mirror of
https://github.com/krahets/hello-algo.git
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1050 lines
27 KiB
Markdown
Executable file
1050 lines
27 KiB
Markdown
Executable file
---
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comments: true
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---
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# 6.1. 哈希表
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哈希表通过建立「键 key」和「值 value」之间的映射，实现高效的元素查找。具体地，输入一个 key ，在哈希表中查询并获取 value ，时间复杂度为 $O(1)$ 。
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例如，给定一个包含 $n$ 个学生的数据库，每个学生有“姓名 `name` ”和“学号 `id` ”两项数据，希望实现一个查询功能：**输入一个学号，返回对应的姓名**，则可以使用哈希表实现。
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<p align="center"> Fig. 哈希表抽象表示 </p>
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## 6.1.1. 哈希表效率
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除了哈希表之外，还可以使用以下数据结构来实现上述查询功能：
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1. **无序数组**：每个元素为 `[学号, 姓名]` ；
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2. **有序数组**：将 `1.` 中的数组按照学号从小到大排序；
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3. **链表**：每个结点的值为 `[学号, 姓名]` ；
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4. **二叉搜索树**：每个结点的值为 `[学号, 姓名]` ，根据学号大小来构建树；
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使用上述方法，各项操作的时间复杂度如下表所示（在此不做赘述，详解可见 [二叉搜索树章节](https://www.hello-algo.com/chapter_tree/binary_search_tree/#_6)）。无论是查找元素、还是增删元素，哈希表的时间复杂度都是 $O(1)$ ，全面胜出！
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<div class="center-table" markdown>
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| | 无序数组 | 有序数组 | 链表 | 二叉搜索树 | 哈希表 |
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| -------- | -------- | ----------- | ------ | ----------- | ------ |
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| 查找元素 | $O(n)$ | $O(\log n)$ | $O(n)$ | $O(\log n)$ | $O(1)$ |
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| 插入元素 | $O(1)$ | $O(n)$ | $O(1)$ | $O(\log n)$ | $O(1)$ |
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| 删除元素 | $O(n)$ | $O(n)$ | $O(n)$ | $O(\log n)$ | $O(1)$ |
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</div>
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## 6.1.2. 哈希表常用操作
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哈希表的基本操作包括 **初始化、查询操作、添加与删除键值对**。
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=== "Java"
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```java title="hash_map.java"
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/* 初始化哈希表 */
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Map<Integer, String> map = new HashMap<>();
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/* 添加操作 */
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// 在哈希表中添加键值对 (key, value)
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map.put(12836, "小哈");
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map.put(15937, "小啰");
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map.put(16750, "小算");
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map.put(13276, "小法");
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map.put(10583, "小鸭");
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/* 查询操作 */
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// 向哈希表输入键 key ，得到值 value
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String name = map.get(15937);
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/* 删除操作 */
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// 在哈希表中删除键值对 (key, value)
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map.remove(10583);
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```
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=== "C++"
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```cpp title="hash_map.cpp"
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/* 初始化哈希表 */
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unordered_map<int, string> map;
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/* 添加操作 */
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// 在哈希表中添加键值对 (key, value)
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map[12836] = "小哈";
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map[15937] = "小啰";
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map[16750] = "小算";
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map[13276] = "小法";
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map[10583] = "小鸭";
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/* 查询操作 */
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// 向哈希表输入键 key ，得到值 value
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string name = map[15937];
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/* 删除操作 */
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// 在哈希表中删除键值对 (key, value)
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map.erase(10583);
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```
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=== "Python"
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```python title="hash_map.py"
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""" 初始化哈希表 """
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mapp = {}
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""" 添加操作 """
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# 在哈希表中添加键值对 (key, value)
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mapp[12836] = "小哈"
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mapp[15937] = "小啰"
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mapp[16750] = "小算"
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mapp[13276] = "小法"
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mapp[10583] = "小鸭"
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""" 查询操作 """
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# 向哈希表输入键 key ，得到值 value
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name = mapp[15937]
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""" 删除操作 """
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# 在哈希表中删除键值对 (key, value)
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mapp.pop(10583)
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```
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=== "Go"
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```go title="hash_map.go"
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/* 初始化哈希表 */
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mapp := make(map[int]string)
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/* 添加操作 */
