> 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/basic-sorts.md).

# 冒泡、插入、选择排序

### 冒泡排序

相邻两两比较，大的往后“冒泡”。稳定。时间复杂度 O(n²)。

```cpp
void bubbleSort(int a[], int n) {
    for (int i = 0; i < n - 1; i++) {
        bool swapped = false;
        for (int j = 0; j < n - 1 - i; j++)
            if (a[j] > a[j + 1]) { swap(a[j], a[j + 1]); swapped = true; }
        if (!swapped) break;   // 已有序，提前结束
    }
}
```

### 选择排序

每轮选出最小值放到前面。**不稳定**。O(n²)。

```cpp
void selectSort(int a[], int n) {
    for (int i = 0; i < n - 1; i++) {
        int pos = i;
        for (int j = i + 1; j < n; j++)
            if (a[j] < a[pos]) pos = j;
        swap(a[i], a[pos]);
    }
}
```

### 插入排序

把元素插入到前面已排好序的部分。稳定。O(n²)，近似有序时接近 O(n)。

```cpp
void insertSort(int a[], int n) {
    for (int i = 1; i < n; i++) {
        int key = a[i], j = i - 1;
        while (j >= 0 && a[j] > key) { a[j + 1] = a[j]; j--; }
        a[j + 1] = key;
    }
}
```

### 三者对比

| 算法 | 稳定性 | 最好    | 最坏    |
| -- | --- | ----- | ----- |
| 冒泡 | 稳定  | O(n)  | O(n²) |
| 选择 | 不稳定 | O(n²) | O(n²) |
| 插入 | 稳定  | O(n)  | O(n²) |


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