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en/docs/chapter_hashing/hash_algorithm.md
+52 -435
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@@ -56,7 +56,7 @@ The design of hash algorithms is a complex issue that requires consideration of
```python title="simple_hash.py"
def add_hash(key: str) -> int:
"""加法哈希"""
"""Additive hash"""
hash = 0
modulus = 1000000007
for c in key:
@@ -64,7 +64,7 @@ The design of hash algorithms is a complex issue that requires consideration of
return hash % modulus
def mul_hash(key: str) -> int:
"""乘法哈希"""
"""Multiplicative hash"""
hash = 0
modulus = 1000000007
for c in key:
@@ -72,7 +72,7 @@ The design of hash algorithms is a complex issue that requires consideration of
return hash % modulus
def xor_hash(key: str) -> int:
"""异或哈希"""
"""XOR hash"""
hash = 0
modulus = 1000000007
for c in key:
@@ -80,7 +80,7 @@ The design of hash algorithms is a complex issue that requires consideration of
return hash % modulus
def rot_hash(key: str) -> int:
"""旋转哈希"""
"""Rotational hash"""
hash = 0
modulus = 1000000007
for c in key:
@@ -91,51 +91,19 @@ The design of hash algorithms is a complex issue that requires consideration of
=== "C++"
```cpp title="simple_hash.cpp"
/* 加法哈希 */
int addHash(string key) {
long long hash = 0;
const int MODULUS = 1000000007;
for (unsigned char c : key) {
hash = (hash + (int)c) % MODULUS;
}
return (int)hash;
}
[class]{}-[func]{addHash}
/* 乘法哈希 */
int mulHash(string key) {
long long hash = 0;
const int MODULUS = 1000000007;
for (unsigned char c : key) {
hash = (31 * hash + (int)c) % MODULUS;
}
return (int)hash;
}
[class]{}-[func]{mulHash}
/* 异或哈希 */
int xorHash(string key) {
int hash = 0;
const int MODULUS = 1000000007;
for (unsigned char c : key) {
hash ^= (int)c;
}
return hash & MODULUS;
}
[class]{}-[func]{xorHash}
/* 旋转哈希 */
int rotHash(string key) {
long long hash = 0;
const int MODULUS = 1000000007;
for (unsigned char c : key) {
hash = ((hash << 4) ^ (hash >> 28) ^ (int)c) % MODULUS;
}
return (int)hash;
}
[class]{}-[func]{rotHash}
```
=== "Java"
```java title="simple_hash.java"
/* 加法哈希 */
/* Additive hash */
int addHash(String key) {
long hash = 0;
final int MODULUS = 1000000007;
@@ -145,7 +113,7 @@ The design of hash algorithms is a complex issue that requires consideration of
return (int) hash;
}
/* 乘法哈希 */
/* Multiplicative hash */
int mulHash(String key) {
long hash = 0;
final int MODULUS = 1000000007;
@@ -155,7 +123,7 @@ The design of hash algorithms is a complex issue that requires consideration of
return (int) hash;
}
/* 异或哈希 */
/* XOR hash */
int xorHash(String key) {
int hash = 0;
final int MODULUS = 1000000007;
@@ -165,7 +133,7 @@ The design of hash algorithms is a complex issue that requires consideration of
return hash & MODULUS;
}
/* 旋转哈希 */
/* Rotational hash */
int rotHash(String key) {
long hash = 0;
final int MODULUS = 1000000007;
@@ -179,467 +147,121 @@ The design of hash algorithms is a complex issue that requires consideration of
=== "C#"
```csharp title="simple_hash.cs"
/* 加法哈希 */
