Implementing the Bubble Sort Algorithm in Java

Bubble Sort is a basic sorting algorithm whose core idea is to repeatedly compare adjacent elements and swap their positions, allowing larger elements to "bubble up" to the end of the array (in ascending order). Its sorting process is completed through multiple iterations: each iteration determines the position of the largest element in the current unsorted portion and moves it to the end until the array is sorted. In Java implementation, the outer loop controls the number of sorting rounds (at most n-1 rounds), while the inner loop compares adjacent elements and performs swaps. A key optimization is using a `swapped` flag; if no swaps occur in a round, the algorithm terminates early, reducing the best-case time complexity to O(n). The worst and average-case time complexities are O(n²), with a space complexity of O(1) (in-place sorting). Despite its simple and intuitive principle, which makes it suitable for teaching the core concepts of sorting, bubble sort is inefficient and only applicable for small-scale data or educational scenarios. For large-scale data sorting, more efficient algorithms like Quick Sort are typically used.