# Python Program to Implement Radix Sort

This is a Python program to implement radix sort.

Problem Description

The program sorts a list by radix sort.

Problem Solution

1. Create a function radix_sort that takes a list and a variable base as arguments.
2. Create an inner function key_factory that takes two variables digit and base as arguments and returns a function.
3. The function key returned takes a list and a variable index as arguments. It returns a digit of the element at that index in the list. The position of the digit it returns is given by the variable digit passed to key_factory. The digit position is found with the element represented in that base. The digit position uses zero-based numbering.
4. Inside the function radix_sort, find the largest element in the list.
5. Let exp iterate from 0 to the highest digit position of the largest element in the list.
6. For each value of exp, sort the elements of the list on digit exp.
7. The sorting is done by calling the counting_sort function. The function then sorts the list using the fact that the largest element is base – 1 and using the function key. The function key is returned by the key_factory function when it is passed exp as the digit position and base as arguments.
8. Create a function counting_sort that takes a list, a variable largest and a function key as arguments.
9. Inside the function create a list c of zeros of length largest + 1.
10. For each element in the input list, retrieve its key n by calling the function key and then increment the nth index of the list c.
11. The list c now contains the frequency of each key in the input list.
12. For each index from 1 to the length of c – 1, add to the current element the previous element. Before the loop, decrement c since this will cause all the elements to be decremented by one after the loop finishes. Thus, the list c will contain the last index of each element in our sorted array.
13. Create the output array with size the same as that of the input array.
14. Create a loop where the loop variable i iterates from the length of the input list – 1 to 0.
15. In each iteration of the loop set the pth element of the output list equal to the ith element of the input list. The value p is the element of the list c at the index given by the key of the element of the input list. The value where p is stored in c is then decremented.

Program/Source Code

Here is the source code of a Python program to implement radix sort. The program output is shown below.

```def radix_sort(alist, base=10):
if alist == []:
return

def key_factory(digit, base):
def key(alist, index):
return ((alist[index]//(base**digit)) % base)
return key
largest = max(alist)
exp = 0
while base**exp <= largest:
alist = counting_sort(alist, base - 1, key_factory(exp, base))
exp = exp + 1
return alist

def counting_sort(alist, largest, key):
c = *(largest + 1)
for i in range(len(alist)):
c[key(alist, i)] = c[key(alist, i)] + 1

# Find the last index for each element
c = c - 1 # to decrement each element for zero-based indexing
for i in range(1, largest + 1):
c[i] = c[i] + c[i - 1]

result = [None]*len(alist)
for i in range(len(alist) - 1, -1, -1):
result[c[key(alist, i)]] = alist[i]
c[key(alist, i)] = c[key(alist, i)] - 1

return result

alist = input('Enter the list of (nonnegative) numbers: ').split()
alist = [int(x) for x in alist]
print('Sorted list: ', end='')
print(sorted_list)```
Program Explanation

1. The user is prompted to enter a list of numbers.
2. The list is passed to the radix_sort function and the returned list is the sorted list.
3. The sorted list is displayed.

Runtime Test Cases
```Case 1:
Enter the list of (nonnegative) numbers: 38 20 1 3 4 0 2 5 1 3 8 2 9 10
Sorted list: [0, 1, 1, 2, 2, 3, 3, 4, 5, 8, 9, 10, 20, 38]

Case 2:
Enter the list of (nonnegative) numbers: 7 5 3 2 1
Sorted list: [1, 2, 3, 5, 7]

Case 3:
Enter the list of (nonnegative) numbers: 3
Sorted list: ```

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