int AddHash(string key) {
long hash = 0;
const int MODULUS = 1000000007;
foreach (char c in key) {
hash = (hash + c) % MODULUS;
}
return (int)hash;
}
[class]{simple_hash}-[func]{AddHash}
/* 乘法哈希 */
int MulHash(string key) {
long hash = 0;
const int MODULUS = 1000000007;
foreach (char c in key) {
hash = (31 * hash + c) % MODULUS;
}
return (int)hash;
}
[class]{simple_hash}-[func]{MulHash}
/* 异或哈希 */
int XorHash(string key) {
int hash = 0;
const int MODULUS = 1000000007;
foreach (char c in key) {
hash ^= c;
}
return hash & MODULUS;
}
[class]{simple_hash}-[func]{XorHash}
/* 旋转哈希 */
int RotHash(string key) {
long hash = 0;
const int MODULUS = 1000000007;
foreach (char c in key) {
hash = ((hash << 4) ^ (hash >> 28) ^ c) % MODULUS;
}
return (int)hash;
}
[class]{simple_hash}-[func]{RotHash}
```
=== "Go"
```go title="simple_hash.go"
/* 加法哈希 */
func addHash(key string) int {
var hash int64
var modulus int64
[class]{}-[func]{addHash}
modulus = 1000000007
for _, b := range []byte(key) {
hash = (hash + int64(b)) % modulus
}
return int(hash)
}
[class]{}-[func]{mulHash}
/* 乘法哈希 */
func mulHash(key string) int {
var hash int64
var modulus int64
[class]{}-[func]{xorHash}
modulus = 1000000007
for _, b := range []byte(key) {
hash = (31*hash + int64(b)) % modulus
}
return int(hash)
}
/* 异或哈希 */
func xorHash(key string) int {
hash := 0
modulus := 1000000007
for _, b := range []byte(key) {
fmt.Println(int(b))
hash ^= int(b)
hash = (31*hash + int(b)) % modulus
}
return hash & modulus
}
/* 旋转哈希 */
func rotHash(key string) int {
var hash int64
var modulus int64
modulus = 1000000007
for _, b := range []byte(key) {
hash = ((hash << 4) ^ (hash >> 28) ^ int64(b)) % modulus
}
return int(hash)
}
[class]{}-[func]{rotHash}
```
=== "Swift"
```swift title="simple_hash.swift"
/* 加法哈希 */
func addHash(key: String) -> Int {
var hash = 0
let MODULUS = 1_000_000_007
for c in key {
for scalar in c.unicodeScalars {
hash = (hash + Int(scalar.value)) % MODULUS
}
}
return hash
}
[class]{}-[func]{addHash}
/* 乘法哈希 */
func mulHash(key: String) -> Int {
var hash = 0
let MODULUS = 1_000_000_007
for c in key {
for scalar in c.unicodeScalars {
hash = (31 * hash + Int(scalar.value)) % MODULUS
}
}
return hash
}
[class]{}-[func]{mulHash}
/* 异或哈希 */
func xorHash(key: String) -> Int {
var hash = 0
let MODULUS = 1_000_000_007
for c in key {
for scalar in c.unicodeScalars {
hash ^= Int(scalar.value)
}
}
return hash & MODULUS
}
[class]{}-[func]{xorHash}
/* 旋转哈希 */
func rotHash(key: String) -> Int {
var hash = 0
let MODULUS = 1_000_000_007
for c in key {
for scalar in c.unicodeScalars {
hash = ((hash << 4) ^ (hash >> 28) ^ Int(scalar.value)) % MODULUS
}
}
return hash
}
[class]{}-[func]{rotHash}
```
=== "JS"
```javascript title="simple_hash.js"
/* 加法哈希 */
function addHash(key) {
let hash = 0;
const MODULUS = 1000000007;
for (const c of key) {
hash = (hash + c.charCodeAt(0)) % MODULUS;
}
return hash;
}
[class]{}-[func]{addHash}
/* 乘法哈希 */
function mulHash(key) {
let hash = 0;
const MODULUS = 1000000007;
for (const c of key) {