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// 在哈希表中添加键值对 (key, value)
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mapp[12836] = "小哈"
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mapp[15937] = "小啰"
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mapp[16750] = "小算"
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mapp[13276] = "小法"
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mapp[10583] = "小鸭"
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/* 查询操作 */
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// 向哈希表输入键 key ，得到值 value
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name := mapp[15937]
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/* 删除操作 */
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// 在哈希表中删除键值对 (key, value)
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delete(mapp, 10583)
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```
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=== "JavaScript"
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```javascript title="hash_map.js"
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/* 初始化哈希表 */
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const map = new ArrayHashMap();
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/* 添加操作 */
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// 在哈希表中添加键值对 (key, value)
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map.set(12836, '小哈');
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map.set(15937, '小啰');
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map.set(16750, '小算');
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map.set(13276, '小法');
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map.set(10583, '小鸭');
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/* 查询操作 */
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// 向哈希表输入键 key ，得到值 value
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let name = map.get(15937);
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/* 删除操作 */
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// 在哈希表中删除键值对 (key, value)
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map.delete(10583);
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```
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=== "TypeScript"
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```typescript title="hash_map.ts"
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/* 初始化哈希表 */
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const map = new Map<number, string>();
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/* 添加操作 */
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// 在哈希表中添加键值对 (key, value)
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map.set(12836, '小哈');
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map.set(15937, '小啰');
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map.set(16750, '小算');
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map.set(13276, '小法');
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map.set(10583, '小鸭');
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console.info('\n添加完成后，哈希表为\nKey -> Value');
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console.info(map);
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/* 查询操作 */
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// 向哈希表输入键 key ，得到值 value
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let name = map.get(15937);
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console.info('\n输入学号 15937 ，查询到姓名 ' + name);
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/* 删除操作 */
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// 在哈希表中删除键值对 (key, value)
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map.delete(10583);
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console.info('\n删除 10583 后，哈希表为\nKey -> Value');
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console.info(map);
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```
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=== "C"
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```c title="hash_map.c"
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```
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=== "C#"
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```csharp title="hash_map.cs"
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/* 初始化哈希表 */
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Dictionary<int, String> map = new ();
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/* 添加操作 */
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// 在哈希表中添加键值对 (key, value)
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map.Add(12836, "小哈");
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map.Add(15937, "小啰");
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map.Add(16750, "小算");
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map.Add(13276, "小法");
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map.Add(10583, "小鸭");
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/* 查询操作 */
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// 向哈希表输入键 key ，得到值 value
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String name = map[15937];
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/* 删除操作 */
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// 在哈希表中删除键值对 (key, value)
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map.Remove(10583);
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```
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=== "Swift"
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```swift title="hash_map.swift"
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/* 初始化哈希表 */
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var map: [Int: String] = [:]
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/* 添加操作 */
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// 在哈希表中添加键值对 (key, value)
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map[12836] = "小哈"
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map[15937] = "小啰"
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map[16750] = "小算"
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map[13276] = "小法"
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map[10583] = "小鸭"
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/* 查询操作 */
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// 向哈希表输入键 key ，得到值 value
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let name = map[15937]!
