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1. Least Significant Digit (LSD) radix sorts
2. Most Significant Digit (MSD) radix sorts
Radix Sort is generalization of bucket sort.
It uses several passes of bucket sort.
Why It is called ‘ Radix ’ ???
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.
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.
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
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
 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
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
 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
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
 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
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
1, 5, 10,15, 25, 50, 60, 100
So, the numbers are sorted in ascending order.
Radix sort
Radix sort

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Radix sort

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  • 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.