hash = (31 * hash + c.charCodeAt(0)) % MODULUS;
}
return hash;
}
[class]{}-[func]{mulHash}
/* 异或哈希 */
function xorHash(key) {
let hash = 0;
const MODULUS = 1000000007;
for (const c of key) {
hash ^= c.charCodeAt(0);
}
return hash & MODULUS;
}
[class]{}-[func]{xorHash}
/* 旋转哈希 */
function rotHash(key) {
let hash = 0;
const MODULUS = 1000000007;
for (const c of key) {
hash = ((hash << 4) ^ (hash >> 28) ^ c.charCodeAt(0)) % MODULUS;
}
return hash;
}
[class]{}-[func]{rotHash}
```
=== "TS"
```typescript title="simple_hash.ts"
/* 加法哈希 */
function addHash(key: string): number {
let hash = 0;
const MODULUS = 1000000007;
for (const c of key) {
hash = (hash + c.charCodeAt(0)) % MODULUS;
}
return hash;
}
[class]{}-[func]{addHash}
/* 乘法哈希 */
function mulHash(key: string): number {
let hash = 0;
const MODULUS = 1000000007;
for (const c of key) {
hash = (31 * hash + c.charCodeAt(0)) % MODULUS;
}
return hash;
}
[class]{}-[func]{mulHash}
/* 异或哈希 */
function xorHash(key: string): number {
let hash = 0;
const MODULUS = 1000000007;
for (const c of key) {
hash ^= c.charCodeAt(0);
}
return hash & MODULUS;
}
[class]{}-[func]{xorHash}
/* 旋转哈希 */
function rotHash(key: string): number {
let hash = 0;
const MODULUS = 1000000007;
for (const c of key) {
hash = ((hash << 4) ^ (hash >> 28) ^ c.charCodeAt(0)) % MODULUS;
}
return hash;
}
[class]{}-[func]{rotHash}
```
=== "Dart"
```dart title="simple_hash.dart"
/* 加法哈希 */
int addHash(String key) {
int hash = 0;
final int MODULUS = 1000000007;
for (int i = 0; i < key.length; i++) {
hash = (hash + key.codeUnitAt(i)) % MODULUS;
}
return hash;
}
[class]{}-[func]{addHash}
/* 乘法哈希 */
int mulHash(String key) {
int hash = 0;
final int MODULUS = 1000000007;
for (int i = 0; i < key.length; i++) {
hash = (31 * hash + key.codeUnitAt(i)) % MODULUS;
}
return hash;
}
[class]{}-[func]{mulHash}
/* 异或哈希 */
int xorHash(String key) {
int hash = 0;
final int MODULUS = 1000000007;
for (int i = 0; i < key.length; i++) {
hash ^= key.codeUnitAt(i);
}
return hash & MODULUS;
}
[class]{}-[func]{xorHash}
/* 旋转哈希 */
int rotHash(String key) {
int hash = 0;
final int MODULUS = 1000000007;
for (int i = 0; i < key.length; i++) {
hash = ((hash << 4) ^ (hash >> 28) ^ key.codeUnitAt(i)) % MODULUS;
}
return hash;
}
[class]{}-[func]{rotHash}
```
=== "Rust"
```rust title="simple_hash.rs"
/* 加法哈希 */
fn add_hash(key: &str) -> i32 {
let mut hash = 0_i64;
const MODULUS: i64 = 1000000007;
[class]{}-[func]{add_hash}
for c in key.chars() {
hash = (hash + c as i64) % MODULUS;
}
[class]{}-[func]{mul_hash}
hash as i32
}
[class]{}-[func]{xor_hash}
/* 乘法哈希 */
fn mul_hash(key: &str) -> i32 {
let mut hash = 0_i64;
const MODULUS: i64 = 1000000007;
for c in key.chars() {
hash = (31 * hash + c as i64) % MODULUS;
}
hash as i32
}
/* 异或哈希 */
fn xor_hash(key: &str) -> i32 {
let mut hash = 0_i64;
const MODULUS: i64 = 1000000007;
for c in key.chars() {
hash ^= c as i64;
}
(hash & MODULUS) as i32
}
/* 旋转哈希 */
fn rot_hash(key: &str) -> i32 {
let mut hash = 0_i64;
const MODULUS: i64 = 1000000007;
for c in key.chars() {
