Radix Sort

What You’ll Learn 📚

• Understanding the core concepts of Radix Sort
• Key terminology and definitions
• Step-by-step examples from simple to complex
• Common questions and answers
• Troubleshooting common issues

Introduction to Radix Sort

Radix Sort is a non-comparative sorting algorithm that sorts numbers by processing individual digits. It’s particularly useful for sorting numbers with a fixed number of digits. Unlike other sorting algorithms like Quick Sort or Merge Sort, Radix Sort doesn’t compare elements directly. Instead, it exploits the structure of the number system. Sounds interesting, right? Let’s break it down further.

Key Terminology

• Radix: The base of a number system. For example, the decimal system has a radix of 10.
• Stable Sort: A sorting algorithm is stable if it maintains the relative order of records with equal keys.
• Bucket: A container used to hold elements temporarily during sorting.

Simple Example

def counting_sort(arr, exp):
    n = len(arr)
    output = [0] * n
    count = [0] * 10

    for i in range(n):
        index = arr[i] // exp
        count[index % 10] += 1

    for i in range(1, 10):
        count[i] += count[i - 1]

    i = n - 1
    while i >= 0:
        index = arr[i] // exp
        output[count[index % 10] - 1] = arr[i]
        count[index % 10] -= 1
        i -= 1

    for i in range(n):
        arr[i] = output[i]


def radix_sort(arr):
    max1 = max(arr)
    exp = 1
    while max1 // exp > 0:
        counting_sort(arr, exp)
        exp *= 10

arr = [170, 45, 75, 90, 802, 24, 2, 66]
radix_sort(arr)
print(arr)

Progressively Complex Examples

Example 1: Sorting with More Digits

# Example code here with explanation

Example 2: Sorting Strings

# Example code here with explanation

Example 3: Visualizing the Process

# Example code here with explanation

Common Questions and Answers

1. What is the time complexity of Radix Sort?

   The time complexity of Radix Sort is O(nk), where n is the number of elements and k is the number of digits in the largest number.

2. Is Radix Sort stable?

   Yes, Radix Sort is a stable sorting algorithm.

3. Can Radix Sort be used for negative numbers?

   Radix Sort is typically used for non-negative integers, but it can be adapted to handle negative numbers with additional modifications.

4. Why use Radix Sort over other sorting algorithms?

   Radix Sort is efficient for sorting large lists of numbers with a fixed number of digits, especially when the range of numbers is large compared to the number of elements.

Troubleshooting Common Issues

Ensure that the counting sort used within Radix Sort is stable, as instability can lead to incorrect sorting results.

Remember to handle edge cases, such as when all numbers have the same number of digits or when the list is already sorted.

Practice Exercises

• Try sorting a list of phone numbers using Radix Sort.
• Adapt Radix Sort to handle negative numbers.
• Visualize the sorting process for a list of strings.

For further reading, check out the Wikipedia page on Radix Sort and the GeeksforGeeks tutorial.