Radix Sort Algorithm in DSA C - Build from Scratch

Radix Sort Algorithm

📖 Scenario: You work in a warehouse where packages have unique ID numbers. You want to sort these package IDs quickly to organize shipments. Radix Sort is a great way to sort numbers digit by digit.

🎯 Goal: Build a program that sorts an array of package ID numbers using the Radix Sort algorithm.

📋 What You'll Learn

Create an array called arr with the exact values: 170, 45, 75, 90, 802, 24, 2, 66

Create an integer variable n to store the size of the array

Create a function getMax that returns the maximum value in arr

Create a function countSort that sorts arr based on the digit represented by exp

Create a function radixSort that uses countSort to sort arr by each digit

Print the sorted array after applying Radix Sort

💡 Why This Matters

🌍 Real World

Radix Sort is used in systems where sorting large sets of numbers quickly is important, such as organizing package IDs in warehouses or sorting phone numbers.

💼 Career

Understanding Radix Sort helps in roles involving data processing, optimization, and software development where efficient sorting algorithms improve performance.

1

Create the array of package IDs

Create an integer array called arr with these exact values: 170, 45, 75, 90, 802, 24, 2, 66. Also create an integer variable n that stores the size of arr.

DSA C

int arr[] = {170, 45, 75, 90, 802, 24, 2, 66};
int n = sizeof(arr) / sizeof(arr[0]);
// Your code here

Hint

Use sizeof(arr) / sizeof(arr[0]) to find the number of elements in the array.

2

Create the getMax function

Create a function called getMax that takes the array arr and its size n as parameters and returns the maximum value in arr.

DSA C

int arr[] = {170, 45, 75, 90, 802, 24, 2, 66};
int n = sizeof(arr) / sizeof(arr[0]);

int getMax(int arr[], int n) {
    // Your code here
}

Hint

Start with the first element as max, then check each element to update max if needed.

3

Create the countSort function

Create a function called countSort that takes the array arr, its size n, and an integer exp representing the digit position. This function should sort arr based on the digit at exp using counting sort logic.

DSA C

int arr[] = {170, 45, 75, 90, 802, 24, 2, 66};
int n = sizeof(arr) / sizeof(arr[0]);

int getMax(int arr[], int n) {
    int max = arr[0];
    for (int i = 1; i  max) {
            max = arr[i];
        }
    }
    return max;
}

void countSort(int arr[], int n, int exp) {
    // Your code here
}

Hint

Use an array count of size 10 to count digits, then build the output array from right to left.

4

Create the radixSort function and print the sorted array

Create a function called radixSort that takes the array arr and its size n. Use getMax to find the maximum number and then call countSort for each digit place (1, 10, 100, etc.). Finally, print the sorted array with the format: Sorted array: 2 24 45 66 75 90 170 802.

DSA C

int arr[] = {170, 45, 75, 90, 802, 24, 2, 66};
int n = sizeof(arr) / sizeof(arr[0]);

int getMax(int arr[], int n) {
    int max = arr[0];
    for (int i = 1; i  max) {
            max = arr[i];
        }
    }
    return max;
}

void countSort(int arr[], int n, int exp) {
    int output[n];
    int count[10] = {0};

    for (int i = 0; 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) {
    // Your code here
}

int main() {
    radixSort(arr, n);
    printf("Sorted array: ");
    for (int i = 0; i < n; i++) {
        printf("%d ", arr[i]);
    }
    printf("\n");
    return 0;
}

Hint

Use getMax to find the largest number, then loop over each digit place calling countSort. Finally, print the sorted array.

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