hash = ((hash << 4) ^ (hash >> 28) ^ c as i64) % MODULUS;
}
hash as i32
}
[class]{}-[func]{rot_hash}
```
=== "C"
```c title="simple_hash.c"
/* 加法哈希 */
int addHash(char *key) {
long long hash = 0;
const int MODULUS = 1000000007;
for (int i = 0; i < strlen(key); i++) {
hash = (hash + (unsigned char)key[i]) % MODULUS;
}
return (int)hash;
}
[class]{}-[func]{addHash}
/* 乘法哈希 */
int mulHash(char *key) {
long long hash = 0;
const int MODULUS = 1000000007;
for (int i = 0; i < strlen(key); i++) {
hash = (31 * hash + (unsigned char)key[i]) % MODULUS;
}
return (int)hash;
}
[class]{}-[func]{mulHash}
/* 异或哈希 */
int xorHash(char *key) {
int hash = 0;
const int MODULUS = 1000000007;
[class]{}-[func]{xorHash}
for (int i = 0; i < strlen(key); i++) {
hash ^= (unsigned char)key[i];
}
return hash & MODULUS;
}
/* 旋转哈希 */
int rotHash(char *key) {
long long hash = 0;
const int MODULUS = 1000000007;
for (int i = 0; i < strlen(key); i++) {
hash = ((hash << 4) ^ (hash >> 28) ^ (unsigned char)key[i]) % MODULUS;
}
return (int)hash;
}
[class]{}-[func]{rotHash}
```
=== "Kotlin"
```kotlin title="simple_hash.kt"
/* 加法哈希 */
fun addHash(key: String): Int {
var hash = 0L
val MODULUS = 1000000007
for (c in key.toCharArray()) {
hash = (hash + c.code) % MODULUS
}
return hash.toInt()
}
[class]{}-[func]{addHash}
/* 乘法哈希 */
fun mulHash(key: String): Int {
var hash = 0L
val MODULUS = 1000000007
for (c in key.toCharArray()) {
hash = (31 * hash + c.code) % MODULUS
}
return hash.toInt()
}
[class]{}-[func]{mulHash}
/* 异或哈希 */
fun xorHash(key: String): Int {
var hash = 0
val MODULUS = 1000000007
for (c in key.toCharArray()) {
hash = hash xor c.code
}
return hash and MODULUS
}
[class]{}-[func]{xorHash}
/* 旋转哈希 */
fun rotHash(key: String): Int {
var hash = 0L
val MODULUS = 1000000007
for (c in key.toCharArray()) {
hash = ((hash shl 4) xor (hash shr 28) xor c.code.toLong()) % MODULUS
}
return hash.toInt()
}
[class]{}-[func]{rotHash}
```
=== "Ruby"
```ruby title="simple_hash.rb"
### 加法哈希 ###
def add_hash(key)
hash = 0
modulus = 1_000_000_007
[class]{}-[func]{add_hash}
key.each_char { |c| hash += c.ord }
[class]{}-[func]{mul_hash}
hash % modulus
end
[class]{}-[func]{xor_hash}
### 乘法哈希 ###
def mul_hash(key)
hash = 0
modulus = 1_000_000_007
key.each_char { |c| hash = 31 * hash + c.ord }
hash % modulus
end
### 异或哈希 ###
def xor_hash(key)
hash = 0
modulus = 1_000_000_007
key.each_char { |c| hash ^= c.ord }
hash % modulus
end
### 旋转哈希 ###
def rot_hash(key)
hash = 0
modulus = 1_000_000_007
key.each_char { |c| hash = (hash << 4) ^ (hash >> 28) ^ c.ord }
hash % modulus
end
[class]{}-[func]{rot_hash}
```
=== "Zig"
@@ -654,11 +276,6 @@ The design of hash algorithms is a complex issue that requires consideration of
[class]{}-[func]{rotHash}
```
??? pythontutor "Code Visualization"
