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hello-algo/en/docs/chapter_hashing/hash_map.md

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---
comments: true
---
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# 6.1   Hash table
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A "hash table", also known as a "hash map", achieves efficient element querying by establishing a mapping between keys and values. Specifically, when we input a `key` into the hash table, we can retrieve the corresponding `value` in $O(1)$ time.
As shown in the Figure 6-1 , given $n$ students, each with two pieces of data: "name" and "student number". If we want to implement a query feature that returns the corresponding name when given a student number, we can use the hash table shown in the Figure 6-1 .
![Abstract representation of a hash table](hash_map.assets/hash_table_lookup.png){ class="animation-figure" }
<p align="center"> Figure 6-1 &nbsp; Abstract representation of a hash table </p>
Apart from hash tables, arrays and linked lists can also be used to implement querying functions. Their efficiency is compared in the Table 6-1 .
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- **Adding elements**: Simply add the element to the end of the array (or linked list), using $O(1)$ time.
- **Querying elements**: Since the array (or linked list) is unordered, it requires traversing all the elements, using $O(n)$ time.
- **Deleting elements**: First, locate the element, then delete it from the array (or linked list), using $O(n)$ time.
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<p align="center"> Table 6-1 &nbsp; Comparison of element query efficiency </p>
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<div class="center-table" markdown>
| | Array | Linked List | Hash Table |
| -------------- | ------ | ----------- | ---------- |
| Find Element | $O(n)$ | $O(n)$ | $O(1)$ |
| Add Element | $O(1)$ | $O(1)$ | $O(1)$ |
| Delete Element | $O(n)$ | $O(n)$ | $O(1)$ |
</div>
Observations reveal that **the time complexity for adding, deleting, and querying in a hash table is $O(1)$**, which is highly efficient.
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## 6.1.1 &nbsp; Common operations of hash table
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Common operations of a hash table include initialization, querying, adding key-value pairs, and deleting key-value pairs, etc. Example code is as follows:
=== "Python"
```python title="hash_map.py"
# Initialize hash table
hmap: dict = {}
# Add operation
# Add key-value pair (key, value) to the hash table
hmap[12836] = "Xiao Ha"
hmap[15937] = "Xiao Luo"
hmap[16750] = "Xiao Suan"
hmap[13276] = "Xiao Fa"
hmap[10583] = "Xiao Ya"
# Query operation
# Input key into hash table, get value
name: str = hmap[15937]
# Delete operation
# Delete key-value pair (key, value) from hash table
hmap.pop(10583)
```
=== "C++"
```cpp title="hash_map.cpp"
/* Initialize hash table */
unordered_map<int, string> map;
/* Add operation */
// Add key-value pair (key, value) to the hash table
map[12836] = "Xiao Ha";
map[15937] = "Xiao Luo";
map[16750] = "Xiao Suan";
map[13276] = "Xiao Fa";
map[10583] = "Xiao Ya";
/* Query operation */
// Input key into hash table, get value
string name = map[15937];
/* Delete operation */
// Delete key-value pair (key, value) from hash table
map.erase(10583);
```
=== "Java"
```java title="hash_map.java"
/* Initialize hash table */
Map<Integer, String> map = new HashMap<>();
/* Add operation */
// Add key-value pair (key, value) to the hash table
map.put(12836, "Xiao Ha");
map.put(15937, "Xiao Luo");
map.put(16750, "Xiao Suan");
map.put(13276, "Xiao Fa");
map.put(10583, "Xiao Ya");
/* Query operation */
// Input key into hash table, get value
String name = map.get(15937);
/* Delete operation */
// Delete key-value pair (key, value) from hash table
map.remove(10583);
```
=== "C#"
```csharp title="hash_map.cs"
/* Initialize hash table */
Dictionary<int, string> map = new() {
/* Add operation */
// Add key-value pair (key, value) to the hash table
{ 12836, "Xiao Ha" },
{ 15937, "Xiao Luo" },
{ 16750, "Xiao Suan" },
{ 13276, "Xiao Fa" },
{ 10583, "Xiao Ya" }
};
/* Query operation */
// Input key into hash table, get value
string name = map[15937];
/* Delete operation */
// Delete key-value pair (key, value) from hash table
map.Remove(10583);
```
=== "Go"
```go title="hash_map_test.go"
/* Initialize hash table */
hmap := make(map[int]string)
/* Add operation */
// Add key-value pair (key, value) to the hash table
hmap[12836] = "Xiao Ha"
hmap[15937] = "Xiao Luo"
hmap[16750] = "Xiao Suan"
hmap[13276] = "Xiao Fa"
hmap[10583] = "Xiao Ya"
/* Query operation */
// Input key into hash table, get value
name := hmap[15937]
/* Delete operation */
// Delete key-value pair (key, value) from hash table
delete(hmap, 10583)
```
=== "Swift"
```swift title="hash_map.swift"
/* Initialize hash table */
var map: [Int: String] = [:]
/* Add operation */
// Add key-value pair (key, value) to the hash table
map[12836] = "Xiao Ha"
map[15937] = "Xiao Luo"
map[16750] = "Xiao Suan"
map[13276] = "Xiao Fa"
map[10583] = "Xiao Ya"
/* Query operation */
// Input key into hash table, get value
let name = map[15937]!
