2023-02-26 20:16:55 +08:00
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# 数组(Array)
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2022-11-22 17:47:26 +08:00
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「数组 Array」是一种将 **相同类型元素** 存储在 **连续内存空间** 的数据结构,将元素在数组中的位置称为元素的「索引 Index」。
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2023-02-26 18:18:34 +08:00
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![数组定义与存储方式](array.assets/array_definition.png)
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2022-11-22 17:47:26 +08:00
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!!! note
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观察上图,我们发现 **数组首元素的索引为 $0$** 。你可能会想,这并不符合日常习惯,首个元素的索引为什么不是 $1$ 呢,这不是更加自然吗?我认同你的想法,但请先记住这个设定,后面讲内存地址计算时,我会尝试解答这个问题。
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2023-02-15 03:34:06 +08:00
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**数组初始化**。一般会用到无初始值、给定初始值两种写法,可根据需求选取。在不给定初始值的情况下,一般所有元素会被初始化为默认值 $0$ 。
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2022-11-22 17:47:26 +08:00
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=== "Java"
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```java title="array.java"
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/* 初始化数组 */
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int[] arr = new int[5]; // { 0, 0, 0, 0, 0 }
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int[] nums = { 1, 3, 2, 5, 4 };
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```
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=== "C++"
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```cpp title="array.cpp"
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2022-11-27 19:07:35 +08:00
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/* 初始化数组 */
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2023-02-15 03:34:06 +08:00
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// 存储在栈上
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int arr[5];
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int nums[5] { 1, 3, 2, 5, 4 };
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// 存储在堆上
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int* arr1 = new int[5];
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int* nums1 = new int[5] { 1, 3, 2, 5, 4 };
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2022-11-22 17:47:26 +08:00
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```
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=== "Python"
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```python title="array.py"
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2022-11-25 03:59:38 +08:00
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""" 初始化数组 """
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arr = [0] * 5 # [ 0, 0, 0, 0, 0 ]
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nums = [1, 3, 2, 5, 4]
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2022-11-22 17:47:26 +08:00
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```
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2022-12-03 01:31:29 +08:00
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=== "Go"
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```go title="array.go"
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2022-12-27 11:25:30 +08:00
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/* 初始化数组 */
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2023-01-06 03:28:27 +08:00
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var arr [5]int
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// 在 Go 中,指定长度时([5]int)为数组,不指定长度时([]int)为切片
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// 由于 Go 的数组被设计为在编译期确定长度,因此只能使用常量来指定长度
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// 为了方便实现扩容 extend() 方法,以下将切片(Slice)看作数组(Array)
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2022-12-28 10:46:12 +08:00
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nums := []int{1, 3, 2, 5, 4}
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2022-12-03 01:31:29 +08:00
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```
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=== "JavaScript"
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```javascript title="array.js"
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/* 初始化数组 */
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2022-12-12 21:39:48 +08:00
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var arr = new Array(5).fill(0);
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var nums = [1, 3, 2, 5, 4];
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2022-12-03 01:31:29 +08:00
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```
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=== "TypeScript"
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```typescript title="array.ts"
