Radix Sort

Preview

1. What is Radix Sort, and how does it work?
2. When is it appropriate to use Radix Sort compared to other sorting algorithms?
3. What are the advantages and disadvantages of using Radix Sort?
4. What makes Radix Sort more efficient than comparison-based sorting algorithms?
5. How can Radix Sort be implemented in a programming language such as Java or Python?

Explain

Radix sort is a non-comparative sorting algorithm that sorts data by grouping elements into buckets based on their radix, which is the number of digits or symbols in the base system being used, and then sorting the elements in each bucket by the next digit, from right to left. This process is continued for all digits, resulting in a fully sorted array.

For example, given the array [170, 45, 75, 90, 802, 24, 2, 66], we can sort by first grouping elements based on their ones digit, resulting in the buckets

Bucket 0:
Bucket 1: 170
Bucket 2: 802, 2, 24
Bucket 3:
Bucket 4: 45
Bucket 5: 75
Bucket 6: 66
Bucket 7:
Bucket 8: 90

We can then combine the buckets in order, resulting in the intermediate array [170, 802, 2, 24, 45, 75, 66, 90].

Next, we repeat the process for the tens digit, resulting in the buckets

Bucket 0: 802, 2, 24, 45, 66
Bucket 1: 170
Bucket 2:
Bucket 3: 75
Bucket 4:
Bucket 5:
Bucket 6:
Bucket 7:
Bucket 8: 90

Combining the buckets in order gives us the sorted array [2, 24, 45, 66, 75, 90, 170, 802].

Keypoint

1. Radix Sort is a non-comparative algorithm for sorting data.
2. It is used for sorting integers and strings in ascending or descending order.
3. Radix Sort is a linear time algorithm, which means its time complexity is O(n).
4. The sorting is done by grouping numbers based on their digits or characters.
5. Radix Sort uses bucket sort or counting sort to sort the numbers at each digit position.
6. The digits or characters considered for sorting are processed from the least significant to the most significant.
7. Radix Sort is stable, meaning it maintains the relative order of equal elements.
8. The algorithm can be modified to handle negative numbers by using a two’s complement representation.
9. Radix Sort is commonly used for sorting large data sets with a fixed number of digits or characters.
10. Radix Sort can be implemented in both iterative and recursive ways.

Review

1. What is Radix Sort and how does it differ from other sorting algorithms?
   Answer: Radix Sort is a non-comparative sorting algorithm that sorts data by processing individual digits or characters. It differs from other sorting algorithms because it sorts data based on the value of the individual digits rather than the value of the entire element.

2. What is the time complexity of Radix Sort and how does it compare to other sorting algorithms?
   Answer: The time complexity of Radix Sort is O(w * n), where w is the number of digits or characters in the largest element and n is the number of elements. It is considered to be faster than other comparison-based sorting algorithms such as quicksort, mergesort, and heapsort, especially when the number of elements to be sorted is very large.

3. What is the space complexity of Radix Sort and how can it be improved?
   Answer: The space complexity of Radix Sort is O(n + k), where k is the size of the radix or the number of distinct digits or characters. However, this can be improved by using an in-place radix sort where the input array is replaced by a partially sorted array.

4. What is the stability of Radix Sort and why is it important?
   Answer: Radix Sort is a stable sorting algorithm which means that it maintains the relative order of equal elements. This is important when there are multiple elements with the same value such as when sorting by last name and age where there may be multiple people with the same last name.

5. What are the limitations of Radix Sort and when should it be used?
   Answer: Radix Sort can only be used to sort elements that have a finite number of digits or characters such as integers, strings, and characters. It is not suitable for sorting floating-point numbers or data with variable-length elements. Additionally, it may not be the best choice when the size of the input data is small or when the input data is randomly distributed.