Radix sort processes the elements the same way in which the names of the students are sorted according to their alphabetical order. There are 26 radix in that case due to the fact that, there are 26 alphabets in English. In the first pass, the names are grouped according to the ascending order of the first letter of names.

In the second pass, the names are grouped according to the ascending order of the second letter. The same process continues until we find the sorted list of names. The bucket are used to store the names produced in each pass. The number of passes depends upon the length of the name with the maximum letter.

In the case of integers, radix sort sorts the numbers according to their digits. The comparisons are made among the digits of the number from LSB to MSB. The number of passes depend upon the length of the number with the most number of digits.

## Complexity

Complexity Best Case Average Case Worst Case
Time Complexity Ω(n+k) θ(nk) O(nk)
Space Complexity O(n+k)

## Example

Consider the array of length 6 given below. Sort the array by using Radix sort.

A = {10, 2, 901, 803, 1024}

Pass 1: (Sort the list according to the digits at 0's place)

10, 901, 2, 803, 1024.

Pass 2: (Sort the list according to the digits at 10's place)

02, 10, 901, 803, 1024

Pass 3: (Sort the list according to the digits at 100's place)

02, 10, 1024, 803, 901.

Pass 4: (Sort the list according to the digits at 1000's place)

02, 10, 803, 901, 1024

Therefore, the list generated in the step 4 is the sorted list, arranged from radix sort.

## Algorithm

• Step 1:Find the largest number in ARR as LARGE
• Step 2: [INITIALIZE] SET NOP = Number of digits
in LARGE
• Step 3: SET PASS =0
• Step 4: Repeat Step 5 while PASS <= NOP-1
• Step 5: SET I = 0 and INITIALIZE buckets
• Step 6:Repeat Steps 7 to 9 while I
• Step 7: SET DIGIT = digit at PASSth place in A[I]
• Step 8: Add A[I] to the bucket numbered DIGIT
• Step 9: INCREMENT bucket count for bucket
numbered DIGIT
[END OF LOOP]
• Step 10: Collect the numbers in the bucket
[END OF LOOP]
• Step 11: END

## C Program

Output:

```The sorted array is:
23
23
23
34
45
65
67
89
90
101
```

## Java Program

Output:

```The sorted array is:
23
23
23
34
45
65
67
89
90
101
```

## C# Program

Output:

```The sorted array is:
23
23
23
34
45
65
67
89
90
101
```

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