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/* 删除操作 */
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// 在哈希表中删除键值对 (key, value)
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map.removeValue(forKey: 10583)
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```
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=== "Zig"
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```zig title="hash_map.zig"
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```
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遍历哈希表有三种方式，即 **遍历键值对、遍历键、遍历值**。
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=== "Java"
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```java title="hash_map.java"
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/* 遍历哈希表 */
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// 遍历键值对 key->value
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for (Map.Entry <Integer, String> kv: map.entrySet()) {
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System.out.println(kv.getKey() + " -> " + kv.getValue());
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}
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// 单独遍历键 key
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for (int key: map.keySet()) {
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System.out.println(key);
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}
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// 单独遍历值 value
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for (String val: map.values()) {
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System.out.println(val);
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}
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```
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=== "C++"
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```cpp title="hash_map.cpp"
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/* 遍历哈希表 */
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// 遍历键值对 key->value
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for (auto kv: map) {
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cout << kv.first << " -> " << kv.second << endl;
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}
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// 单独遍历键 key
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for (auto key: map) {
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cout << key.first << endl;
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}
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// 单独遍历值 value
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for (auto val: map) {
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cout << val.second << endl;
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}
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```
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=== "Python"
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```python title="hash_map.py"
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""" 遍历哈希表 """
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# 遍历键值对 key->value
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for key, value in mapp.items():
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print(key, "->", value)
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# 单独遍历键 key
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for key in mapp.keys():
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print(key)
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# 单独遍历值 value
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for value in mapp.values():
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print(value)
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```
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=== "Go"
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```go title="hash_map_test.go"
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/* 遍历哈希表 */
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// 遍历键值对 key->value
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for key, value := range mapp {
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fmt.Println(key, "->", value)
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}
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// 单独遍历键 key
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for key := range mapp {
