Organizing all the code blocks.

This commit is contained in:
Yudong Jin
2022-12-03 01:31:29 +08:00
parent fec56afd5f
commit 9bd5980a81
21 changed files with 2520 additions and 310 deletions

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@@ -99,6 +99,36 @@ comments: true
return a + b + c # 输出数据
```
=== "Go"
```go title=""
```
=== "JavaScript"
```js title=""
```
=== "TypeScript"
```typescript title=""
```
=== "C"
```c title=""
```
=== "C#"
```csharp title=""
```
## 推算方法
空间复杂度的推算方法和时间复杂度总体类似,只是从统计 “计算操作数量” 变为统计 “使用空间大小” 。与时间复杂度不同的是,**我们一般只关注「最差空间复杂度」**。这是因为内存空间是一个硬性要求,我们必须保证在所有输入数据下都有足够的内存空间预留。
@@ -140,6 +170,36 @@ comments: true
nums = [0] * n # O(n)
```
=== "Go"
```go title=""
```
=== "JavaScript"
```js title=""
```
=== "TypeScript"
```typescript title=""
```
=== "C"
```c title=""
```
=== "C#"
```csharp title=""
```
**在递归函数中,需要注意统计栈帧空间。** 例如函数 `loop()`,在循环中调用了 $n$ 次 `function()` ,每轮中的 `function()` 都返回并释放了栈帧空间,因此空间复杂度仍为 $O(1)$ 。而递归函数 `recur()` 在运行中会同时存在 $n$ 个未返回的 `recur()` ,从而使用 $O(n)$ 的栈帧空间。
=== "Java"
@@ -200,6 +260,36 @@ comments: true
return recur(n - 1)
```
=== "Go"
```go title=""
```
=== "JavaScript"
```js title=""
```
=== "TypeScript"
```typescript title=""
```
=== "C"
```c title=""
```
=== "C#"
```csharp title=""
```
## 常见类型
设输入数据大小为 $n$ ,常见的空间复杂度类型有(从低到高排列)
@@ -284,6 +374,36 @@ $$
function()
```
=== "Go"
```go title="space_complexity_types.go"
```
=== "JavaScript"
```js title="space_complexity_types.js"
```
=== "TypeScript"
```typescript title="space_complexity_types.ts"
```
=== "C"
```c title="space_complexity_types.c"
```
=== "C#"
```csharp title="space_complexity_types.cs"
```
### 线性阶 $O(n)$
线性阶常见于元素数量与 $n$ 成正比的数组、链表、栈、队列等。
@@ -341,6 +461,36 @@ $$
mapp[i] = str(i)
```
=== "Go"
```go title="space_complexity_types.go"
```
=== "JavaScript"
```js title="space_complexity_types.js"
```
=== "TypeScript"
```typescript title="space_complexity_types.ts"
```
=== "C"
```c title="space_complexity_types.c"
```
=== "C#"
```csharp title="space_complexity_types.cs"
```
以下递归函数会同时存在 $n$ 个未返回的 `algorithm()` 函数,使用 $O(n)$ 大小的栈帧空间。
=== "Java"
@@ -375,6 +525,36 @@ $$
linearRecur(n - 1)
```
=== "Go"
```go title="space_complexity_types.go"
```
=== "JavaScript"
```js title="space_complexity_types.js"
```
=== "TypeScript"
```typescript title="space_complexity_types.ts"
```
=== "C"
```c title="space_complexity_types.c"
```
=== "C#"
```csharp title="space_complexity_types.cs"
```
![space_complexity_recursive_linear](space_complexity.assets/space_complexity_recursive_linear.png)
<p align="center"> Fig. 递归函数产生的线性阶空间复杂度 </p>
@@ -428,6 +608,36 @@ $$
num_matrix = [[0] * n for _ in range(n)]
```
=== "Go"
```go title="space_complexity_types.go"
```
=== "JavaScript"
```js title="space_complexity_types.js"
```
=== "TypeScript"
```typescript title="space_complexity_types.ts"
```
=== "C"
```c title="space_complexity_types.c"
```
=== "C#"
```csharp title="space_complexity_types.cs"
```
在以下递归函数中,同时存在 $n$ 个未返回的 `algorihtm()` ,并且每个函数中都初始化了一个数组,长度分别为 $n, n-1, n-2, ..., 2, 1$ ,平均长度为 $\frac{n}{2}$ ,因此总体使用 $O(n^2)$ 空间。
=== "Java"
@@ -465,6 +675,36 @@ $$
return quadratic_recur(n - 1)
```
=== "Go"
```go title="space_complexity_types.go"
```
=== "JavaScript"
```js title="space_complexity_types.js"
```
=== "TypeScript"
```typescript title="space_complexity_types.ts"
```
=== "C"
```c title="space_complexity_types.c"
```
=== "C#"
```csharp title="space_complexity_types.cs"
```
![space_complexity_recursive_quadratic](space_complexity.assets/space_complexity_recursive_quadratic.png)
<p align="center"> Fig. 递归函数产生的平方阶空间复杂度 </p>
@@ -511,6 +751,36 @@ $$
return root
```
=== "Go"
```go title="space_complexity_types.go"
```
=== "JavaScript"
```js title="space_complexity_types.js"
```
=== "TypeScript"
```typescript title="space_complexity_types.ts"
```
=== "C"
```c title="space_complexity_types.c"
```
=== "C#"
```csharp title="space_complexity_types.cs"
```
![space_complexity_exponential](space_complexity.assets/space_complexity_exponential.png)
<p align="center"> Fig. 满二叉树下的指数阶空间复杂度 </p>