/* Delete operation */
// Delete key-value pair (key, value) from hash table
map.removeValue(forKey: 10583)
```
=== "JS"
```javascript title="hash_map.js"
/* Initialize hash table */
const map = new Map();
/* Add operation */
// Add key-value pair (key, value) to the hash table
map.set(12836, 'Xiao Ha');
map.set(15937, 'Xiao Luo');
map.set(16750, 'Xiao Suan');
map.set(13276, 'Xiao Fa');
map.set(10583, 'Xiao Ya');
/* Query operation */
// Input key into hash table, get value
let name = map.get(15937);
/* Delete operation */
// Delete key-value pair (key, value) from hash table
map.delete(10583);
```
=== "TS"
```typescript title="hash_map.ts"
/* Initialize hash table */
const map = new Map<number, string>();
/* Add operation */
// Add key-value pair (key, value) to the hash table
map.set(12836, 'Xiao Ha');
map.set(15937, 'Xiao Luo');
map.set(16750, 'Xiao Suan');
map.set(13276, 'Xiao Fa');
map.set(10583, 'Xiao Ya');
console.info('\nAfter adding, the hash table is\nKey -> Value');
console.info(map);
/* Query operation */
// Input key into hash table, get value
let name = map.get(15937);
console.info('\nInput student number 15937, query name ' + name);
/* Delete operation */
// Delete key-value pair (key, value) from hash table
map.delete(10583);
console.info('\nAfter deleting 10583, the hash table is\nKey -> Value');
console.info(map);
```
=== "Dart"
```dart title="hash_map.dart"
/* Initialize hash table */
Map<int, String> map = {};
/* Add operation */
// Add key-value pair (key, value) to the hash table
map[12836] = "Xiao Ha";
map[15937] = "Xiao Luo";
map[16750] = "Xiao Suan";
map[13276] = "Xiao Fa";
map[10583] = "Xiao Ya";
/* Query operation */
// Input key into hash table, get value
String name = map[15937];
/* Delete operation */
// Delete key-value pair (key, value) from hash table
map.remove(10583);
```
=== "Rust"
```rust title="hash_map.rs"
use std::collections::HashMap;
/* Initialize hash table */
let mut map: HashMap<i32, String> = HashMap::new();
/* Add operation */
// Add key-value pair (key, value) to the hash table
map.insert(12836, "Xiao Ha".to_string());
map.insert(15937, "Xiao Luo".to_string());
map.insert(16750, "Xiao Suan".to_string());
map.insert(13279, "Xiao Fa".to_string());
map.insert(10583, "Xiao Ya".to_string());
/* Query operation */
// Input key into hash table, get value
let _name: Option<&String> = map.get(&15937);
/* Delete operation */
// Delete key-value pair (key, value) from hash table
let _removed_value: Option<String> = map.remove(&10583);
```
=== "C"
```c title="hash_map.c"
// C does not provide a built-in hash table
```
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=== "Kotlin"
```kotlin title="hash_map.kt"
```
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=== "Zig"
```zig title="hash_map.zig"
```
??? pythontutor "Code Visualization"
<div style="height: 549px; width: 100%;"><iframe class="pythontutor-iframe" src="https://pythontutor.com/iframe-embed.html#code=%22%22%22Driver%20Code%22%22%22%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20%23%20%E5%88%9D%E5%A7%8B%E5%8C%96%E5%93%88%E5%B8%8C%E8%A1%A8%0A%20%20%20%20hmap%20%3D%20%7B%7D%0A%20%20%20%20%0A%20%20%20%20%23%20%E6%B7%BB%E5%8A%A0%E6%93%8D%E4%BD%9C%0A%20%20%20%20%23%20%E5%9C%A8%E5%93%88%E5%B8%8C%E8%A1%A8%E4%B8%AD%E6%B7%BB%E5%8A%A0%E9%94%AE%E5%80%BC%E5%AF%B9%20%28key,%20value%29%0A%20%20%20%20hmap%5B12836%5D%20%3D%20%22%E5%B0%8F%E5%93%88%22%0A%20%20%20%20hmap%5B15937%5D%20%3D%20%22%E5%B0%8F%E5%95%B0%22%0A%20%20%20%20hmap%5B16750%5D%20%3D%20%22%E5%B0%8F%E7%AE%97%22%0A%20%20%20%20hmap%5B13276%5D%20%3D%20%22%E5%B0%8F%E6%B3%95%22%0A%20%20%20%20hmap%5B10583%5D%20%3D%20%22%E5%B0%8F%E9%B8%AD%22%0A%20%20%20%20%0A%20%20%20%20%23%20%E6%9F%A5%E8%AF%A2%E6%93%8D%E4%BD%9C%0A%20%20%20%20%23%20%E5%90%91%E5%93%88%E5%B8%8C%E8%A1%A8%E4%B8%AD%E8%BE%93%E5%85%A5%E9%94%AE%20key%20%EF%BC%8C%E5%BE%97%E5%88%B0%E5%80%BC%20value%0A%20%20%20%20name%20%3D%20hmap%5B15937%5D%0A%20%20%20%20%0A%20%20%20%20%23%20%E5%88%A0%E9%99%A4%E6%93%8D%E4%BD%9C%0A%20%20%20%20%23%20%E5%9C%A8%E5%93%88%E5%B8%8C%E8%A1%A8%E4%B8%AD%E5%88%A0%E9%99%A4%E9%94%AE%E5%80%BC%E5%AF%B9%20%28key,%20value%29%0A%20%20%20%20hmap.pop%2810583%29&codeDivHeight=472&codeDivWidth=350&cumulative=false&curInstr=2&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false"> </iframe></div>
<div style="margin-top: 5px;"><a href="https://pythontutor.com/iframe-embed.html#code=%22%22%22Driver%20Code%22%22%22%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20%23%20%E5%88%9D%E5%A7%8B%E5%8C%96%E5%93%88%E5%B8%8C%E8%A1%A8%0A%20%20%20%20hmap%20%3D%20%7B%7D%0A%20%20%20%20%0A%20%20%20%20%23%20%E6%B7%BB%E5%8A%A0%E6%93%8D%E4%BD%9C%0A%20%20%20%20%23%20%E5%9C%A8%E5%93%88%E5%B8%8C%E8%A1%A8%E4%B8%AD%E6%B7%BB%E5%8A%A0%E9%94%AE%E5%80%BC%E5%AF%B9%20%28key,%20value%29%0A%20%20%20%20hmap%5B12836%5D%20%3D%20%22%E5%B0%8F%E5%93%88%22%0A%20%20%20%20hmap%5B15937%5D%20%3D%20%22%E5%B0%8F%E5%95%B0%22%0A%20%20%20%20hmap%5B16750%5D%20%3D%20%22%E5%B0%8F%E7%AE%97%22%0A%20%20%20%20hmap%5B13276%5D%20%3D%20%22%E5%B0%8F%E6%B3%95%22%0A%20%20%20%20hmap%5B10583%5D%20%3D%20%22%E5%B0%8F%E9%B8%AD%22%0A%20%20%20%20%0A%20%20%20%20%23%20%E6%9F%A5%E8%AF%A2%E6%93%8D%E4%BD%9C%0A%20%20%20%20%23%20%E5%90%91%E5%93%88%E5%B8%8C%E8%A1%A8%E4%B8%AD%E8%BE%93%E5%85%A5%E9%94%AE%20key%20%EF%BC%8C%E5%BE%97%E5%88%B0%E5%80%BC%20value%0A%20%20%20%20name%20%3D%20hmap%5B15937%5D%0A%20%20%20%20%0A%20%20%20%20%23%20%E5%88%A0%E9%99%A4%E6%93%8D%E4%BD%9C%0A%20%20%20%20%23%20%E5%9C%A8%E5%93%88%E5%B8%8C%E8%A1%A8%E4%B8%AD%E5%88%A0%E9%99%A4%E9%94%AE%E5%80%BC%E5%AF%B9%20%28key,%20value%29%0A%20%20%20%20hmap.pop%2810583%29&codeDivHeight=800&codeDivWidth=600&cumulative=false&curInstr=2&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false" target="_blank" rel="noopener noreferrer">Full Screen ></a></div>