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fmt.Println(key)
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}
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// 单独遍历值 value
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for _, value := range mapp {
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fmt.Println(value)
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}
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```
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=== "JavaScript"
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```javascript title="hash_map.js"
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/* 遍历哈希表 */
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// 遍历键值对 key->value
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for (const entry of map.entries()) {
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if (!entry) continue;
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console.info(entry.key + ' -> ' + entry.val);
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}
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// 单独遍历键 key
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for (const key of map.keys()) {
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console.info(key);
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}
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// 单独遍历值 value
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for (const val of map.values()) {
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console.info(val);
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}
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```
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=== "TypeScript"
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```typescript title="hash_map.ts"
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/* 遍历哈希表 */
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console.info('\n遍历键值对 Key->Value');
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for (const [k, v] of map.entries()) {
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console.info(k + ' -> ' + v);
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}
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console.info('\n单独遍历键 Key');
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for (const k of map.keys()) {
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console.info(k);
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}
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console.info('\n单独遍历值 Value');
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for (const v of map.values()) {
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console.info(v);
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}
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```
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=== "C"
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```c title="hash_map.c"
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```
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=== "C#"
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```csharp title="hash_map.cs"
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/* 遍历哈希表 */
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// 遍历键值对 Key->Value
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foreach (var kv in map) {
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Console.WriteLine(kv.Key + " -> " + kv.Value);
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}
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// 单独遍历键 key
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foreach (int key in map.Keys) {
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Console.WriteLine(key);
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}
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// 单独遍历值 value
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foreach (String val in map.Values) {
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Console.WriteLine(val);
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}
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```
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=== "Swift"
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```swift title="hash_map.swift"
