> For the complete documentation index, see [llms.txt](https://rachel2011.gitbook.io/leetcode_cc150/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://rachel2011.gitbook.io/leetcode_cc150/data-structure/bubble-sort.md).

# Bubble Sort

Start at the beginning of the array and swap the first two elements if the first is greater than the second. Then we go to the next pair, and so on, continuously making sweeps of the array until it is sorted.

核心：**冒泡**，持续比较相邻元素，大的挪到后面，因此大的会逐步往后挪，故称之为冒泡。

冒泡排序对![n](https://wikimedia.org/api/rest_v1/media/math/render/svg/a601995d55609f2d9f5e233e36fbe9ea26011b3b)个项目需要[O](https://zh.wikipedia.org/wiki/大O符号)(![n^{2}](https://wikimedia.org/api/rest_v1/media/math/render/svg/ac9810bbdafe4a6a8061338db0f74e25b7952620))的比较次数，且可以[原地](https://zh.wikipedia.org/wiki/原地算法)排序。尽管这个算法是最简单了解和实现的排序算法之一，但它对于包含大量的元素的数列排序是很没有效率的。

冒泡排序算法的运作如下：

1. 比较相邻的元素。如果第一个比第二个大，就交换他们两个。
2. 对每一对相邻元素作同样的工作，从开始第一对到结尾的最后一对。这步做完后，最后的元素会是最大的数。
3. 针对所有的元素重复以上的步骤，除了最后一个。
4. 持续每次对越来越少的元素重复上面的步骤，直到没有任何一对数字需要比较。

## 复杂度分析 <a href="#fu-za-du-fen-xi" id="fu-za-du-fen-xi"></a>

平均情况与最坏情况均为 $$O(n^2)$$, 使用了 temp 作为临时交换变量，空间复杂度为 $$O(1)$$.+

## Reference

### <https://einsqiang.gitbooks.io/python-algorithm/content/basics_sorting/bubble_sort.html>


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