Sorting Algorithms: An Introduction to Bubble Sort, Step-by-Step Explanation + Code Examples
Bubble Sort is one of the simplest sorting algorithms in computer science. Its core idea is to repeatedly compare adjacent elements and swap their positions, allowing larger elements to gradually "bubble" up to the end of the array. The basic steps are: the outer loop controls n-1 rounds of comparisons (each round determines the position of one large element), and the inner loop starts from the first element, comparing adjacent elements in sequence; if the previous element is larger and the next is smaller, they are swapped. An optimization is that if no swaps occur in a round, it indicates the array is already sorted, and the process can terminate early. In terms of time complexity, the worst-case scenario (completely reverse ordered) is O(n²), while the best case (already sorted) is O(n). The space complexity is O(1) (only constant extra space is required). This algorithm is simple to implement and easy to understand, making it suitable for sorting small-scale data and serving as a foundational entry point for sorting algorithms.
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### 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.
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