Implementing the Bubble Sort Algorithm with Python

### Bubble Sort: A Comprehensive Analysis of a Basic Sorting Algorithm Bubble Sort is based on the "bubble rising" principle. Its core idea is to repeatedly compare adjacent elements and swap those in the wrong order, allowing larger elements to gradually "bubble" to the end of the array until the entire array is sorted. The working steps are as follows: traverse the array for multiple rounds, compare and swap adjacent elements with reverse order pairs in each round, and after each round, the largest unsorted element is placed in its correct position; if no swaps occur in a round, the array is already sorted, and the process terminates early. In Python implementation, the outer loop controls the number of sorting rounds (at most n-1 rounds), the inner loop compares adjacent elements and swaps them, and a `swapped` flag is used to optimize the termination condition. The worst-case time complexity is O(n²) (for a completely reversed array), the best-case is O(n) (for a sorted array with optimization), the space complexity is O(1), and it is a stable sorting algorithm. Bubble Sort is simple and intuitive, suitable for small-scale data, and serves as a foundational understanding of sorting concepts. By examining its principles and Python code implementation, one can quickly grasp the core logic of comparing and swapping adjacent elements.