🧮 冒泡排序 (Bubble Sort)

难度 / Difficulty: 简单 (Easy)
分类 / Category: 排序 (Sorting)
时间复杂度 / Time Complexity: O(n²)
空间复杂度 / Space Complexity: O(1)

📖 算法简介 / Introduction

冒泡排序是一种简单的排序算法，通过相邻元素的比较和交换将最大（或最小）的元素逐步冒泡到序列的一端。

Bubble sort is a simple sorting algorithm that repeatedly steps through the list, compares adjacent elements and swaps them if they are in the wrong order.

💡 算法原理 / Principle

重复遍历数组，比较相邻元素，大的往后冒泡。优化版本可在提前排好序时停止。

Repeatedly traverse the array, comparing adjacent elements and bubbling the larger one to the end. The optimized version stops early when no swaps are needed.

📝 代码实现 / Implementation

def bubble_sort(arr):
    n = len(arr)
    for i in range(n):
        swapped = False
        for j in range(0, n - i - 1):
            if arr[j] > arr[j + 1]:
                arr[j], arr[j + 1] = arr[j + 1], arr[j]
                swapped = True
        if not swapped:
            break
    return arr

✨ 示例 / Example

数组 [64, 34, 25, 12, 22, 11] 排序后为 [11, 12, 22, 25, 34, 64]。

Array [64, 34, 25, 12, 22, 11] becomes [11, 12, 22, 25, 34, 64] after sorting.

🎯 适用场景 / Scenarios

教学理解, 小规模数据排序, 检查是否已排序

Educational purposes, Small datasets, Checking if already sorted

🔄 扩展阅读 / Further Reading

• 建议在 LeetCode 或 HackerRank 上刷相关题目
• 尝试自己实现非递归版本
• 对比其他同类型算法的性能差异