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/* 遍历哈希表 */
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// 遍历键值对 Key->Value
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for (key, value) in map {
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print("\(key) -> \(value)")
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}
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// 单独遍历键 Key
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for key in map.keys {
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print(key)
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}
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// 单独遍历值 Value
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for value in map.values {
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print(value)
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}
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```
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=== "Zig"
|
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```zig title="hash_map.zig"
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```
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## 6.1.3. 哈希函数
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哈希表中存储元素的数据结构被称为「桶 Bucket」，底层实现可能是数组、链表、二叉树（红黑树），或是它们的组合。
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最简单地，**我们可以仅用一个「数组」来实现哈希表**。首先，将所有 value 放入数组中，那么每个 value 在数组中都有唯一的「索引」。显然，访问 value 需要给定索引，而为了 **建立 key 和索引之间的映射关系**，我们需要使用「哈希函数 Hash Function」。
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设数组为 `bucket` ，哈希函数为 `f(x)` ，输入键为 `key` 。那么获取 value 的步骤为：
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1. 通过哈希函数计算出索引，即 `index = f(key)` ；
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2. 通过索引在数组中获取值，即 `value = bucket[index]` ；
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以上述学生数据 `key 学号 -> value 姓名` 为例，我们可以将「哈希函数」设计为
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$$
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f(x) = x \% 100
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$$
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|
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|
||
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<p align="center"> Fig. 哈希函数 </p>
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|
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=== "Java"
|
||
|
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```java title="array_hash_map.java"
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/* 键值对 int->String */
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class Entry {
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public int key;
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public String val;
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public Entry(int key, String val) {
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this.key = key;
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this.val = val;
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}
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}
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/* 基于数组简易实现的哈希表 */
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class ArrayHashMap {
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private List<Entry> bucket;
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public ArrayHashMap() {
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// 初始化一个长度为 100 的桶（数组）
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bucket = new ArrayList<>();
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for (int i = 0; i < 100; i++) {
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bucket.add(null);
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}
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}
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/* 哈希函数 */
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private int hashFunc(int key) {
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int index = key % 100;
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return index;
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}
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/* 查询操作 */
|
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public String get(int key) {
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int index = hashFunc(key);
|
