In the bubble sort algorithm, an array is typically used as the data structure to store the elements being sorted. The bubble sort algorithm is a simple and straightforward sorting algorithm that works by repeatedly swapping adjacent elements if they are in the wrong order.

## Array – The Data Structure

The array data structure is used in bubble sort because it provides a convenient way to store and access the elements being sorted. An array is a collection of elements of the same type, stored in contiguous memory locations.

Using an array allows us to easily compare adjacent elements and swap them if necessary. The index of each element in the array represents its position in the sorting order.

## Bubble Sort Algorithm

The bubble sort algorithm compares adjacent pairs of elements in the array and swaps them if they are in the wrong order. This process is repeated until all elements are in their correct positions.

Here’s how the bubble sort algorithm works:

**Step 1:**Start with an unsorted array.**Step 2:**Compare each pair of adjacent elements from left to right.**Step 3:**If the elements are out of order, swap them.**Step 4:**Repeat steps 2 and 3 until no more swaps are needed.

## An Example

To illustrate how bubble sort works, let’s consider an example:

Initial Array: [5, 3, 8, 4, 2] Pass 1: [3, 5, 4, 2,8] -> [3,4, 2,5, 8] -> [3, 2,4,5, 8] -> [2,3,4,5, 8] Pass 2: [2, 3,4,5, 8] -> [2,3,4,5, 8] Pass 3: [2,3,4,,,] -> [2,^{[5]}] -> [2, [,~~,~~^{[3]}[] - ] - ] - ] - ] - ] -[] -~~[~~] -~~[~~] -[[3]] -

In this example, the array is sorted in ascending order using bubble sort.

### Analyzing Bubble Sort Efficiency and Performance:

The bubble sort algorithm has an average and worst-case time complexity of O(n^2), where ‘n’ is the number of elements in the array. This means that for large arrays, bubble sort can be inefficient compared to other sorting algorithms like quicksort or mergesort.

However, bubble sort has a space complexity of O(1), as it only requires a constant amount of additional memory to perform the sorting operation.

Despite its simplicity, bubble sort is often not the preferred choice for large datasets due to its slower performance compared to more efficient sorting algorithms. However, it can still be useful for small arrays or educational purposes to understand the basic concepts of sorting algorithms.

### Conclusion

In conclusion, the bubble sort algorithm uses an array as the data structure to store and sort elements. The algorithm works by repeatedly comparing adjacent elements and swapping them if they are in the wrong order.

While bubble sort is simple to understand and implement, it can be inefficient for large datasets. Nonetheless, it serves as a good starting point for learning about sorting algorithms.