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<div style="margin-top: 5px;"><a href="https://pythontutor.com/iframe-embed.html#code=def%20add_hash%28key%3A%20str%29%20-%3E%20int%3A%0A%20%20%20%20%22%22%22%E5%8A%A0%E6%B3%95%E5%93%88%E5%B8%8C%22%22%22%0A%20%20%20%20hash%20%3D%200%0A%20%20%20%20modulus%20%3D%201000000007%0A%20%20%20%20for%20c%20in%20key%3A%0A%20%20%20%20%20%20%20%20hash%20%2B%3D%20ord%28c%29%0A%20%20%20%20return%20hash%20%25%20modulus%0A%0A%0Adef%20mul_hash%28key%3A%20str%29%20-%3E%20int%3A%0A%20%20%20%20%22%22%22%E4%B9%98%E6%B3%95%E5%93%88%E5%B8%8C%22%22%22%0A%20%20%20%20hash%20%3D%200%0A%20%20%20%20modulus%20%3D%201000000007%0A%20%20%20%20for%20c%20in%20key%3A%0A%20%20%20%20%20%20%20%20hash%20%3D%2031%20*%20hash%20%2B%20ord%28c%29%0A%20%20%20%20return%20hash%20%25%20modulus%0A%0A%0Adef%20xor_hash%28key%3A%20str%29%20-%3E%20int%3A%0A%20%20%20%20%22%22%22%E5%BC%82%E6%88%96%E5%93%88%E5%B8%8C%22%22%22%0A%20%20%20%20hash%20%3D%200%0A%20%20%20%20modulus%20%3D%201000000007%0A%20%20%20%20for%20c%20in%20key%3A%0A%20%20%20%20%20%20%20%20hash%20%5E%3D%20ord%28c%29%0A%20%20%20%20return%20hash%20%25%20modulus%0A%0A%0Adef%20rot_hash%28key%3A%20str%29%20-%3E%20int%3A%0A%20%20%20%20%22%22%22%E6%97%8B%E8%BD%AC%E5%93%88%E5%B8%8C%22%22%22%0A%20%20%20%20hash%20%3D%200%0A%20%20%20%20modulus%20%3D%201000000007%0A%20%20%20%20for%20c%20in%20key%3A%0A%20%20%20%20%20%20%20%20hash%20%3D%20%28hash%20%3C%3C%204%29%20%5E%20%28hash%20%3E%3E%2028%29%20%5E%20ord%28c%29%0A%20%20%20%20return%20hash%20%25%20modulus%0A%0A%0A%22%22%22Driver%20Code%22%22%22%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20key%20%3D%20%22Hello%20%E7%AE%97%E6%B3%95%22%0A%0A%20%20%20%20hash%20%3D%20add_hash%28key%29%0A%20%20%20%20print%28f%22%E5%8A%A0%E6%B3%95%E5%93%88%E5%B8%8C%E5%80%BC%E4%B8%BA%20%7Bhash%7D%22%29%0A%0A%20%20%20%20hash%20%3D%20mul_hash%28key%29%0A%20%20%20%20print%28f%22%E4%B9%98%E6%B3%95%E5%93%88%E5%B8%8C%E5%80%BC%E4%B8%BA%20%7Bhash%7D%22%29%0A%0A%20%20%20%20hash%20%3D%20xor_hash%28key%29%0A%20%20%20%20print%28f%22%E5%BC%82%E6%88%96%E5%93%88%E5%B8%8C%E5%80%BC%E4%B8%BA%20%7Bhash%7D%22%29%0A%0A%20%20%20%20hash%20%3D%20rot_hash%28key%29%0A%20%20%20%20print%28f%22%E6%97%8B%E8%BD%AC%E5%93%88%E5%B8%8C%E5%80%BC%E4%B8%BA%20%7Bhash%7D%22%29%0A&codeDivHeight=800&codeDivWidth=600&cumulative=false&curInstr=6&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false" target="_blank" rel="noopener noreferrer">Full Screen ></a></div>
It is observed that the last step of each hash algorithm is to take the modulus of the large prime number $1000000007$ to ensure that the hash value is within an appropriate range. It is worth pondering why emphasis is placed on modulo a prime number, or what are the disadvantages of modulo a composite number? This is an interesting question.
To conclude: **Using a large prime number as the modulus can maximize the uniform distribution of hash values**. Since a prime number does not share common factors with other numbers, it can reduce the periodic patterns caused by the modulo operation, thus avoiding hash collisions.
en/docs/chapter_hashing/hash_collision.md
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en/docs/chapter_hashing/hash_map.md
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