There are three common ways to traverse a hash table: traversing key-value pairs, keys, and values. Example code is as follows:
=== "Python"
```python title="hash_map.py"
# Traverse hash table
# Traverse key-value pairs key->value
for key, value in hmap.items():
print(key, "->", value)
# Traverse keys only
for key in hmap.keys():
print(key)
# Traverse values only
for value in hmap.values():
print(value)
```
=== "C++"
```cpp title="hash_map.cpp"
/* Traverse hash table */
// Traverse key-value pairs key->value
for (auto kv: map) {
cout << kv.first << " -> " << kv.second << endl;
}
// Traverse using iterator key->value
for (auto iter = map.begin(); iter != map.end(); iter++) {
cout << iter->first << "->" << iter->second << endl;
}
```
=== "Java"
```java title="hash_map.java"
/* Traverse hash table */
// Traverse key-value pairs key->value
for (Map.Entry<Integer, String> kv: map.entrySet()) {
System.out.println(kv.getKey() + " -> " + kv.getValue());
}
// Traverse keys only
for (int key: map.keySet()) {
System.out.println(key);
}
// Traverse values only
for (String val: map.values()) {
System.out.println(val);
}
```
=== "C#"
```csharp title="hash_map.cs"
/* Traverse hash table */
// Traverse key-value pairs Key->Value
foreach (var kv in map) {
Console.WriteLine(kv.Key + " -> " + kv.Value);
}
// Traverse keys only
foreach (int key in map.Keys) {
Console.WriteLine(key);
}
// Traverse values only
foreach (string val in map.Values) {
Console.WriteLine(val);
}
```
=== "Go"
```go title="hash_map_test.go"
/* Traverse hash table */
// Traverse key-value pairs key->value
for key, value := range hmap {
fmt.Println(key, "->", value)
}
// Traverse keys only
for key := range hmap {
fmt.Println(key)
}
// Traverse values only
for _, value := range hmap {
fmt.Println(value)
}
```
=== "Swift"
```swift title="hash_map.swift"
/* Traverse hash table */
// Traverse key-value pairs Key->Value
for (key, value) in map {
print("\(key) -> \(value)")
}
// Traverse keys only
for key in map.keys {
print(key)
}
// Traverse values only
for value in map.values {
print(value)
}
```
=== "JS"
```javascript title="hash_map.js"
/* Traverse hash table */
console.info('\nTraverse key-value pairs Key->Value');
for (const [k, v] of map.entries()) {
console.info(k + ' -> ' + v);
}
console.info('\nTraverse keys only Key');
for (const k of map.keys()) {
console.info(k);
}
console.info('\nTraverse values only Value');
for (const v of map.values()) {
console.info(v);
}
```
=== "TS"
```typescript title="hash_map.ts"
/* Traverse hash table */
console.info('\nTraverse key-value pairs Key->Value');
for (const [k, v] of map.entries()) {
console.info(k + ' -> ' + v);
}
console.info('\nTraverse keys only Key');
for (const k of map.keys()) {
console.info(k);
}
console.info('\nTraverse values only Value');
for (const v of map.values()) {
console.info(v);
}
```
=== "Dart"
```dart title="hash_map.dart"
/* Traverse hash table */
// Traverse key-value pairs Key->Value
map.forEach((key, value) {
print('$key -> $value');
});
// Traverse keys only Key
map.keys.forEach((key) {
print(key);
});
// Traverse values only Value
map.values.forEach((value) {
print(value);
});
```
=== "Rust"
```rust title="hash_map.rs"
/* Traverse hash table */
// Traverse key-value pairs Key->Value
for (key, value) in &map {
println!("{key} -> {value}");
}
// Traverse keys only Key
for key in map.keys() {
println!("{key}");
}
// Traverse values only Value
for value in map.values() {
println!("{value}");
}
```
=== "C"
```c title="hash_map.c"
// C does not provide a built-in hash table
```
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=== "Kotlin"
```kotlin title="hash_map.kt"
```
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=== "Zig"
```zig title="hash_map.zig"
// Zig example is not provided
```
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## 6.1.2 &nbsp; Simple implementation of hash table
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First, let's consider the simplest case: **implementing a hash table using just an array**. In the hash table, each empty slot in the array is called a "bucket", and each bucket can store one key-value pair. Therefore, the query operation involves finding the bucket corresponding to the `key` and retrieving the `value` from it.
So, how do we locate the appropriate bucket based on the `key`? This is achieved through a "hash function". The role of the hash function is to map a larger input space to a smaller output space. In a hash table, the input space is all possible keys, and the output space is all buckets (array indices). In other words, input a `key`, **and we can use the hash function to determine the storage location of the corresponding key-value pair in the array**.
