Why Radix Sort Algorithm in DSA C?

The Big Idea

What if you could sort millions of numbers without comparing them directly, just by looking at their digits one by one?

The Scenario

Imagine you have a huge stack of mail envelopes with different zip codes, and you need to sort them by zip code to deliver them quickly.

Doing this by checking each envelope one by one and comparing full zip codes manually would take forever.

The Problem

Sorting by comparing whole numbers or strings directly is slow and confusing when the list is very long.

It's easy to make mistakes, and it takes a lot of time to check every number against every other number.

The Solution

Radix Sort breaks down the sorting task into smaller steps by sorting numbers digit by digit, starting from the least significant digit.

This way, it organizes the data quickly and without comparing whole numbers directly.

Before vs After

✗ Before

for (int i = 0; i < n-1; i++) {
  for (int j = 0; j < n-i-1; j++) {
    if (arr[j] > arr[j+1]) {
      int temp = arr[j];
      arr[j] = arr[j+1];
      arr[j+1] = temp;
    }
  }
}

✓ After

void radixSort(int arr[], int n) {
  int max = getMax(arr, n);
  for (int exp = 1; max/exp > 0; exp *= 10) {
    countSort(arr, n, exp);
  }
}

What It Enables

It enables fast and efficient sorting of large lists of numbers by processing digits step-by-step instead of comparing whole numbers.

Real Life Example

Sorting millions of phone numbers or zip codes quickly in a postal system or a phone directory.

Key Takeaways

Manual sorting by full number comparison is slow and error-prone for large data.

Radix Sort sorts numbers digit by digit, making sorting faster and simpler.

This method is especially useful for sorting large sets of numbers like phone numbers or zip codes.

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