前言

我在Internet上浏览了很多遍，找到了很多有关哈希表的有趣文章，但是我没有找到关于它们如何实现的可理解的完整描述。在这方面，我迫不及待想写一个关于这个如此有趣的主题的文章。

也许对于经验丰富的程序员而言，它并没有那么有用，但是对于技术大学的学生和新手自学的程序员而言，它将会很有趣。

使用哈希表的动机

.

, -

, -. : ?

: , , : , . - , , , .

-

- — . , , , .

. , . () . O(1) .

, -.

, , , , , . , , - .

: . , , , .

( ) -, .

- ( g) s, . , , g s . , ? -, t — , , g.

s, s + t, s + 2*t .. , , ( ).

, , . .

-

-, .

-, . - , . , , -.

int HashFunctionHorner(const std::string& s, int table_size, const int key)
{
    int hash_result = 0;
    for (int i = 0; s[i] != 0; ++i)
        hash_result = (key * hash_result + s[i]) % table_size;
    hash_result = (hash_result * 2 + 1) % table_size;
    return hash_result;
}
struct HashFunction1 
{
    int operator()(const std::string& s, int table_size) const
    {
        return HashFunctionHorner(s, table_size, table_size - 1); //    ,   < >    .
    }
};
struct HashFunction2 
{
    int operator()(const std::string& s, int table_size) const
    {
        return HashFunctionHorner(s, table_size, table_size + 1);
    }
};

, : , ? , deleted, . , ( - ) . , , , , - . .

.

template <class T, class THash1 = HashFunction1, class THash2 = HashFunction2>
class HashTable
{
    static const int default_size = 8; //    
    constexpr static const double rehash_size = 0.75; // ,     
    struct Node
    {
        T value;
        bool state; //    state = false,      (deleted)
        Node(const T& value_) : value(value_), state(true) {}
    };
    Node** arr; //       Node*
    int size; //        (  deleted)
    int buffer_size; //   ,       
    int size_all_non_nullptr; //        (  deleted)
};

- , . .

...
public:
    HashTable()
    {
        buffer_size = default_size;
        size = 0;
        size_all_non_nullptr = 0;
        arr = new Node*[buffer_size];
        for (int i = 0; i < buffer_size; ++i)
            arr[i] = nullptr; //  nullptr -     ,        
    }
    ~HashTable()
    {
        for (int i = 0; i < buffer_size; ++i)
            if (arr[i])
                delete arr[i];
        delete[] arr;
    }

, — Resize.

.

void Resize()
    {
        int past_buffer_size = buffer_size;
        buffer_size *= 2;
        size_all_non_nullptr = 0;
        size = 0;
        Node** arr2 = new Node * [buffer_size];
        for (int i = 0; i < buffer_size; ++i)
            arr2[i] = nullptr;
        std::swap(arr, arr2);
        for (int i = 0; i < past_buffer_size; ++i)
        {
            if (arr2[i] && arr2[i]->state)
                Add(arr2[i]->value); //     
        }
        //   
        for (int i = 0; i < past_buffer_size; ++i)
            if (arr2[i])
                delete arr2[i];
        delete[] arr2;
    }

O(1) . ? (deleted). , , , . . - ( , ).

, 50, Rehash, , (resize), . , , . - , . deleted- , , .

, :

void Rehash()
    {
        size_all_non_nullptr = 0;
        size = 0;
        Node** arr2 = new Node * [buffer_size];
        for (int i = 0; i < buffer_size; ++i)
            arr2[i] = nullptr;
        std::swap(arr, arr2);
        for (int i = 0; i < buffer_size; ++i)
        {
            if (arr2[i] && arr2[i]->state)
                Add(arr2[i]->value);
        }
        //   
        for (int i = 0; i < buffer_size; ++i)
            if (arr2[i])
                delete arr2[i];
        delete[] arr2;
    }

, , , . (Add), (Remove) (Find) .

— Find .

bool Find(const T& value, const THash1& hash1 = THash1(), const THash2& hash2 = THash2())
    {
        int h1 = hash1(value, buffer_size); // ,    
        int h2 = hash2(value, buffer_size); // ,   ""  
        int i = 0;
        while (arr[h1] != nullptr && i < buffer_size)
        {
            if (arr[h1]->value == value && arr[h1]->state)
                return true; //   
            h1 = (h1 + h2) % buffer_size;
            ++i; //    i >=  buffer_size,       ,      i,     .
        }
        return false;
    }

— Remove. ? ( Find), , state false, Node .

bool Remove(const T& value, const THash1& hash1 = THash1(), const THash2& hash2 = THash2())
    {
        int h1 = hash1(value, buffer_size);
        int h2 = hash2(value, buffer_size);
        int i = 0;
        while (arr[h1] != nullptr && i < buffer_size)
        {
            if (arr[h1]->value == value && arr[h1]->state)
            {
                arr[h1]->state = false;
                --size;
                return true;
            }
            h1 = (h1 + h2) % buffer_size;
            ++i;
        }
        return false;
    }

Add. . .