The calculation process of the hash function for a given `key` is divided into the following two steps:
1. Calculate the hash value using a certain hash algorithm `hash()`.
2. Take the modulus of the hash value with the number of buckets (array length) `capacity` to obtain the array index `index`.
```shell
index = hash(key) % capacity
```
Afterward, we can use `index` to access the corresponding bucket in the hash table and thereby retrieve the `value`.
Assuming array length `capacity = 100` and hash algorithm `hash(key) = key`, the hash function is `key % 100`. The Figure 6-2 uses `key` as the student number and `value` as the name to demonstrate the working principle of the hash function.
![Working principle of hash function](hash_map.assets/hash_function.png){ class="animation-figure" }
<p align="center"> Figure 6-2 &nbsp; Working principle of hash function </p>
The following code implements a simple hash table. Here, we encapsulate `key` and `value` into a class `Pair` to represent the key-value pair.
=== "Python"
```python title="array_hash_map.py"
class Pair:
"""键值对"""
def __init__(self, key: int, val: str):
self.key = key
self.val = val
class ArrayHashMap:
"""基于数组实现的哈希表"""
def __init__(self):
"""构造方法"""
# 初始化数组，包含 100 个桶
self.buckets: list[Pair | None] = [None] * 100
def hash_func(self, key: int) -> int:
"""哈希函数"""
index = key % 100
return index
def get(self, key: int) -> str:
"""查询操作"""
index: int = self.hash_func(key)
pair: Pair = self.buckets[index]
if pair is None:
return None
return pair.val
def put(self, key: int, val: str):
"""添加操作"""
pair = Pair(key, val)
index: int = self.hash_func(key)
self.buckets[index] = pair
def remove(self, key: int):
"""删除操作"""
index: int = self.hash_func(key)
# 置为 None ，代表删除
self.buckets[index] = None
def entry_set(self) -> list[Pair]:
"""获取所有键值对"""
result: list[Pair] = []
for pair in self.buckets:
if pair is not None:
result.append(pair)
return result
def key_set(self) -> list[int]:
"""获取所有键"""
result = []
for pair in self.buckets:
if pair is not None:
result.append(pair.key)
return result
def value_set(self) -> list[str]:
"""获取所有值"""
result = []
for pair in self.buckets:
if pair is not None:
result.append(pair.val)
return result
def print(self):
"""打印哈希表"""
for pair in self.buckets:
if pair is not None:
print(pair.key, "->", pair.val)
```
=== "C++"
```cpp title="array_hash_map.cpp"
/* 键值对 */
struct Pair {
public:
int key;
string val;
Pair(int key, string val) {
this->key = key;
this->val = val;
}
};
/* 基于数组实现的哈希表 */
class ArrayHashMap {
private:
vector<Pair *> buckets;
public:
ArrayHashMap() {
// 初始化数组，包含 100 个桶
buckets = vector<Pair *>(100);
}
~ArrayHashMap() {
// 释放内存
for (const auto &bucket : buckets) {
delete bucket;
}
buckets.clear();
}
/* 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);
Pair *pair = buckets[index];
if (pair == nullptr)
return "";
return pair->val;
}
/* 添加操作 */
void put(int key, string val) {
Pair *pair = new Pair(key, val);
int index = hashFunc(key);
buckets[index] = pair;
}
/* 删除操作 */
void remove(int key) {
int index = hashFunc(key);
// 释放内存并置为 nullptr
delete buckets[index];
buckets[index] = nullptr;
}
/* 获取所有键值对 */
vector<Pair *> pairSet() {
vector<Pair *> pairSet;
for (Pair *pair : buckets) {
if (pair != nullptr) {
pairSet.push_back(pair);
}
}
return pairSet;
}
/* 获取所有键 */
vector<int> keySet() {
vector<int> keySet;
for (Pair *pair : buckets) {
if (pair != nullptr) {
keySet.push_back(pair->key);
}
}
return keySet;
}
/* 获取所有值 */
vector<string> valueSet() {
vector<string> valueSet;
for (Pair *pair : buckets) {
if (pair != nullptr) {
valueSet.push_back(pair->val);
}
}
return valueSet;
}
/* 打印哈希表 */
void print() {
for (Pair *kv : pairSet()) {
cout << kv->key << " -> " << kv->val << endl;
}
}
};
```
=== "Java"
```java title="array_hash_map.java"
/* 键值对 */
class Pair {
public int key;
public String val;
public Pair(int key, String val) {
this.key = key;
this.val = val;
}
}
/* 基于数组实现的哈希表 */
class ArrayHashMap {
private List<Pair> buckets;
public ArrayHashMap() {
// 初始化数组，包含 100 个桶
buckets = new ArrayList<>();
for (int i = 0; i < 100; i++) {
buckets.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);
Pair pair = buckets.get(index);
if (pair == null)
return null;
return pair.val;
}
/* 添加操作 */
public void put(int key, String val) {
Pair pair = new Pair(key, val);
int index = hashFunc(key);
buckets.set(index, pair);
}
/* 删除操作 */
public void remove(int key) {
int index = hashFunc(key);
// 置为 null ，代表删除
buckets.set(index, null);
}
/* 获取所有键值对 */
public List<Pair> pairSet() {
List<Pair> pairSet = new ArrayList<>();
for (Pair pair : buckets) {
if (pair != null)
pairSet.add(pair);
}
return pairSet;
}
/* 获取所有键 */
public List<Integer> keySet() {
List<Integer> keySet = new ArrayList<>();
for (Pair pair : buckets) {
if (pair != null)
keySet.add(pair.key);
}
return keySet;
}
/* 获取所有值 */
public List<String> valueSet() {
List<String> valueSet = new ArrayList<>();
for (Pair pair : buckets) {
if (pair != null)
valueSet.add(pair.val);
}
return valueSet;
}
/* 打印哈希表 */
public void print() {
for (Pair kv : pairSet()) {
System.out.println(kv.key + " -> " + kv.val);
}
}
}
```
=== "C#"