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Entry pair = bucket.get(index);
|
||
if (pair == null) return null;
|
||
return pair.val;
|
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}
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|
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/* 添加操作 */
|
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public void put(int key, String val) {
|
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Entry pair = new Entry(key, val);
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int index = hashFunc(key);
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bucket.set(index, pair);
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}
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|
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/* 删除操作 */
|
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public void remove(int key) {
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||
int index = hashFunc(key);
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// 置为 null ，代表删除
|
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bucket.set(index, null);
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}
|
||
|
||
/* 获取所有键值对 */
|
||
public List<Entry> entrySet() {
|
||
List<Entry> entrySet = new ArrayList<>();
|
||
for (Entry pair : bucket) {
|
||
if (pair != null)
|
||
entrySet.add(pair);
|
||
}
|
||
return entrySet;
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}
|
||
|
||
/* 获取所有键 */
|
||
public List<Integer> keySet() {
|
||
List<Integer> keySet = new ArrayList<>();
|
||
for (Entry pair : bucket) {
|
||
if (pair != null)
|
||
keySet.add(pair.key);
|
||
}
|
||
return keySet;
|
||
}
|
||
|
||
/* 获取所有值 */
|
||
public List<String> valueSet() {
|
||
List<String> valueSet = new ArrayList<>();
|
||
for (Entry pair : bucket) {
|
||
if (pair != null)
|
||
valueSet.add(pair.val);
|
||
}
|
||
return valueSet;
|
||
}
|
||
|
||
/* 打印哈希表 */
|
||
public void print() {
|
||
for (Entry kv: entrySet()) {
|
||
System.out.println(kv.key + " -> " + kv.val);
|
||
}
|
||
}
|
||
}
|
||
```
|
||
|
||
=== "C++"
|
||
|
||
```cpp title="array_hash_map.cpp"
|
||
/* 键值对 int->String */
|
||
struct Entry {
|
||
public:
|
||
int key;
|
||
string val;
|
||
Entry(int key, string val) {
|
||
this->key = key;
|
||
this->val = val;
|
||
}
|
||
};
|
||
|
||
/* 基于数组简易实现的哈希表 */
|
||
class ArrayHashMap {
|
||
private:
|
||
vector<Entry*> bucket;
|
||
public:
|
||
ArrayHashMap() {
|
||
// 初始化一个长度为 100 的桶（数组）
|
||
bucket= vector<Entry*>(100);
|
||
}
|
||
|
||
/* 哈希函数 */
|
||
int hashFunc(int key) {
|
||
int index = key % 100;
|
||
return index;
|
||
}
|
||
|
||
/* 查询操作 */
|
||
string get(int key) {
|
||
int index = hashFunc(key);
|
||
Entry* pair = bucket[index];
|
||
if (pair == nullptr)
|
||
return nullptr;
|
||
return pair->val;
|
||
}
|
||
|
||
/* 添加操作 */
|
||
void put(int key, string val) {
|
||
Entry* pair = new Entry(key, val);
|
||
int index = hashFunc(key);
|
||
bucket[index] = pair;
|
||
}
|
||
|
||
/* 删除操作 */
|
||
void remove(int key) {
|
||
int index = hashFunc(key);
|
||
// 置为 nullptr ，代表删除
|
||
bucket[index] = nullptr;
|
||
}
|
||
|
||
/* 获取所有键值对 */
|
||
vector<Entry*> entrySet() {
|
||
vector<Entry*> entrySet;
|
||
for (Entry* pair: bucket) {
|
||
if (pair != nullptr) {
|
||
entrySet.push_back(pair);
|
||
}
|
||
}
|
||
return entrySet;
|
||
}
|
||
|
||
/* 获取所有键 */
|
||
vector<int> keySet() {
|
||
vector<int> keySet;
|
||
for (Entry* pair: bucket) {
|
||
if (pair != nullptr) {
|
||
keySet.push_back(pair->key);
|
||
}
|
||
}
|
||
return keySet;
|
||
}
|
||
|
||
/* 获取所有值 */
|
||
vector<string> valueSet() {
|
||
vector<string> valueSet;
|
||
for (Entry* pair: bucket) {
|
||
if (pair != nullptr){
|
||
valueSet.push_back(pair->val);
|
||
}
|
||
}
|
||
return valueSet;
|
||
}
|
||
|
||
/* 打印哈希表 */
|
||
void print() {
|
||
for (Entry* kv: entrySet()) {
|
||
cout << kv->key << " -> " << kv->val << endl;
|
||
}
|
||
}
|
||
};
|
||
```
|
||
|
||
=== "Python"
|
||
|
||
```python title="array_hash_map.py"
|
||
""" 键值对 int->String """
|
||
class Entry:
|
||
def __init__(self, key, val):
|
||
self.key = key
|
||
self.val = val
|
||
|
||
""" 基于数组简易实现的哈希表 """
|
||
class ArrayHashMap:
|
||
def __init__(self):
|
||
# 初始化一个长度为 100 的桶（数组）
|
||
self.bucket = [None] * 100
|
||
|
||
""" 哈希函数 """
|
||
def hash_func(self, key):
|
||
index = key % 100
|
||
return index
|
||
|
||
""" 查询操作 """
|
||
def get(self, key):
|
||