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2022-12-04 18:00:44 +08:00
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/* 初始化数组 */
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2022-12-12 21:25:07 +08:00
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let arr: number[] = new Array(5).fill(0);
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let nums: number[] = [1, 3, 2, 5, 4];
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2022-12-03 01:31:29 +08:00
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```
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=== "C"
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```c title="array.c"
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2023-02-11 00:43:04 +08:00
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int arr[5] = { 0 }; // { 0, 0, 0, 0, 0 }
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int nums[5] = { 1, 3, 2, 5, 4 };
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2022-12-03 01:31:29 +08:00
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```
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=== "C#"
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```csharp title="array.cs"
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2022-12-14 15:11:25 +08:00
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/* 初始化数组 */
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2022-12-14 11:03:28 +08:00
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int[] arr = new int[5]; // { 0, 0, 0, 0, 0 }
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int[] nums = { 1, 3, 2, 5, 4 };
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2022-12-03 01:31:29 +08:00
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```
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2023-01-05 21:16:05 +08:00
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=== "Swift"
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```swift title="array.swift"
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2023-01-08 20:53:24 +08:00
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/* 初始化数组 */
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2023-01-05 21:16:05 +08:00
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let arr = Array(repeating: 0, count: 5) // [0, 0, 0, 0, 0]
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let nums = [1, 3, 2, 5, 4]
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```
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2023-02-01 22:03:04 +08:00
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=== "Zig"
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```zig title="array.zig"
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2023-02-03 19:15:34 +08:00
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// 初始化数组
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var arr = [_]i32{0} ** 5; // { 0, 0, 0, 0, 0 }
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var nums = [_]i32{ 1, 3, 2, 5, 4 };
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2023-02-01 22:03:04 +08:00
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```
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2023-02-16 03:39:01 +08:00
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## 数组优点
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2022-11-22 17:47:26 +08:00
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2023-01-07 20:34:32 +08:00
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**在数组中访问元素非常高效**。这是因为在数组中,计算元素的内存地址非常容易。给定数组首个元素的地址、和一个元素的索引,利用以下公式可以直接计算得到该元素的内存地址,从而直接访问此元素。
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2022-11-22 17:47:26 +08:00
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2023-02-26 18:18:34 +08:00
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![数组元素的内存地址计算](array.assets/array_memory_location_calculation.png)
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2022-11-22 17:47:26 +08:00
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2023-02-22 19:02:26 +08:00
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```shell
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# 元素内存地址 = 数组内存地址 + 元素长度 * 元素索引
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2022-11-22 17:47:26 +08:00
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elementAddr = firtstElementAddr + elementLength * elementIndex
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```
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**为什么数组元素索引从 0 开始编号?** 根据地址计算公式,**索引本质上表示的是内存地址偏移量**,首个元素的地址偏移量是 $0$ ,那么索引是 $0$ 也就很自然了。
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访问元素的高效性带来了许多便利。例如,我们可以在 $O(1)$ 时间内随机获取一个数组中的元素。
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=== "Java"
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```java title="array.java"
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2023-02-07 04:43:52 +08:00