```csharp title="array_hash_map.cs"
/* 键值对 int->string */
class Pair(int key, string val) {
public int key = key;
public string val = val;
}
/* 基于数组实现的哈希表 */
class ArrayHashMap {
List<Pair?> buckets;
public ArrayHashMap() {
// 初始化数组，包含 100 个桶
buckets = [];
for (int i = 0; i < 100; i++) {
buckets.Add(null);
}
}
/* 哈希函数 */
int HashFunc(int key) {
int index = key % 100;
return index;
}
/* 查询操作 */
public string? Get(int key) {
int index = HashFunc(key);
Pair? pair = buckets[index];
if (pair == null) return null;
return pair.val;
}
/* 添加操作 */
public void Put(int key, string val) {
Pair pair = new(key, val);
int index = HashFunc(key);
buckets[index] = pair;
}
/* 删除操作 */
public void Remove(int key) {
int index = HashFunc(key);
// 置为 null ，代表删除
buckets[index] = null;
}
/* 获取所有键值对 */
public List<Pair> PairSet() {
List<Pair> pairSet = [];
foreach (Pair? pair in buckets) {
if (pair != null)
pairSet.Add(pair);
}
return pairSet;
}
/* 获取所有键 */
public List<int> KeySet() {
List<int> keySet = [];
foreach (Pair? pair in buckets) {
if (pair != null)
keySet.Add(pair.key);
}
return keySet;
}
/* 获取所有值 */
public List<string> ValueSet() {
List<string> valueSet = [];
foreach (Pair? pair in buckets) {
if (pair != null)
valueSet.Add(pair.val);
}
return valueSet;
}
/* 打印哈希表 */
public void Print() {
foreach (Pair kv in PairSet()) {
Console.WriteLine(kv.key + " -> " + kv.val);
}
}
}
```
=== "Go"
```go title="array_hash_map.go"
/* 键值对 */
type pair struct {
key int
val string
}
/* 基于数组实现的哈希表 */
type arrayHashMap struct {
buckets []*pair
}
/* 初始化哈希表 */
func newArrayHashMap() *arrayHashMap {
// 初始化数组，包含 100 个桶
buckets := make([]*pair, 100)
return &arrayHashMap{buckets: buckets}
}
/* 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.buckets[index]
if pair == nil {
return "Not Found"
}
return pair.val
}
/* 添加操作 */
func (a *arrayHashMap) put(key int, val string) {
pair := &pair{key: key, val: val}
index := a.hashFunc(key)
a.buckets[index] = pair
}
/* 删除操作 */
func (a *arrayHashMap) remove(key int) {
index := a.hashFunc(key)
// 置为 nil ，代表删除
a.buckets[index] = nil
}
/* 获取所有键对 */
func (a *arrayHashMap) pairSet() []*pair {
var pairs []*pair
for _, pair := range a.buckets {
if pair != nil {
pairs = append(pairs, pair)
}
}
return pairs
}
/* 获取所有键 */
func (a *arrayHashMap) keySet() []int {
var keys []int
for _, pair := range a.buckets {
if pair != nil {
keys = append(keys, pair.key)
}
}
return keys
}
/* 获取所有值 */
func (a *arrayHashMap) valueSet() []string {
var values []string
for _, pair := range a.buckets {
if pair != nil {
values = append(values, pair.val)
}
}
return values
}
/* 打印哈希表 */
func (a *arrayHashMap) print() {
for _, pair := range a.buckets {
if pair != nil {
fmt.Println(pair.key, "->", pair.val)
}
}
}
```
=== "Swift"
```swift title="array_hash_map.swift"
/* 键值对 */
class Pair: Equatable {
public var key: Int
public var val: String
public init(key: Int, val: String) {
self.key = key
self.val = val
}
public static func == (lhs: Pair, rhs: Pair) -> Bool {
lhs.key == rhs.key && lhs.val == rhs.val
}
}
/* 基于数组实现的哈希表 */
class ArrayHashMap {
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private var buckets: [Pair?]
build
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init() {
// 初始化数组，包含 100 个桶
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buckets = Array(repeating: nil, count: 100)
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}
/* 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 = buckets[index]
return pair?.val
}
/* 添加操作 */
func put(key: Int, val: String) {
let pair = Pair(key: key, val: val)
let index = hashFunc(key: key)
buckets[index] = pair
}
/* 删除操作 */
func remove(key: Int) {
let index = hashFunc(key: key)
// 置为 nil ，代表删除
buckets[index] = nil
}
/* 获取所有键值对 */
func pairSet() -> [Pair] {
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buckets.compactMap { $0 }
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}
/* 获取所有键 */
func keySet() -> [Int] {
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buckets.compactMap { $0?.key }
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}
/* 获取所有值 */
func valueSet() -> [String] {
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buckets.compactMap { $0?.val }
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}
/* 打印哈希表 */
func print() {
for pair in pairSet() {
Swift.print("\(pair.key) -> \(pair.val)")
}
}
}
```
=== "JS"
```javascript title="array_hash_map.js"
/* 键值对 Number -> String */
class Pair {
constructor(key, val) {
this.key = key;
this.val = val;
}
}
/* 基于数组实现的哈希表 */
class ArrayHashMap {
#buckets;
constructor() {
// 初始化数组，包含 100 个桶
this.#buckets = 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 pair = this.#buckets[index];
if (pair === null) return null;
return pair.val;
}
/* 添加操作 */
set(key, val) {
let index = this.#hashFunc(key);
this.#buckets[index] = new Pair(key, val);
}
/* 删除操作 */
delete(key) {
let index = this.#hashFunc(key);
// 置为 null ，代表删除
this.#buckets[index] = null;
}
/* 获取所有键值对 */
entries() {
let arr = [];
for (let i = 0; i < this.#buckets.length; i++) {
if (this.#buckets[i]) {
arr.push(this.#buckets[i]);
}
}
return arr;
}
/* 获取所有键 */
keys() {
let arr = [];