index = self.hash_func(key)
|
||
pair = self.bucket[index]
|
||
if pair is None:
|
||
return None
|
||
return pair.val
|
||
|
||
""" 添加操作 """
|
||
def put(self, key, val):
|
||
pair = Entry(key, val)
|
||
index = self.hash_func(key)
|
||
self.bucket[index] = pair
|
||
|
||
""" 删除操作 """
|
||
def remove(self, key):
|
||
index = self.hash_func(key)
|
||
# 置为 None ，代表删除
|
||
self.bucket[index] = None
|
||
|
||
""" 获取所有键值对 """
|
||
def entry_set(self):
|
||
result = []
|
||
for pair in self.bucket:
|
||
if pair is not None:
|
||
result.append(pair)
|
||
return result
|
||
|
||
""" 获取所有键 """
|
||
def key_set(self):
|
||
result = []
|
||
for pair in self.bucket:
|
||
if pair is not None:
|
||
result.append(pair.key)
|
||
return result
|
||
|
||
""" 获取所有值 """
|
||
def value_set(self):
|
||
result = []
|
||
for pair in self.bucket:
|
||
if pair is not None:
|
||
result.append(pair.val)
|
||
return result
|
||
|
||
""" 打印哈希表 """
|
||
def print(self):
|
||
for pair in self.bucket:
|
||
if pair is not None:
|
||
print(pair.key, "->", pair.val)
|
||
```
|
||
|
||
=== "Go"
|
||
|
||
```go title="array_hash_map.go"
|
||
/* 键值对 int->String */
|
||
type entry struct {
|
||
key int
|
||
val string
|
||
}
|
||
|
||
/* 基于数组简易实现的哈希表 */
|
||
type arrayHashMap struct {
|
||
bucket []*entry
|
||
}
|
||
|
||
func newArrayHashMap() *arrayHashMap {
|
||
// 初始化一个长度为 100 的桶（数组）
|
||
bucket := make([]*entry, 100)
|
||
return &arrayHashMap{bucket: bucket}
|
||
}
|
||
|
||
/* 哈希函数 */
|
||
func (a *arrayHashMap) hashFunc(key int) int {
|
||
index := key % 100
|
||
return index
|
||
}
|
||
|
||
/* 查询操作 */
|
||
func (a *arrayHashMap) get(key int) string {
|
||
index := a.hashFunc(key)
|
||
pair := a.bucket[index]
|
||
if pair == nil {
|
||
return "Not Found"
|
||
}
|
||
return pair.val
|
||
}
|
||
|
||
/* 添加操作 */
|
||
func (a *arrayHashMap) put(key int, val string) {
|
||
pair := &entry{key: key, val: val}
|
||
index := a.hashFunc(key)
|
||
a.bucket[index] = pair
|
||
}
|
||
|
||
/* 删除操作 */
|
||
func (a *arrayHashMap) remove(key int) {
|
||
index := a.hashFunc(key)
|
||
// 置为 nil ，代表删除
|
||
a.bucket[index] = nil
|
||
}
|
||
```
|
||
|
||
=== "JavaScript"
|
||
|
||
```javascript title="array_hash_map.js"
|
||
/* 键值对 Number -> String */
|
||
class Entry {
|
||
constructor(key, val) {
|
||
this.key = key;
|
||
this.val = val;
|
||
}
|
||
}
|
||
|
||
/* 基于数组简易实现的哈希表 */
|
||
class ArrayHashMap {
|
||
#bucket;
|
||
constructor() {
|
||
// 初始化一个长度为 100 的桶（数组）
|
||
this.#bucket = new Array(100).fill(null);
|
||
}
|
||
|
||
/* 哈希函数 */
|
||
#hashFunc(key) {
|
||
return key % 100;
|
||
}
|
||
|
||
/* 查询操作 */
|
||
get(key) {
|
||
let index = this.#hashFunc(key);
|
||
let entry = this.#bucket[index];
|
||
if (entry === null) return null;
|
||
return entry.val;
|
||
}
|
||
|
||
/* 添加操作 */
|
||
set(key, val) {
|
||
let index = this.#hashFunc(key);
|
||
this.#bucket[index] = new Entry(key, val);
|
||
}
|
||
|
||
/* 删除操作 */
|
||
delete(key) {
|
||
let index = this.#hashFunc(key);
|
||
// 置为 null ，代表删除
|
||
this.#bucket[index] = null;
|
||
}
|
||
|
||
/* 获取所有键值对 */
|
||
entries() {
|
||
let arr = [];
|
||
for (let i = 0; i < this.#bucket.length; i++) {
|
||
if (this.#bucket[i]) {
|
||
arr.push(this.#bucket[i]);
|
||
}
|
||
}
|
||
return arr;
|
||
}
|
||
|
||
/* 获取所有键 */
|
||
keys() {
|
||
let arr = [];
|
||
for (let i = 0; i < this.#bucket.length; i++) {
|
||
if (this.#bucket[i]) {
|
||
arr.push(this.#bucket[i]?.key);
|
||
}
|
||
}
|
||
return arr;
|
||
}
|
||
|
||
/* 获取所有值 */
|
||
values() {
|
||
let arr = [];
|
||
for (let i = 0; i < this.#bucket.length; i++) {
|
||
if (this.#bucket[i]) {
|
||
arr.push(this.#bucket[i]?.val);
|
||
}
|
||
}
|
||
return arr;
|
||
}
|
||
|
||
/* 打印哈希表 */
|
||
print() {
|
||
let entrySet = this.entries();
|
||
for (const entry of entrySet) {
|
||
if (!entry) continue;
|
||
console.info(`${entry.key} -> ${entry.val}`);
|
||
}
|
||
}
|
||
}
|
||
```
|
||
|
||
=== "TypeScript"
|
||
|
||
```typescript title="array_hash_map.ts"
|
||
/* 键值对 Number -> String */
|
||
class Entry {
|
||
public key: number;
|
||
public val: string;
|
||
|
||
constructor(key: number, val: string) {
|
||
this.key = key;
|
||
this.val = val;
|
||
}
|
||
}
|
||
|
||
/* 基于数组简易实现的哈希表 */
|
||
class ArrayHashMap {
|
||
|
||
private readonly bucket: (Entry | null)[];
|
||
|
||
constructor() {
|
||
// 初始化一个长度为 100 的桶（数组）
|
||
this.bucket = (new Array(100)).fill(null);
|
||
}
|
||
|
||
/* 哈希函数 */
|
