The document describes Radix sort, a sorting algorithm that sorts numbers by their individual digits by making multiple passes through the data. It works by first sorting the numbers based on the units place value, then the tens place, and so on. This is more efficient than other general-purpose sorting algorithms for large data sets with uniformly distributed values. Radix sort runs in O(d(n+k)) time, where d is the number of digits, n is the number of elements, and k is the maximum value of a digit.

1. Design and Analysis of Algorithm

2.  Heap sort
 Quick sort
 Radix sort
 Bucket sort
 Counting sort

3.  Radix sort is generalization of bucket sort.
 It use several passes to sort Array.
 Perform the sorting by “least significant
digits”.
 First sort by digit in units pace.
 Second sort by digit in tens pace
 Third sort by digit in hundreds pace.

4. Assume the following Array:
Pass #1
Pass#2
Pass#3

5. 170 90 802 2 24 45 75 66
170 45 75 90 802 24 2 66

6. 2 24 45 66 75 90 170 802
 Array is now sorted
802 2 24 45 66 170 75 90

7. 802 2 24 45 66 170 75 90
170 90 802 02 24 45 75 66

8. Radix_sort (A,d)
for i=1..to d
do use a stable sort to sort array A on digit i
“N d-digit numbers in which each digit can
take up to k possible values, Radix_sort
correctly sort these numbers in O(d(n+k))
time, if the stable sort it use O(n=k) time.”