for (let i = 0; i < this.#buckets.length; i++) {
if (this.#buckets[i]) {
arr.push(this.#buckets[i].key);
}
}
return arr;
}
/* 获取所有值 */
values() {
let arr = [];
for (let i = 0; i < this.#buckets.length; i++) {
if (this.#buckets[i]) {
arr.push(this.#buckets[i].val);
}
}
return arr;
}
/* 打印哈希表 */
print() {
let pairSet = this.entries();
for (const pair of pairSet) {
console.info(`${pair.key} -> ${pair.val}`);
}
}
}
```
=== "TS"
```typescript title="array_hash_map.ts"
/* 键值对 Number -> String */
class Pair {
public key: number;
public val: string;
constructor(key: number, val: string) {
this.key = key;
this.val = val;
}
}
/* 基于数组实现的哈希表 */
class ArrayHashMap {
private readonly buckets: (Pair | null)[];
constructor() {
// 初始化数组，包含 100 个桶
this.buckets = new Array(100).fill(null);
}
/* 哈希函数 */
private hashFunc(key: number): number {
return key % 100;
}
/* 查询操作 */
public get(key: number): string | null {
let index = this.hashFunc(key);
let pair = this.buckets[index];
if (pair === null) return null;
return pair.val;
}
/* 添加操作 */
public set(key: number, val: string) {
let index = this.hashFunc(key);
this.buckets[index] = new Pair(key, val);
}
/* 删除操作 */
public delete(key: number) {
let index = this.hashFunc(key);
// 置为 null ，代表删除
this.buckets[index] = null;
}
/* 获取所有键值对 */
public entries(): (Pair | null)[] {
let arr: (Pair | null)[] = [];
for (let i = 0; i < this.buckets.length; i++) {
if (this.buckets[i]) {
arr.push(this.buckets[i]);
}
}
return arr;
}
/* 获取所有键 */
public keys(): (number | undefined)[] {
let arr: (number | undefined)[] = [];
for (let i = 0; i < this.buckets.length; i++) {
if (this.buckets[i]) {
arr.push(this.buckets[i].key);
}
}
return arr;
}
/* 获取所有值 */
public values(): (string | undefined)[] {
let arr: (string | undefined)[] = [];
for (let i = 0; i < this.buckets.length; i++) {
if (this.buckets[i]) {
arr.push(this.buckets[i].val);
}
}
return arr;
}
/* 打印哈希表 */
public print() {
let pairSet = this.entries();
for (const pair of pairSet) {
console.info(`${pair.key} -> ${pair.val}`);
}
}
}
```
=== "Dart"
```dart title="array_hash_map.dart"
/* 键值对 */
class Pair {
int key;
String val;
Pair(this.key, this.val);
}
/* 基于数组实现的哈希表 */
class ArrayHashMap {
late List<Pair?> _buckets;
ArrayHashMap() {
// 初始化数组，包含 100 个桶
_buckets = List.filled(100, null);
}
/* 哈希函数 */
int _hashFunc(int key) {
final int index = key % 100;
return index;
}
/* 查询操作 */
String? get(int key) {
final int index = _hashFunc(key);
final Pair? pair = _buckets[index];
if (pair == null) {
return null;
}
return pair.val;
}
/* 添加操作 */
void put(int key, String val) {
final Pair pair = Pair(key, val);
final int index = _hashFunc(key);
_buckets[index] = pair;
}
/* 删除操作 */
void remove(int key) {
final int index = _hashFunc(key);
_buckets[index] = null;
}
/* 获取所有键值对 */
List<Pair> pairSet() {
List<Pair> pairSet = [];
for (final Pair? pair in _buckets) {
if (pair != null) {
pairSet.add(pair);
}
}
return pairSet;
}
/* 获取所有键 */
List<int> keySet() {
List<int> keySet = [];
for (final Pair? pair in _buckets) {
if (pair != null) {
keySet.add(pair.key);
}
}
return keySet;
}
/* 获取所有值 */
List<String> values() {
List<String> valueSet = [];
for (final Pair? pair in _buckets) {
if (pair != null) {
valueSet.add(pair.val);
}
}
return valueSet;
}
/* 打印哈希表 */
void printHashMap() {
for (final Pair kv in pairSet()) {
print("${kv.key} -> ${kv.val}");
}
}
}
```
=== "Rust"
```rust title="array_hash_map.rs"
/* 键值对 */
#[derive(Debug, Clone, PartialEq)]
pub struct Pair {
pub key: i32,
pub val: String,
}
/* 基于数组实现的哈希表 */
pub struct ArrayHashMap {
build
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buckets: Vec<Option<Pair>>,
build
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}
impl ArrayHashMap {
pub fn new() -> ArrayHashMap {
// 初始化数组，包含 100 个桶
build
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Self {
buckets: vec![None; 100],
}
build
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}
/* 哈希函数 */
fn hash_func(&self, key: i32) -> usize {
key as usize % 100
}
/* 查询操作 */
pub fn get(&self, key: i32) -> Option<&String> {
let index = self.hash_func(key);
self.buckets[index].as_ref().map(|pair| &pair.val)
}
/* 添加操作 */
pub fn put(&mut self, key: i32, val: &str) {
let index = self.hash_func(key);
self.buckets[index] = Some(Pair {
key,
val: val.to_string(),
});
}
/* 删除操作 */
pub fn remove(&mut self, key: i32) {
let index = self.hash_func(key);
// 置为 None ，代表删除
self.buckets[index] = None;
}
/* 获取所有键值对 */
pub fn entry_set(&self) -> Vec<&Pair> {
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self.buckets
.iter()
.filter_map(|pair| pair.as_ref())
.collect()
build
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}
/* 获取所有键 */
pub fn key_set(&self) -> Vec<&i32> {
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self.buckets
.iter()
.filter_map(|pair| pair.as_ref().map(|pair| &pair.key))
.collect()
build
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}
/* 获取所有值 */
pub fn value_set(&self) -> Vec<&String> {
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self.buckets
.iter()
.filter_map(|pair| pair.as_ref().map(|pair| &pair.val))
.collect()
build
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}
/* 打印哈希表 */
