Bubble Sort is a simple sorting algorithm that works by repeatedly stepping through the list to be sorted, comparing adjacent elements, and swapping them if they are in the wrong order. The process is repeated until the list is sorted. Here’s a step-by-step breakdown of how it operates:

1. Compare Adjacent Elements: Start from the beginning of the array and compare the first two elements.
2. Swap if Necessary: If the first element is greater than the second, swap them.
3. Continue: Move to the next pair of adjacent elements and repeat the comparison and swap if necessary.
4. Repeat Passes: After each pass through the array, the largest unsorted element will have "bubbled up" to its correct position. Repeat the process for the remaining unsorted elements until no swaps are needed.

Here’s a simple implementation of the Bubble Sort algorithm in C#:```csharpusing System;class Program{static void Main(){int[] arr = { 64, 34, 25, 12, 22, 11, 90 };BubbleSort(arr);Console.WriteLine("Sorted array: ");foreach (int value in arr){Console.Write(value + " ");}}static void BubbleSort(int[] arr){int n = arr.Length;for (int i = 0; i < n - 1; i++){for (int j = 0; j < n - i - 1; j++){if (arr[j] > arr[j + 1]){// Swap arr[j] and arr[j+1]int temp = arr[j];arr[j] = arr[j + 1];arr[j + 1] = temp;}}}}}```

• Outer Loop: The outer loop runs from the first element to the second last element, ensuring that each pass places the next largest element in its correct position.
• Inner Loop: The inner loop compares each pair of adjacent elements and swaps them if they are in the wrong order.
• Time Complexity: The average and worst-case time complexity of Bubble Sort is (O(n^2)), making it inefficient for large datasets. However, it is easy to understand and implement, which is why it is often taught in introductory programming courses.This implementation will sort the array in ascending order. You can modify the comparison in the inner loop to sort in descending order if needed.

To implement Bubble Sort in Python, follow these steps:

1. Define the function: Create a function that takes an array as an argument.
2. Outer loop: Use a loop to iterate through the array multiple times.
3. Inner loop: Inside the outer loop, use another loop to compare adjacent elements and swap them if they are in the wrong order.
4. Repeat: Continue this process until the array is sorted.

Here’s a simple implementation:

```pythondef bubble_sort(arr):n = len(arr)for i in range(n):for j in range(0, n-i-1):if arr[j] > arr[j+1]:arr[j], arr[j+1] = arr[j+1], arr[j]return arr```

This code sorts the array in ascending order.

1. Comparison and Swapping: The algorithm starts at the beginning of the list and compares the first two adjacent elements. If the first element is greater than the second, they are swapped. This process is repeated for each pair of adjacent elements in the list until the end is reached.
2. Multiple Passes: After each complete pass through the list, the largest unsorted element is guaranteed to be in its correct position at the end of the list. The algorithm then repeats the process for the remaining unsorted elements, effectively reducing the number of comparisons needed in subsequent passes.
3. Termination: The algorithm continues to iterate through the list until a complete pass is made without any swaps, indicating that the list is sorted.

• Time Complexity: The average and worst-case time complexity of bubble sort is (O(n^2)), where (n) is the number of elements in the list. This makes it inefficient for large datasets compared to more advanced algorithms like quicksort or mergesort.
• Space Complexity: Bubble sort is an in-place sorting algorithm, meaning it requires only a constant amount of additional memory space, (O(1)).
• Stability: Bubble sort is a stable sorting algorithm, which means that it maintains the relative order of records with equal keys (values).

• Educational Tool: Due to its simplicity, bubble sort is often used as an introductory algorithm in computer science education to teach the concepts of sorting and algorithm design.
• Limited Practical Use: In practice, bubble sort is rarely used for large datasets due to its inefficiency. It is more suitable for small or nearly sorted datasets where its simplicity can be an advantage.In summary, while bubble sort is a fundamental algorithm that is easy to understand and implement, its inefficiency makes it less suitable for practical applications in modern computing, where faster sorting algorithms are preferred.