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[class]{array}-[func]{randomAccess}
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2022-11-22 17:47:26 +08:00
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```
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=== "C++"
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```cpp title="array.cpp"
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2023-02-08 04:17:26 +08:00
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[class]{}-[func]{randomAccess}
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2022-11-22 17:47:26 +08:00
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```
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=== "Python"
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```python title="array.py"
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2023-02-06 23:23:21 +08:00
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[class]{}-[func]{random_access}
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2022-11-22 17:47:26 +08:00
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```
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2022-12-03 01:31:29 +08:00
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=== "Go"
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```go title="array.go"
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2023-02-09 04:45:06 +08:00
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[class]{}-[func]{randomAccess}
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2022-12-03 01:31:29 +08:00
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```
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=== "JavaScript"
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```javascript title="array.js"
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2023-02-08 19:45:06 +08:00
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[class]{}-[func]{randomAccess}
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2022-12-03 01:31:29 +08:00
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```
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=== "TypeScript"
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```typescript title="array.ts"
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2023-02-08 19:45:06 +08:00
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[class]{}-[func]{randomAccess}
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2022-12-03 01:31:29 +08:00
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```
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=== "C"
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```c title="array.c"
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2023-02-11 00:43:04 +08:00
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[class]{}-[func]{randomAccess}
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2022-12-03 01:31:29 +08:00
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```
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=== "C#"
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```csharp title="array.cs"
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2023-02-08 22:18:02 +08:00
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[class]{array}-[func]{randomAccess}
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2022-12-03 01:31:29 +08:00
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```
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2023-01-05 21:16:05 +08:00
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=== "Swift"
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```swift title="array.swift"
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2023-02-08 20:30:05 +08:00
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[class]{}-[func]{randomAccess}
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2023-01-05 21:16:05 +08:00
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```
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2023-02-01 22:03:04 +08:00
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=== "Zig"
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```zig title="array.zig"
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2023-02-09 22:57:25 +08:00
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[class]{}-[func]{randomAccess}
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2023-02-01 22:03:04 +08:00
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```
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2023-02-16 03:39:01 +08:00
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## 数组缺点
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2022-11-22 17:47:26 +08:00
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2023-01-07 20:34:32 +08:00
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**数组在初始化后长度不可变**。由于系统无法保证数组之后的内存空间是可用的,因此数组长度无法扩展。而若希望扩容数组,则需新建一个数组,然后把原数组元素依次拷贝到新数组,在数组很大的情况下,这是非常耗时的。