||
private hashFunc(key: number): number {
|
||
return key % 100;
|
||
}
|
||
|
||
/* 查询操作 */
|
||
public get(key: number): string | null {
|
||
let index = this.hashFunc(key);
|
||
let entry = this.bucket[index];
|
||
if (entry === null) return null;
|
||
return entry.val;
|
||
}
|
||
|
||
/* 添加操作 */
|
||
public set(key: number, val: string) {
|
||
let index = this.hashFunc(key);
|
||
this.bucket[index] = new Entry(key, val);
|
||
}
|
||
|
||
/* 删除操作 */
|
||
public delete(key: number) {
|
||
let index = this.hashFunc(key);
|
||
// 置为 null ，代表删除
|
||
this.bucket[index] = null;
|
||
}
|
||
|
||
/* 获取所有键值对 */
|
||
public entries(): (Entry | null)[] {
|
||
let arr: (Entry | null)[] = [];
|
||
for (let i = 0; i < this.bucket.length; i++) {
|
||
if (this.bucket[i]) {
|
||
arr.push(this.bucket[i]);
|
||
}
|
||
}
|
||
return arr;
|
||
}
|
||
|
||
/* 获取所有键 */
|
||
public keys(): (number | undefined)[] {
|
||
let arr: (number | undefined)[] = [];
|
||
for (let i = 0; i < this.bucket.length; i++) {
|
||
if (this.bucket[i]) {
|
||
arr.push(this.bucket[i]?.key);
|
||
}
|
||
}
|
||
return arr;
|
||
}
|
||
|
||
/* 获取所有值 */
|
||
public values(): (string | undefined)[] {
|
||
let arr: (string | undefined)[] = [];
|
||
for (let i = 0; i < this.bucket.length; i++) {
|
||
if (this.bucket[i]) {
|
||
arr.push(this.bucket[i]?.val);
|
||
}
|
||
}
|
||
return arr;
|
||
}
|
||
|
||
/* 打印哈希表 */
|
||
public print() {
|
||
let entrySet = this.entries();
|
||
for (const entry of entrySet) {
|
||
if (!entry) continue;
|
||
console.info(`${entry.key} -> ${entry.val}`);
|
||
}
|
||
}
|
||
}
|
||
```
|
||
|
||
=== "C"
|
||
|
||
```c title="array_hash_map.c"
|
||
|
||
```
|
||
|
||
=== "C#"
|
||
|
||
```csharp title="array_hash_map.cs"
|
||
/* 键值对 int->String */
|
||
class Entry
|
||
{
|
||
public int key;
|
||
public String val;
|
||
public Entry(int key, String val)
|
||
{
|
||
this.key = key;
|
||
this.val = val;
|
||
}
|
||
}
|
||
|
||
/* 基于数组简易实现的哈希表 */
|
||
class ArrayHashMap
|
||
{
|
||
private List<Entry?> bucket;
|
||
public ArrayHashMap()
|
||
{
|
||
// 初始化一个长度为 100 的桶（数组）
|
||
bucket = new ();
|
||
for (int i = 0; i < 100; i++)
|
||
{
|
||
bucket.Add(null);
|
||
}
|
||
}
|
||
/* 哈希函数 */
|
||
private int hashFunc(int key)
|
||
{
|
||
int index = key % 100;
|
||
return index;
|
||
}
|
||
/* 查询操作 */
|
||
public String? get(int key)
|
||
{
|
||
int index = hashFunc(key);
|
||
Entry? pair = bucket[index];
|
||
if (pair == null) return null;
|
||
return pair.val;
|
||
}
|
||
/* 添加操作 */
|
||
public void put(int key, String val)
|
||
{
|
||
Entry pair = new Entry(key, val);
|
||
int index = hashFunc(key);
|
||
bucket[index]=pair;
|
||
}
|
||
/* 删除操作 */
|
||
public void remove(int key)
|
||
{
|
||
int index = hashFunc(key);
|
||
// 置为 null ，代表删除
|
||
bucket[index]=null;
|
||
}
|
||
}
|
||
```
|
||
|
||
=== "Swift"
|
||
|
||
```swift title="array_hash_map.swift"
|
||
/* 键值对 int->String */
|
||
class Entry {
|
||
var key: Int
|
||
var val: String
|
||
|
||
init(key: Int, val: String) {
|
||
self.key = key
|
||
self.val = val
|
||
}
|
||
}
|
||
|
||
/* 基于数组简易实现的哈希表 */
|
||
class ArrayHashMap {
|
||
private var bucket: [Entry?] = []
|
||
|
||
init() {
|
||
// 初始化一个长度为 100 的桶（数组）
|
||
for _ in 0 ..< 100 {
|
||
bucket.append(nil)
|
||
}
|
||
}
|
||
|
||
/* 哈希函数 */
|
||
private func hashFunc(key: Int) -> Int {
|
||
let index = key % 100
|
||
return index
|
||
}
|
||
|
||
/* 查询操作 */
|
||
func get(key: Int) -> String? {
|
||
let index = hashFunc(key: key)
|
||
let pair = bucket[index]
|
||
return pair?.val
|
||
}
|
||
|
||
/* 添加操作 */
|
||
func put(key: Int, val: String) {
|
||
let pair = Entry(key: key, val: val)
|
||
let index = hashFunc(key: key)
|
||
bucket[index] = pair
|
||
}
|
||
|
||
/* 删除操作 */
|
||
func remove(key: Int) {
|
||
let index = hashFunc(key: key)
|
||
// 置为 nil ，代表删除
|
||
bucket[index] = nil
|
||
}
|
||
}
|
||
```
|
||
|
||
=== "Zig"
|
||
|
||
```zig title="array_hash_map.zig"
|
||
|
||
```
|
||
|
||
## 6.1.4. 哈希冲突
|
||
|
||
细心的同学可能会发现，**哈希函数 $f(x) = x \% 100$ 会在某些情况下失效**。具体地，当输入的 key 后两位相同时，哈希函数的计算结果也相同，指向同一个 value 。例如，分别查询两个学号 $12836$ 和 $20336$ ，则有
|
||
|
||
$$
|
||
f(12836) = f(20336) = 36
|
||
$$
|
||
|
||
两个学号指向了同一个姓名，这明显是不对的，我们将这种现象称为「哈希冲突 Hash Collision」。如何避免哈希冲突的问题将被留在下章讨论。
|
||
|
||
|
||
|
||
<p align="center"> Fig. 哈希冲突 </p>
|
||
|
||
综上所述，一个优秀的「哈希函数」应该具备以下特性：
|
||
|
||
- 尽量少地发生哈希冲突；
|
||
- 时间复杂度 $O(1)$ ，计算尽可能高效；
|
||
- 空间使用率高，即“键值对占用空间 / 哈希表总占用空间”尽可能大；
|