit by digit, starting from the least significant digit to the most significant digit.

beginner

How does Radix Sort handle sorting of numbers?

It sorts numbers by grouping them based on each digit, starting from the rightmost digit and moving left, using a stable sorting method at each step.

intermediate

Why is Radix Sort considered stable?

Because it preserves the order of numbers with the same digit value during each digit-level sorting step.

intermediate

What is the time complexity of Radix Sort?

The time complexity is O(d*(n+b)) where d is the number of digits, n is the number of elements, and b is the base of the number system (usually 10).

intermediate

Which sorting algorithm is commonly used internally by Radix Sort for sorting digits?

Counting Sort is commonly used because it is stable and efficient for sorting digits within a fixed range.

Radix Sort processes digits starting from which side?

A Least significant digit (rightmost)

B Most significant digit (leftmost)

C Middle digit

D Random digit

Radix Sort starts sorting from the least significant digit to ensure correct order after all passes.

Which sorting method is best suited for sorting digits in Radix Sort?

A Quick Sort

B Merge Sort

C Counting Sort

D Bubble Sort

Counting Sort is stable and efficient for sorting digits within a limited range, making it ideal for Radix Sort.

What is the main advantage of Radix Sort over comparison-based sorts?

A It works only on strings

B It uses less memory

C It is easier to implement

D It sorts in linear time for fixed digit length

Radix Sort can sort numbers in linear time when the number of digits is fixed, unlike comparison sorts which are O(n log n).

Radix Sort is best used when:

A Sorting numbers with fixed digit length

B Sorting very large numbers with many digits

C Sorting small arrays

D Sorting floating point numbers

Radix Sort performs best when numbers have fixed digit length, allowing predictable passes.

Is Radix Sort a comparison-based sorting algorithm?

A Yes

B No

C Only for strings

D Only for integers

Radix Sort does not compare elements directly; it sorts based on digit positions.

Explain how Radix Sort sorts an array of numbers step-by-step.

Think about sorting by digits from right to left.

Describe why stability is important in Radix Sort.

Consider what happens if order changes during digit sorting.

Practice

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

easy

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

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

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

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

Solution

1. Step 1: Understand Radix Sort process

   Radix Sort sorts numbers by processing each digit from least significant to most significant.

2. Step 2: Compare with other sorting methods

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

3. Final Answer:

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

4. Quick Check:

   Radix Sort = Digit by digit sorting [OK]

Hint: Remember: Radix Sort sorts 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 pivot or recursion

2. Which of the following is the correct way to initialize the counting array for Radix Sort in C?

easy

A. int count[10] = {0};

B. int count[10]; // no initialization

C. int count[10] = {1};

D. int count[10] = NULL;

Solution

1. Step 1: Understand counting array role

   The counting array stores frequency of digits 0-9 and must start at zero.

2. Step 2: Check initialization options

   Only int count[10] = {0}; sets all elements to zero correctly in C.

3. Final Answer:

   int count[10] = {0}; -> Option A

4. Quick Check:

   Counting array must start with zeros [OK]

Hint: Initialize counting array with zeros using {0} [OK]

Common Mistakes:

• Leaving counting array uninitialized
• Initializing with all ones
• Assigning NULL to an int array

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

void printArray(int arr[], int n) {
    for (int i = 0; i < n; i++)
        printf("%d ", arr[i]);
    printf("\n");
}

int main() {
    int arr[] = {170, 45, 75, 90, 802, 24, 2, 66};
    int n = sizeof(arr)/sizeof(arr[0]);
    radixSort(arr, n); // Assume radixSort is correctly implemented
    printArray(arr, n);
    return 0;
}

medium

A. 24 2 45 66 75 90 170 802

B. 170 45 75 90 802 24 2 66

C. 802 170 90 75 66 45 24 2

D. 2 24 45 66 75 90 170 802

Solution

1. Step 1: Understand Radix Sort output

   Radix Sort sorts the array fully in ascending order after processing all digits.

2. Step 2: Sort given array

   Sorted array is [2, 24, 45, 66, 75, 90, 170, 802].

3. Final Answer:

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

4. Quick Check:

   Sorted array matches 2 24 45 66 75 90 170 802 [OK]

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

Common Mistakes:

• Assuming output is unchanged
• Thinking output is reversed
• Confusing partial digit sorting with final output

4. Identify the error in this Radix Sort counting step code snippet:

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]] = arr[i];
    count[(arr[i] / exp) % 10]--;
}

medium

A. Counting array size should be 100, not 10

B. Indexing output array should be count[...] - 1

C. Loop for count prefix sum should start from 0

D. Division by exp should be replaced by modulo exp

Solution

1. Step 1: Analyze output array indexing

   Indexing output array must use count[...] - 1 because count stores cumulative counts.

2. Step 2: Check other parts

   Counting array size 10 is correct for digits 0-9; prefix sum loop starts at 1; division by exp is correct.

3. Final Answer:

   Indexing output array should be count[...] - 1 -> Option B

4. Quick Check:

   Output index = count - 1 [OK]

Hint: Subtract 1 from count for output indexing [OK]

Common Mistakes:

• Using count directly as index without subtracting 1
• Wrong counting array size
• Incorrect loop start for prefix sums
• Misusing division and modulo operators

5. Given an array of strings representing numbers with leading zeros, e.g., ["002", "010", "001", "100"], how can Radix Sort be adapted to sort them correctly as numbers?

hard

A. Pad all strings to equal length and sort digit by digit from right to left

B. Sort strings lexicographically without changes

C. Convert strings to integers first, then apply Radix Sort

D. Use Radix Sort only on the first character of each string

Solution

1. Step 1: Understand string number sorting

   Strings with leading zeros must be equal length to compare digits correctly.

2. Step 2: Adapt Radix Sort

   Pad strings to same length, then sort digit by digit from right to left to preserve numeric order.

3. Final Answer:

   Pad all strings to equal length and sort digit by digit from right to left -> Option A

4. Quick Check:

   Equal length padding + digit-wise sort = correct numeric order [OK]

Hint: Pad strings to same length before digit-wise sorting [OK]

Common Mistakes:

• Sorting strings lexicographically without padding
• Converting to int loses leading zeros importance
• Sorting only first character causes wrong order