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2022-11-22 17:47:26 +08:00
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=== "Java"
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```java title="array.java"
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2023-02-07 04:43:52 +08:00
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[class]{array}-[func]{extend}
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2022-11-22 17:47:26 +08:00
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```
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=== "C++"
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```cpp title="array.cpp"
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2023-02-08 04:17:26 +08:00
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[class]{}-[func]{extend}
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2022-11-22 17:47:26 +08:00
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```
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=== "Python"
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```python title="array.py"
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2023-02-06 23:23:21 +08:00
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[class]{}-[func]{extend}
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2022-11-22 17:47:26 +08:00
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```
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2022-12-03 01:31:29 +08:00
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=== "Go"
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```go title="array.go"
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2023-02-09 04:45:06 +08:00
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[class]{}-[func]{extend}
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2022-12-03 01:31:29 +08:00
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```
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=== "JavaScript"
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```javascript title="array.js"
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2023-02-08 19:45:06 +08:00
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[class]{}-[func]{extend}
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2022-12-03 01:31:29 +08:00
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```
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=== "TypeScript"
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```typescript title="array.ts"
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2023-02-08 19:45:06 +08:00
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[class]{}-[func]{extend}
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2022-12-03 01:31:29 +08:00
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```
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=== "C"
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```c title="array.c"
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2023-02-11 00:43:04 +08:00
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[class]{}-[func]{extend}
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2022-12-03 01:31:29 +08:00
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```
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=== "C#"
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```csharp title="array.cs"
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2023-02-08 22:18:02 +08:00
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[class]{array}-[func]{extend}
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2022-12-03 01:31:29 +08:00
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```
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2023-01-05 21:16:05 +08:00
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=== "Swift"
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```swift title="array.swift"
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2023-02-08 20:30:05 +08:00
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[class]{}-[func]{extend}
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2023-01-05 21:16:05 +08:00
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```
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2023-02-01 22:03:04 +08:00
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=== "Zig"
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```zig title="array.zig"
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2023-02-09 22:57:25 +08:00
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[class]{}-[func]{extend}
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2023-02-01 22:03:04 +08:00
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```
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2023-02-25 23:35:39 +08:00
