Radix Sort is a fascinating sorting algorithm known for its unique approach to sorting elements in a specific order. Unlike comparison-based sorting algorithms, Radix Sort leverages the positional values of digits within elements to achieve efficient sorting. In this, we’ll dive into the inner workings of Radix Sort, understand its algorithmic approach, explore its time complexity, and discuss its practical applications.
Radix Sort is a non-comparison-based sorting algorithm that operates on integers or strings by processing digits or characters at different positions. It sorts elements by considering their individual digits (or characters) from the least significant digit (LSD) to the most significant digit (MSD) or vice versa. Radix Sort follows these key steps:
- Digit Selection: Determine the range of values for the digits at each position (typically 0-9 for base 10 integers) and the order in which they will be processed (LSD or MSD).
- Bucket Distribution: Distribute elements into buckets based on the value of the currently processed digit. Elements with the same digit value go into the same bucket.
- Bucket Sorting: Sort the elements within each bucket using any sorting technique, often another Radix Sort iteration.
- Repeat: Continue the process for all digits, moving from the least significant digit to the most significant digit (or vice versa).
- Combine: Combine the sorted buckets to produce the fully sorted array.
In the below PDF we discuss about Radix sorting techniques in detail in simple language, Hope this will help in better understanding.
Radix Sort Example :
Let’s walk through a simple example of Radix Sort for a list of integers:
Input Array: [170, 45, 75, 90, 802, 24, 2, 66]
Least Significant Digit (LSD) Pass:
Bucket Sorting within each bucket.
Bucket 0: [170, 90, 802]
Bucket 1: 
Bucket 2: 
Bucket 3: 
Bucket 4: 
Bucket 5: 
Bucket 6: 
Bucket 7: 
Bucket 8: 
Bucket 9: 
- Second Least Significant Digit Pass (and so on):
- Repeat the Bucket Distribution, Sorting, and Combine steps for the tens digit.
- Repeat for hundreds, thousands, and so on.
- Combine the Sorted Buckets: Combine the sorted buckets to produce the fully sorted array: [2, 24, 45, 66, 75, 90, 170, 802]
Time Complexity Analysis :
The time complexity of Radix Sort depends on the number of digits in the largest element and the number of elements to be sorted. In the average and worst cases, Radix Sort has a time complexity of O(k * n), where “k” is the number of digits and “n” is the number of elements. It is a stable sorting algorithm.
Applications of Radix Sort :
Radix Sort has practical applications in various domains:
- Integer Sorting: It is commonly used to sort integers, particularly when the range of values is limited.
- String Sorting: Radix Sort can be adapted for sorting strings based on characters at different positions.
- Digital Circuit Design: Radix Sort is used for optimizing digital circuit designs and minimizing the number of logic gates required.
- Data Compression: It is employed in data compression algorithms and image processing.
- External Sorting: Radix Sort can be adapted for external sorting when data cannot fit entirely in memory.
Radix Sort is a non-comparison-based sorting algorithm that sorts elements by processing their individual digits or characters at different positions within the elements.
Radix Sort works by considering the digits or characters of elements from the least significant digit (LSD) to the most significant digit (MSD) or vice versa, distributing elements into buckets based on the value of the currently processed digit, sorting the elements within each bucket, and repeating the process for all digits.
No, Radix Sort is not a comparison-based sorting algorithm. It sorts elements based on their digit values rather than comparing elements directly.
The time complexity of Radix Sort is O(k * n), where “k” is the number of digits in the largest element, and “n” is the number of elements to be sorted.
The key steps of Radix Sort include digit selection (determining the range of digit values and their order), bucket distribution (assigning elements to buckets based on digit values), bucket sorting (sorting elements within each bucket), repeating the process for all digits, and combining the sorted buckets to produce the fully sorted array.
The main advantage of Radix Sort is its efficiency for sorting elements with multiple digits or characters by considering their positional values, making it suitable for certain specialized sorting tasks.