> For the complete documentation index, see [llms.txt](https://docs.1l.lol/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://docs.1l.lol/sorting/quick-sort.md).

# 快速排序

### 分治思想

快速排序选取一个**基准值（pivot）**，把数组分成“小于基准”和“大于基准”两部分，再分别递归排序。

### 时间复杂度

平均 **O(n log n)**，最坏 O(n²)（如对已排序数组取端点作基准）；**不稳定**。

```cpp
void quickSort(int a[], int l, int r) {
    if (l >= r) return;
    int pivot = a[(l + r) / 2];
    int i = l, j = r;
    while (i <= j) {
        while (a[i] < pivot) i++;
        while (a[j] > pivot) j--;
        if (i <= j) { swap(a[i], a[j]); i++; j--; }
    }
    quickSort(a, l, j);
    quickSort(a, i, r);
}
```

### 与归并排序对比

|     | 快速排序       | 归并排序       |
| --- | ---------- | ---------- |
| 平均  | O(n log n) | O(n log n) |
| 最坏  | O(n²)      | O(n log n) |
| 空间  | O(log n)   | O(n)       |
| 稳定性 | 不稳定        | 稳定         |

### 实践建议

平时可直接用标准库 `sort`（底层为混合排序），自己实现则要注意基准选取，避免退化。


---

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