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**数组中插入或删除元素效率低下**。如果我们想要在数组中间插入一个元素,由于数组元素在内存中是“紧挨着的”,它们之间没有空间再放任何数据。因此,我们不得不将此索引之后的所有元素都向后移动一位,然后再把元素赋值给该索引。
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2022-11-22 17:47:26 +08:00
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2023-02-26 18:18:34 +08:00
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![数组插入元素](array.assets/array_insert_element.png)
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2022-11-22 17:47:26 +08:00
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=== "Java"
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```java title="array.java"
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2023-02-07 04:43:52 +08:00
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[class]{array}-[func]{insert}
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2022-11-22 17:47:26 +08:00
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```
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=== "C++"
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```cpp title="array.cpp"
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2023-02-08 04:17:26 +08:00
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[class]{}-[func]{insert}
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2022-11-22 17:47:26 +08:00
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```
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=== "Python"
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```python title="array.py"
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2023-02-06 23:23:21 +08:00
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[class]{}-[func]{insert}
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2022-11-22 17:47:26 +08:00
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```
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2022-12-03 01:31:29 +08:00
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=== "Go"
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```go title="array.go"
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2023-02-09 04:45:06 +08:00
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[class]{}-[func]{insert}
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2022-12-03 01:31:29 +08:00
|
|
|
|
```
|
|
|
|
|
|
|
|
|
|
=== "JavaScript"
|
|
|
|
|
|
|
|
|
|
```javascript title="array.js"
|
2023-02-08 19:45:06 +08:00
|
|
|
|
[class]{}-[func]{insert}
|
2022-12-03 01:31:29 +08:00
|
|
|
|
```
|
|
|
|
|
|
|
|
|
|
=== "TypeScript"
|
|
|
|
|
|
|
|
|
|
```typescript title="array.ts"
|
2023-02-08 19:45:06 +08:00
|
|
|
|
[class]{}-[func]{insert}
|
2022-12-03 01:31:29 +08:00
|
|
|
|
```
|
|
|
|
|
|
|
|
|
|
=== "C"
|
|
|
|
|
|
|
|
|
|
```c title="array.c"
|
2023-02-11 00:43:04 +08:00
|
|
|
|
[class]{}-[func]{insert}
|
2022-12-03 01:31:29 +08:00
|
|
|
|
```
|
|
|
|
|
|
|
|
|
|
=== "C#"
|
|
|
|
|
|
|
|
|
|
```csharp title="array.cs"
|
2023-02-08 22:18:02 +08:00
|
|
|
|
[class]{array}-[func]{insert}
|
2022-12-03 01:31:29 +08:00
|
|
|
|
```
|
|
|
|
|
|
2023-01-05 21:16:05 +08:00
|
|
|
|
=== "Swift"
|
|
|
|
|
|
|
|
|
|
```swift title="array.swift"
|
2023-02-08 20:30:05 +08:00
|
|
|
|
[class]{}-[func]{insert}
|
2023-02-25 23:35:39 +08:00
|
|
|
|
```
|
2023-01-05 21:16:05 +08:00
|
|
|
|
|
2023-02-25 23:35:39 +08:00
|
|
|
|
删除元素也是类似,如果我们想要删除索引 $i$ 处的元素,则需要把索引 $i$ 之后的元素都向前移动一位。值得注意的是,删除元素后,原先末尾的元素变得“无意义”了,我们无需特意去修改它。
|
|
|
|
|
|
2023-02-26 18:18:34 +08:00
|
|
|
|
![数组删除元素](array.assets/array_remove_element.png)
|
2023-02-25 23:35:39 +08:00
|
|
|
|
|
|
|
|
|
=== "Java"
|
|
|
|
|
|
|
|
|
|
```java title="array.java"
|
|
|
|
|
[class]{array}-[func]{remove}
|
|
|
|
|
```
|
|
|
|
|
|
|
|
|
|
=== "C++"
|
|
|
|
|
|
|
|
|
|
```cpp title="array.cpp"
|
|
|
|
|
[class]{}-[func]{remove}
|
|
|
|
|
```
|
|
|
|
|
|
|
|
|
|
=== "Python"
|
|
|
|
|
|
|
|
|
|
```python title="array.py"
|
|
|
|
|
[class]{}-[func]{remove}
|
|
|
|
|
```
|
|
|
|
|
|
|
|
|
|
=== "Go"
|
|
|
|
|
|
|
|
|
|
```go title="array.go"
|
|
|
|
|
[class]{}-[func]{remove}
|
|
|
|
|
```
|
|
|
|
|
|
|
|
|
|
=== "JavaScript"
|
|
|
|
|
|
|
|
|
|
```javascript title="array.js"
|
|
|
|
|
[class]{}-[func]{remove}
|
|
|
|
|
```
|
|
|
|
|
|
|
|
|
|
=== "TypeScript"
|
|
|
|
|
|
|
|
|
|
```typescript title="array.ts"
|
|
|
|
|
[class]{}-[func]{remove}
|
|
|
|
|
```
|
|
|
|
|
|
|
|
|
|
=== "C"
|
|
|
|
|
|
|
|
|
|
```c title="array.c"
|
|
|
|
|
[class]{}-[func]{removeItem}
|
|
|
|
|
```
|
|
|
|
|
|
|
|
|
|
=== "C#"
|
|
|
|
|
|
|
|
|
|
```csharp title="array.cs"
|
|
|
|
|
[class]{array}-[func]{remove}
|
|
|
|
|
```
|
|
|
|
|
|
|
|
|
|
=== "Swift"
|
|
|
|
|
|
|
|
|
|
```swift title="array.swift"
|
2023-02-08 20:30:05 +08:00
|
|
|
|
[class]{}-[func]{remove}
|
2023-01-05 21:16:05 +08:00
|
|
|
|
```
|
|
|
|
|
|
2023-02-01 22:03:04 +08:00
|
|
|
|
=== "Zig"
|
|
|
|
|
|
|
|
|
|
```zig title="array.zig"
|
2023-02-09 22:57:25 +08:00
|
|
|
|
[class]{}-[func]{remove}
|
2023-02-01 22:03:04 +08:00
