Learning Bubble Sort from Scratch: Step-by-Step Teaching and Code Implementation

### Summary of Bubble Sort Sorting is the process of rearranging unordered data according to a set of rules. Bubble Sort is a fundamental sorting algorithm whose core principle is to gradually "bubble up" larger elements to the end of the array through adjacent element comparisons and swaps. **Core Idea**: In each iteration, start from the beginning of the array and compare adjacent elements sequentially. If a preceding element is larger than the following one, swap them. After each iteration, the largest element "sinks" to its correct position at the end, reducing the length of the unsorted portion by 1. Repeat until all elements are sorted. **Steps**: The outer loop controls the number of iterations (n-1 times, where n is the array length). The inner loop compares and swaps adjacent elements in each iteration. An optimization is to terminate early if no swaps occur in a round. **Complexity**: Time complexity is O(n²) in the worst case (completely reversed order) and O(n) in the best case (already sorted). Space complexity is O(1) (in-place sorting). **Characteristics and Applications**: It is simple to implement but inefficient (O(n²)). Suitable for small datasets or scenarios with low efficiency requirements (e.g., teaching demonstrations). By embodying the comparison-swap paradigm, Bubble Sort lays the foundation for understanding more complex sorting algorithms.