pub fn print(&self) {
for pair in self.entry_set() {
println!("{} -> {}", pair.key, pair.val);
}
}
}
```
=== "C"
```c title="array_hash_map.c"
/* 键值对 int->string */
typedef struct {
int key;
char *val;
} Pair;
/* 基于数组实现的哈希表 */
typedef struct {
Pair *buckets[HASHTABLE_CAPACITY];
} ArrayHashMap;
/* 构造函数 */
ArrayHashMap *newArrayHashMap() {
ArrayHashMap *hmap = malloc(sizeof(ArrayHashMap));
return hmap;
}
/* 析构函数 */
void delArrayHashMap(ArrayHashMap *hmap) {
for (int i = 0; i < HASHTABLE_CAPACITY; i++) {
if (hmap->buckets[i] != NULL) {
free(hmap->buckets[i]->val);
free(hmap->buckets[i]);
}
}
free(hmap);
}
/* 添加操作 */
void put(ArrayHashMap *hmap, const int key, const char *val) {
Pair *Pair = malloc(sizeof(Pair));
Pair->key = key;
Pair->val = malloc(strlen(val) + 1);
strcpy(Pair->val, val);
int index = hashFunc(key);
hmap->buckets[index] = Pair;
}
/* 删除操作 */
void removeItem(ArrayHashMap *hmap, const int key) {
int index = hashFunc(key);
free(hmap->buckets[index]->val);
free(hmap->buckets[index]);
hmap->buckets[index] = NULL;
}
/* 获取所有键值对 */
void pairSet(ArrayHashMap *hmap, MapSet *set) {
Pair *entries;
int i = 0, index = 0;
int total = 0;
/* 统计有效键值对数量 */
for (i = 0; i < HASHTABLE_CAPACITY; i++) {
if (hmap->buckets[i] != NULL) {
total++;
}
}
entries = malloc(sizeof(Pair) * total);
for (i = 0; i < HASHTABLE_CAPACITY; i++) {
if (hmap->buckets[i] != NULL) {
entries[index].key = hmap->buckets[i]->key;
entries[index].val = malloc(strlen(hmap->buckets[i]->val) + 1);
strcpy(entries[index].val, hmap->buckets[i]->val);
index++;
}
}
set->set = entries;
set->len = total;
}
/* 获取所有键 */
void keySet(ArrayHashMap *hmap, MapSet *set) {
int *keys;
int i = 0, index = 0;
int total = 0;
/* 统计有效键值对数量 */
for (i = 0; i < HASHTABLE_CAPACITY; i++) {
if (hmap->buckets[i] != NULL) {
total++;
}
}
keys = malloc(total * sizeof(int));
for (i = 0; i < HASHTABLE_CAPACITY; i++) {
if (hmap->buckets[i] != NULL) {
keys[index] = hmap->buckets[i]->key;
index++;
}
}
set->set = keys;
set->len = total;
}
/* 获取所有值 */
void valueSet(ArrayHashMap *hmap, MapSet *set) {
char **vals;
int i = 0, index = 0;
int total = 0;
/* 统计有效键值对数量 */
for (i = 0; i < HASHTABLE_CAPACITY; i++) {
if (hmap->buckets[i] != NULL) {
total++;
}
}
vals = malloc(total * sizeof(char *));
for (i = 0; i < HASHTABLE_CAPACITY; i++) {
if (hmap->buckets[i] != NULL) {
vals[index] = hmap->buckets[i]->val;
index++;
}
}
set->set = vals;
set->len = total;
}
/* 打印哈希表 */
void print(ArrayHashMap *hmap) {
int i;
MapSet set;
pairSet(hmap, &set);
Pair *entries = (Pair *)set.set;
for (i = 0; i < set.len; i++) {
printf("%d -> %s\n", entries[i].key, entries[i].val);
}
free(set.set);
}
```
build
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=== "Kotlin"
```kotlin title="array_hash_map.kt"
/* 键值对 */
class Pair(
var key: Int,
var value: String
)
/* 基于数组实现的哈希表 */
class ArrayHashMap {
private val buckets = arrayOfNulls<Pair>(100)
init {
// 初始化数组，包含 100 个桶
for (i in 0..<100) {
buckets[i] = null
}
}
/* 哈希函数 */
fun hashFunc(key: Int): Int {
val index = key % 100
return index
}
/* 查询操作 */
fun get(key: Int): String? {
val index = hashFunc(key)
val pair = buckets[index] ?: return null
return pair.value
}
/* 添加操作 */
fun put(key: Int, value: String) {
val pair = Pair(key, value)
val index = hashFunc(key)
buckets[index] = pair
}
/* 删除操作 */
fun remove(key: Int) {
val index = hashFunc(key)
// 置为 null ，代表删除
buckets[index] = null
}
/* 获取所有键值对 */
fun pairSet(): MutableList<Pair> {
val pairSet = ArrayList<Pair>()
for (pair in buckets) {
if (pair != null) pairSet.add(pair)
}
return pairSet
}
/* 获取所有键 */
fun keySet(): MutableList<Int> {
val keySet = ArrayList<Int>()
for (pair in buckets) {
if (pair != null) keySet.add(pair.key)
}
return keySet
}
/* 获取所有值 */
fun valueSet(): MutableList<String> {
val valueSet = ArrayList<String>()
for (pair in buckets) {
pair?.let { valueSet.add(it.value) }
}
return valueSet
}
/* 打印哈希表 */
fun print() {
for (kv in pairSet()) {
val key = kv.key
val value = kv.value
println("${key}->${value}")
}
}
}
/* 基于数组实现的哈希表 */
class ArrayHashMap {
private val buckets = arrayOfNulls<Pair>(100)
init {
// 初始化数组，包含 100 个桶
for (i in 0..<100) {
buckets[i] = null
}
}
/* 哈希函数 */
fun hashFunc(key: Int): Int {
val index = key % 100
return index
}
/* 查询操作 */
fun get(key: Int): String? {
val index = hashFunc(key)
val pair = buckets[index] ?: return null
return pair.value
}
/* 添加操作 */
fun put(key: Int, value: String) {
val pair = Pair(key, value)
val index = hashFunc(key)
buckets[index] = pair
}
/* 删除操作 */
fun remove(key: Int) {
val index = hashFunc(key)
// 置为 null ，代表删除
buckets[index] = null
}
/* 获取所有键值对 */
fun pairSet(): MutableList<Pair> {
val pairSet = ArrayList<Pair>()
for (pair in buckets) {
if (pair != null) pairSet.add(pair)
}
return pairSet
}
/* 获取所有键 */
fun keySet(): MutableList<Int> {
val keySet = ArrayList<Int>()
for (pair in buckets) {
if (pair != null) keySet.add(pair.key)
}
return keySet
}
/* 获取所有值 */
fun valueSet(): MutableList<String> {
val valueSet = ArrayList<String>()
for (pair in buckets) {
pair?.let { valueSet.add(it.value) }
}
return valueSet
}
/* 打印哈希表 */
fun print() {
for (kv in pairSet()) {
val key = kv.key
val value = kv.value
