Code 365 - IT ELECTIVE 4 Ref: https://en.wikipedia.org/wiki/Radix_sort

1. Radix Sort

2. What is Radix Sort?
 In Computer Science Radix Sort is a non- comparative integer sorting algorithm
that sort data with integer keys by sorting grouping keys by individual digits which
share same significant position and value.
 The Radix Sort algorithm is an important sorting algorithm that is integral to suffix
-array construction algorithms. It is also useful on parallel machines.

3.  Radix means: the base of a system of numeration
 The decimal number system that we use every day has 10 digits {0,1,2,3,4,5,6,7,8,9}
and so the radix is 10.

4. Advantages
1. Fast when the keys are short i.e. when the range of the array elements is less.
2. Used in suffix array construction algorithms like Manber's algorithm and DC3
algorithm.

5. Disadvantages
1. Since Radix Sort depends on digits or letters, Radix Sort is much less flexible than
other sorts. Hence, for every different type of data it needs to be rewritten.
2. The constant for Radix sort is greater compared to other sorting algorithms.
3. It takes more space compared to Quicksort which is in place sorting.

6. Two classification of Radix Sort
 Least Significant Digit(LSD)
 Most Significant Digit(MSD)

7. Least Significant Digit(LSD)
 A Least significant digit (LSD) Radix sort is a fast stable sorting algorithm which can
be used to sort keys in integer representation order.
 Keys may be a string of characters, or numerical digits in a given 'radix'.
 The processing of the keys begins at the least significant digit (the rightmost digit),
and proceeds to the most significant digit (the leftmost digit).

8. Most Significant Digit(MSD)
 A most significant digit (MSD) radix sort can be used to sort keys in lexicographic
order.
 Unlike a least significant digit (LSD) radix sort, a most significant digit radix
sort does not necessarily preserve the original order of duplicate keys.
 An MSD radix sort starts processing the keys from the most significant digit,
leftmost digit, to the least significant digit, rightmost digit.

9. How Radix Sort Works
 Take the least significant digit (or group of bits, both being examples of radices) of
each key.
 Group the keys based on that digit, but otherwise keep the original order of keys.
(This is what makes the LSD radix sort a stable sort.)
 Repeat the grouping process with each more significant digit.

10. Examples:
 Unsorted List
35 53 55 33 52 32 25

11. Based on the algorithm, sort the array according to the one’s digit (Leased Significant
Digit)
35 53 55 33 52 32 25
After grouping the array by one’s digit, since the array is not sorted repeat the process
until it is sorted.
Q0 Q1 Q2 Q3 Q4 Q5 Q6 Q7 Q8 Q9
52
32
53
33

12. Now, sort the array according to most significant digit(MSD)
32 52 53 33 35 55 25
Q0 Q1 Q2 Q3 Q4 Q5 Q6 Q7 Q8 Q9
25 32
33
35
52
53
55

13.  After Sorting:
25 32 33 35 52 53 55

14. Analysis of Radix Sort
 Each pass over n d-digit numbers and k base keys then take time O (n+k).
(Assuming counting sort is used for each pass).
 There are d passes, so the total time for radix sort is O (d (n+k)).
 When d is a constant and total run time = O(n)

15. Thank you!