A radix sort is a sorting algorithm that works by distributing the elements into different buckets based on their digits or characters. It is a non-comparative sorting algorithm that can efficiently sort numbers, strings, or other data types. In this article, we will explore the concept of radix sort in data structures and understand how it works.

## How does Radix Sort work?

Radix sort takes advantage of the fact that integers have a finite number of digits. It starts by sorting the elements based on the least significant digit and moves towards the most significant digit. The process is repeated until all the digits have been considered.

**Example:**

Let’s consider an array with the following elements: [170, 45, 75, 90, 802, 24, 2, 66]

### Step 1: Sorting based on least significant digit (unit place)

In this step, we distribute the elements into different buckets based on their unit place digit and then concatenate them back into a single array.

__Bucket 0:__[170, 90]__Bucket 2:__[802, 2]__Bucket 4:__[24]__Bucket 5:__[45, 75]__Bucket 6:__[66]

The concatenated array after step 1: [170, 90, 802, 2, 24, 45, 75, 66]

### Step 2: Sorting based on tens place digit

In this step, we repeat the process of distributing the elements into different buckets based on their tens place digit and then concatenate them back into a single array.

__Bucket 0:__[802, 2, 24]__Bucket 1:__[170]__Bucket 4:__[]__Bucket 5:__[45, 75]__Bucket 6:__[66]__Bucket 9:__[90]

The concatenated array after step 2: [802, 2, 24, 170, 45, 75, 66, 90]

### Step 3: Sorting based on hundreds place digit

In this step, we distribute the elements into different buckets based on their hundreds place digit and then concatenate them back into a single array.

__Bucket 0:__[2, 24, 45, 66, 75, 90]__Bucket 1:__[]__Bucket 2:__[]__Bucket 3:__[]__Bucket 4:__[]__Bucket 5: []__**Bucket 6:**[802]

The concatenated array after step 3: **[2, 24, 45, 66, 75, 90, 802]**

### Step 4: Sorting based on thousands place digit

In this step, we distribute the elements into different buckets based on their thousands place digit and then concatenate them back into a single array. However, in our example, there are no elements with thousands place digits, so we can skip this step.

The final sorted array after all steps: **[2, 24, 45, 66, 75, 90, 802]**

## Time Complexity of Radix Sort

The time complexity of radix sort depends on the number of digits or characters in the input elements. Let ‘n’ be the number of elements and ‘d’ be the maximum number of digits or characters.

The overall time complexity of radix sort is O(d * (n + b)), where ‘b’ is the base for representing numbers or characters (typically 10 for decimal numbers).

## Conclusion

Radix sort is an interesting sorting algorithm that works by distributing elements based on their digits or characters. It is particularly useful when dealing with large quantities of data and can efficiently sort numbers or strings without comparison operations. Understanding the concept and implementation details of radix sort can enhance your knowledge of sorting algorithms in data structures.