|
|
|
|
```
|
|
|
|
|
|
2023-02-25 23:35:39 +08:00
|
|
|
|
总结来看,数组的插入与删除操作有以下缺点:
|
|
|
|
|
|
|
|
|
|
- **时间复杂度高**:数组的插入和删除的平均时间复杂度均为 $O(N)$ ,其中 $N$ 为数组长度。
|
|
|
|
|
- **丢失元素**:由于数组的长度不可变,因此在插入元素后,超出数组长度范围的元素会被丢失。
|
|
|
|
|
- **内存浪费**:我们一般会初始化一个比较长的数组,只用前面一部分,这样在插入数据时,丢失的末尾元素都是我们不关心的,但这样做同时也会造成内存空间的浪费。
|
|
|
|
|
|
2023-02-16 03:39:01 +08:00
|
|
|
|
## 数组常用操作
|
2022-11-22 17:47:26 +08:00
|
|
|
|
|
2023-01-07 20:34:32 +08:00
|
|
|
|
**数组遍历**。以下介绍两种常用的遍历方法。
|
2022-11-22 17:47:26 +08:00
|
|
|
|
|
|
|
|
|
=== "Java"
|
|
|
|
|
|
|
|
|
|
```java title="array.java"
|
2023-02-07 04:43:52 +08:00
|
|
|
|
[class]{array}-[func]{traverse}
|
2022-11-22 17:47:26 +08:00
|
|
|
|
```
|
|
|
|
|
|
|
|
|
|
=== "C++"
|
|
|
|
|
|
|
|
|
|
```cpp title="array.cpp"
|
2023-02-08 04:17:26 +08:00
|
|
|
|
[class]{}-[func]{traverse}
|
2022-11-22 17:47:26 +08:00
|
|
|
|
```
|
|
|
|
|
|
|
|
|
|
=== "Python"
|
|
|
|
|
|
|
|
|
|
```python title="array.py"
|
2023-02-06 23:23:21 +08:00
|
|
|
|
[class]{}-[func]{traverse}
|
2022-11-22 17:47:26 +08:00
|
|
|
|
```
|
|
|
|
|
|
2022-12-03 01:31:29 +08:00
|
|
|
|
=== "Go"
|
|
|
|
|
|
|
|
|
|
```go title="array.go"
|
2023-02-09 04:45:06 +08:00
|
|
|
|
[class]{}-[func]{traverse}
|
2022-12-03 01:31:29 +08:00
|
|
|
|
```
|
|
|
|
|
|
|
|
|
|
=== "JavaScript"
|
|
|
|
|
|
|
|
|
|
```javascript title="array.js"
|
2023-02-08 19:45:06 +08:00
|
|
|
|
[class]{}-[func]{traverse}
|
2022-12-03 01:31:29 +08:00
|
|
|
|
```
|
|
|
|
|
|
|
|
|
|
=== "TypeScript"
|
|
|
|
|
|
|
|
|
|
```typescript title="array.ts"
|
2023-02-08 19:45:06 +08:00
|
|
|
|
[class]{}-[func]{traverse}
|
2022-12-03 01:31:29 +08:00
|
|
|
|
```
|
|
|
|
|
|
|
|
|
|
=== "C"
|
|
|
|
|
|
|
|
|
|
```c title="array.c"
|
2023-02-11 00:43:04 +08:00
|
|
|
|
[class]{}-[func]{traverse}
|
2022-12-03 01:31:29 +08:00
|
|
|
|
```
|
|
|
|
|
|
|
|
|
|
=== "C#"
|
|
|
|
|
|
|
|
|
|
```csharp title="array.cs"
|
2023-02-08 22:18:02 +08:00
|
|
|
|
[class]{array}-[func]{traverse}
|
2022-12-03 01:31:29 +08:00
|
|
|
|
```
|
|
|
|
|
|
2023-01-05 21:16:05 +08:00
|
|
|
|
=== "Swift"
|
|
|
|
|
|
|
|
|
|
```swift title="array.swift"
|
2023-02-08 20:30:05 +08:00
|
|
|
|
[class]{}-[func]{traverse}
|
2023-01-05 21:16:05 +08:00
|
|
|
|
```
|
|
|
|
|
|
2023-02-01 22:03:04 +08:00
|
|
|
|
=== "Zig"
|
|
|
|
|
|
|
|
|
|
```zig title="array.zig"
|
2023-02-09 22:57:25 +08:00
|
|
|
|
[class]{}-[func]{traverse}
|
2023-02-01 22:03:04 +08:00
|
|
|
|
```
|
|
|
|
|
|
2023-01-07 20:34:32 +08:00
|
|
|
|
**数组查找**。通过遍历数组,查找数组内的指定元素,并输出对应索引。
|
2022-11-22 17:47:26 +08:00
|
|
|
|
|
|
|
|
|
=== "Java"
|
|
|
|
|
|
|
|
|
|
```java title="array.java"
|
2023-02-07 04:43:52 +08:00
|
|
|
|
[class]{array}-[func]{find}
|
2022-11-22 17:47:26 +08:00
|
|
|
|
```
|
|
|
|
|
|
|
|
|
|
=== "C++"
|
|
|
|
|
|
|
|
|
|
```cpp title="array.cpp"
|
2023-02-08 04:17:26 +08:00
|
|
|
|
[class]{}-[func]{find}
|
2022-11-22 17:47:26 +08:00
|
|
|
|
```
|
|
|
|
|
|
|
|
|
|
=== "Python"
|
|
|
|
|
|
|
|
|
|
```python title="array.py"
|
2023-02-06 23:23:21 +08:00
|
|
|
|
[class]{}-[func]{find}
|
2022-11-22 17:47:26 +08:00
|
|
|
|
```
|
|
|
|
|
|
2022-12-03 01:31:29 +08:00
|
|
|
|
=== "Go"
|
|
|
|
|
|
|
|
|
|
```go title="array.go"
|
2023-02-09 04:45:06 +08:00
|
|
|
|
[class]{}-[func]{find}
|
2022-12-03 01:31:29 +08:00
|
|
|
|
```
|
|
|
|
|
|
|
|
|
|
=== "JavaScript"
|
|
|
|
|
|
|
|
|
|
```javascript title="array.js"
|
2023-02-08 19:45:06 +08:00
|
|
|
|
[class]{}-[func]{find}
|
2022-12-03 01:31:29 +08:00
|
|
|
|
```
|
|
|
|
|
|
|
|
|
|
=== "TypeScript"
|
|
|
|
|
|
|
|
|
|
```typescript title="array.ts"
|
2023-02-08 19:45:06 +08:00
|
|
|
|
[class]{}-[func]{find}
|
2022-12-03 01:31:29 +08:00
|
|
|
|
```
|
|
|
|
|
|
|
|
|
|
=== "C"
|
|
|
|
|
|
|
|
|
|
```c title="array.c"
|
2023-02-11 00:43:04 +08:00
|
|
|
|
[class]{}-[func]{find}
|
2022-12-03 01:31:29 +08:00
|
|
|
|
```
|
|
|
|
|
|
|
|
|
|
=== "C#"
|
|
|
|
|
|
|
|
|
|
```csharp title="array.cs"
|
2023-02-08 22:18:02 +08:00
|
|
|
|
[class]{array}-[func]{find}
|
2022-12-03 01:31:29 +08:00
|
|
|
|
```
|
|
|
|
|
|
2023-01-05 21:16:05 +08:00
|
|
|
|
=== "Swift"
|
|
|
|
|
|
|
|
|
|
```swift title="array.swift"
|
2023-02-08 20:30:05 +08:00
|
|
|
|
[class]{}-[func]{find}
|
2023-01-05 21:16:05 +08:00
|
|
|
|
```
|
|
|
|
|
|
2023-02-01 22:03:04 +08:00
|
|
|
|
=== "Zig"
|
|
|
|
|
|
|
|
|
|
```zig title="array.zig"
|
2023-02-09 22:57:25 +08:00
|
|
|
|
[class]{}-[func]{find}
|
2023-02-01 22:03:04 +08:00
|
|
|
|
```
|
|
|
|
|
|
2023-02-16 03:39:01 +08:00
|
|
|
|
## 数组典型应用
|
2022-11-22 17:47:26 +08:00
|
|
|
|
|
2023-01-07 20:34:32 +08:00
|
|
|
|
**随机访问**。如果我们想要随机抽取一些样本,那么可以用数组存储,并生成一个随机序列,根据索引实现样本的随机抽取。
|
2022-11-22 17:47:26 +08:00
|
|
|
|
|
2023-01-07 20:34:32 +08:00
|
|
|
|
**二分查找**。例如前文查字典的例子,我们可以将字典中的所有字按照拼音顺序存储在数组中,然后使用与日常查纸质字典相同的“翻开中间,排除一半”的方式,来实现一个查电子字典的算法。
|
2022-11-22 17:47:26 +08:00
|
|
|
|
|
2023-01-07 20:34:32 +08:00
|
|
|
|
**深度学习**。神经网络中大量使用了向量、矩阵、张量之间的线性代数运算,这些数据都是以数组的形式构建的。数组是神经网络编程中最常使用的数据结构。
|