println("${key}->${value}")
}
}
}
```
build
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=== "Ruby"
```ruby title="array_hash_map.rb"
[class]{Pair}-[func]{}
[class]{ArrayHashMap}-[func]{}
```
build
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=== "Zig"
```zig title="array_hash_map.zig"
// 键值对
const Pair = struct {
key: usize = undefined,
val: []const u8 = undefined,
pub fn init(key: usize, val: []const u8) Pair {
return Pair {
.key = key,
.val = val,
};
}
};
// 基于数组实现的哈希表
fn ArrayHashMap(comptime T: type) type {
return struct {
bucket: ?std.ArrayList(?T) = null,
mem_allocator: std.mem.Allocator = undefined,
const Self = @This();
// 构造函数
pub fn init(self: *Self, allocator: std.mem.Allocator) !void {
self.mem_allocator = allocator;
// 初始化一个长度为 100 的桶（数组）
self.bucket = std.ArrayList(?T).init(self.mem_allocator);
var i: i32 = 0;
while (i < 100) : (i += 1) {
try self.bucket.?.append(null);
}
}
// 析构函数
pub fn deinit(self: *Self) void {
if (self.bucket != null) self.bucket.?.deinit();
}
// 哈希函数
fn hashFunc(key: usize) usize {
var index = key % 100;
return index;
}
// 查询操作
pub fn get(self: *Self, key: usize) []const u8 {
var index = hashFunc(key);
var pair = self.bucket.?.items[index];
return pair.?.val;
}
// 添加操作
pub fn put(self: *Self, key: usize, val: []const u8) !void {
var pair = Pair.init(key, val);
var index = hashFunc(key);
self.bucket.?.items[index] = pair;
}
// 删除操作
pub fn remove(self: *Self, key: usize) !void {
var index = hashFunc(key);
// 置为 null ，代表删除
self.bucket.?.items[index] = null;
}
// 获取所有键值对
pub fn pairSet(self: *Self) !std.ArrayList(T) {
var entry_set = std.ArrayList(T).init(self.mem_allocator);
for (self.bucket.?.items) |item| {
if (item == null) continue;
try entry_set.append(item.?);
}
return entry_set;
}
// 获取所有键
pub fn keySet(self: *Self) !std.ArrayList(usize) {
var key_set = std.ArrayList(usize).init(self.mem_allocator);
for (self.bucket.?.items) |item| {
if (item == null) continue;
try key_set.append(item.?.key);
}
return key_set;
}
// 获取所有值
pub fn valueSet(self: *Self) !std.ArrayList([]const u8) {
var value_set = std.ArrayList([]const u8).init(self.mem_allocator);
for (self.bucket.?.items) |item| {
if (item == null) continue;
try value_set.append(item.?.val);
}
return value_set;
}
// 打印哈希表
pub fn print(self: *Self) !void {
var entry_set = try self.pairSet();
defer entry_set.deinit();
for (entry_set.items) |item| {
std.debug.print("{} -> {s}\n", .{item.key, item.val});
}
}
};
}
```
??? pythontutor "Code Visualization"
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## 6.1.3 &nbsp; Hash collision and resizing
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Fundamentally, the role of the hash function is to map the entire input space of all keys to the output space of all array indices. However, the input space is often much larger than the output space. Therefore, **theoretically, there must be situations where "multiple inputs correspond to the same output"**.
For the hash function in the above example, if the last two digits of the input `key` are the same, the output of the hash function will also be the same. For example, when querying for students with student numbers 12836 and 20336, we find:
```shell
12836 % 100 = 36
20336 % 100 = 36
```
As shown in the Figure 6-3 , both student numbers point to the same name, which is obviously incorrect. This situation where multiple inputs correspond to the same output is known as "hash collision".
![Example of hash collision](hash_map.assets/hash_collision.png){ class="animation-figure" }
<p align="center"> Figure 6-3 &nbsp; Example of hash collision </p>
It is easy to understand that the larger the capacity $n$ of the hash table, the lower the probability of multiple keys being allocated to the same bucket, and the fewer the collisions. Therefore, **expanding the capacity of the hash table can reduce hash collisions**.
As shown in the Figure 6-4 , before expansion, key-value pairs `(136, A)` and `(236, D)` collided; after expansion, the collision is resolved.
![Hash table expansion](hash_map.assets/hash_table_reshash.png){ class="animation-figure" }
<p align="center"> Figure 6-4 &nbsp; Hash table expansion </p>
Similar to array expansion, resizing a hash table requires migrating all key-value pairs from the original hash table to the new one, which is time-consuming. Furthermore, since the capacity `capacity` of the hash table changes, we need to recalculate the storage positions of all key-value pairs using the hash function, which adds to the computational overhead of the resizing process. Therefore, programming languages often reserve a sufficiently large capacity for the hash table to prevent frequent resizing.
The "load factor" is an important concept for hash tables. It is defined as the ratio of the number of elements in the hash table to the number of buckets. It is used to measure the severity of hash collisions and **is often used as a trigger for resizing the hash table**. For example, in Java, when the load factor exceeds $0.75$, the system will resize the hash table to twice its original size.
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