Radix sort is a generalization of bucket sort that uses multiple passes of bucket sort and treats digits of numbers separately. It works by sorting numbers based on the place value of their digits, starting from the least significant digit. For example, to radix sort a list of numbers from 0 to 100, it would perform 3 passes of bucket sort using the ones, tens, and hundreds places respectively to fully sort the numbers in ascending order.

4. 1. Least Significant Digit (LSD) radix sorts
2. Most Significant Digit (MSD) radix sorts

5. Radix Sort is generalization of bucket sort.
It uses several passes of bucket sort.

6. Why It is called ‘ Radix ’ ???

7. Radix Means : the base of a system of numeration
Examples:
If we are dealing with unsorted numbers then we know
that there are 10 digits from 0 to 9 that are used to form
any number.
So, we will need 10 buckets labeled 0 to 9 to sort the
unsorted numbers.

8. 10,15,1,60,5,100,25,50
We have some unsorted numbers
And our task is to sort them in ascending order.
We know that there are 10 digits from 0 to 9
So, we will need 10 buckets labeled 0 to 9 in order to
sort the given unsorted numbers.

9. 10, 15, 1, 60, 5,100, 25, 50
Here are 10 bucket labeled 0 to 9
Now , find the number of digits in the biggest number.
In this case, 100 is the biggest number and it has 3 digits.
So, we will pad all the numbers that are smaller then 100 with leading zeros in order to make
them all have 3 digits.
0 1 2 3 4 5 6 7 8
9

10. 010, 015, 001, 060, 005,100, 025, 050
Since all of them have 3 digits
So, the sorting process will require 3 pass.
Pass 1:
Sort the numbers using the 1st digit from right.
0 1 2 3 4 5 6 7 8
9

11.  Pass 1:
010, 015, 001, 060, 005, 100, 025, 050
0 1 2 3 4 5 6 7 8
9
010
1
050
100
060
010
025
005
015
001

12. 010, 060, 100, 050, 001, 015, 005 025
Pass 1 is complete take the numbers out from bucket 0 to 9 from bottom.
Pass 2:
Sort the numbers using the 2nd digit from right.
0 1 2 3 4 5 6 7 8
9

13.  Pass 2:
010, 015, 001, 060, 005, 100, 025, 050
0 1 2 3 4 5 6 7 8
9
025 060050
015
010
100
005
001

14. 100, 001, 005, 010, 015, 025, 050, 060
Pass 1 is complete take the numbers out from bucket 0 to 9 from bottom.
Pass 3:
Sort the numbers using the 3rd digit from right.
0 1 2 3 4 5 6 7 8
9

15.  Pass 3:
100, 001, 005, 010, 015, 025, 050, 060
0 1 2 3 4 5 6 7 8
9
100
060
050
025
015
010
005
001

16. 001, 005, 910, 015, 025,050, 060,100
Pass 3 is complete
take the numbers out from bucket 0 to 9 from bottom.
Since, we have completed pass 3 so we will stop here.
Remove the leading zeros.
0 1 2 3 4 5 6 7 8
9

17. 1, 5, 10,15, 25, 50, 60, 100
So, the numbers are sorted in ascending order.