, . ( deleted). , - . deleted- , Node .

bool Add(const T& value, const THash1& hash1 = THash1(),const THash2& hash2 = THash2())
    {
        if (size + 1 > int(rehash_size * buffer_size))
            Resize();
        else if (size_all_non_nullptr > 2 * size)
            Rehash(); //  ,     deleted-
        int h1 = hash1(value, buffer_size);
        int h2 = hash2(value, buffer_size);
        int i = 0;
        int first_deleted = -1; //    () 
        while (arr[h1] != nullptr && i < buffer_size)
        {
            if (arr[h1]->value == value && arr[h1]->state)
                return false; //    ,      
            if (!arr[h1]->state && first_deleted == -1) //     
                first_deleted = h1;
            h1 = (h1 + h2) % buffer_size;
            ++i;
        }
        if (first_deleted == -1) //     ,   Node
        {
            arr[h1] = new Node(value);
            ++size_all_non_nullptr; //      ,   ,     
        }
        else
        {
            arr[first_deleted]->value = value;
            arr[first_deleted]->state = true;
        }
        ++size; //        
        return true;
    }

int HashFunctionHorner(const std::string& s, int table_size, const int key)
{
    int hash_result = 0;
    for (int i = 0; s[i] != 0; ++i)
    {
        hash_result = (key * hash_result + s[i]) % table_size;
    }
    hash_result = (hash_result * 2 + 1) % table_size;
    return hash_result;
}

struct HashFunction1 
{
    int operator()(const std::string& s, int table_size) const
    {
        return HashFunctionHorner(s, table_size, table_size - 1);
    }
};

struct HashFunction2 
{
    int operator()(const std::string& s, int table_size) const
    {
        return HashFunctionHorner(s, table_size, table_size + 1);
    }
};

template <class T, class THash1 = HashFunction1, class THash2 = HashFunction2>
class HashTable
{
    static const int default_size = 8;
    constexpr static const double rehash_size = 0.75;
    struct Node
    {
        T value;
        bool state;
        Node(const T& value_) : value(value_), state(true) {}
    };
    Node** arr;
    int size;
    int buffer_size;
    int size_all_non_nullptr;

    void Resize()
    {
        int past_buffer_size = buffer_size;
        buffer_size *= 2;
        size_all_non_nullptr = 0;
        size = 0;
        Node** arr2 = new Node * [buffer_size];
        for (int i = 0; i < buffer_size; ++i)
            arr2[i] = nullptr;
        std::swap(arr, arr2);
        for (int i = 0; i < past_buffer_size; ++i)
        {
            if (arr2[i] && arr2[i]->state)
                Add(arr2[i]->value);
        }
        for (int i = 0; i < past_buffer_size; ++i)
            if (arr2[i])
                delete arr2[i];
        delete[] arr2;
    }

    void Rehash()
    {
        size_all_non_nullptr = 0;
        size = 0;
        Node** arr2 = new Node * [buffer_size];
        for (int i = 0; i < buffer_size; ++i)
            arr2[i] = nullptr;
        std::swap(arr, arr2);
        for (int i = 0; i < buffer_size; ++i)
        {
            if (arr2[i] && arr2[i]->state)
                Add(arr2[i]->value);
        }
        for (int i = 0; i < buffer_size; ++i)
            if (arr2[i])
                delete arr2[i];
        delete[] arr2;
    }

public:
    HashTable()
    {
        buffer_size = default_size;
        size = 0;
        size_all_non_nullptr = 0;
        arr = new Node*[buffer_size];
        for (int i = 0; i < buffer_size; ++i)
            arr[i] = nullptr;
    }
    ~HashTable()
    {
        for (int i = 0; i < buffer_size; ++i)
            if (arr[i])
                delete arr[i];
        delete[] arr;
    }
    bool Add(const T& value, const THash1& hash1 = THash1(),const THash2& hash2 = THash2())
    {
        if (size + 1 > int(rehash_size * buffer_size))
            Resize();
        else if (size_all_non_nullptr > 2 * size)
            Rehash();
        int h1 = hash1(value, buffer_size);
        int h2 = hash2(value, buffer_size);
        int i = 0;
        int first_deleted = -1;
        while (arr[h1] != nullptr && i < buffer_size)
        {
            if (arr[h1]->value == value && arr[h1]->state)
                return false;
            if (!arr[h1]->state && first_deleted == -1)
                first_deleted = h1;
            h1 = (h1 + h2) % buffer_size;
            ++i;
        }
        if (first_deleted == -1)
        {
            arr[h1] = new Node(value);
            ++size_all_non_nullptr;
        }
        else
        {
            arr[first_deleted]->value = value;
            arr[first_deleted]->state = true;
        }
        ++size;
        return true;
    }
    bool Remove(const T& value, const THash1& hash1 = THash1(), const THash2& hash2 = THash2())
    {
        int h1 = hash1(value, buffer_size);
        int h2 = hash2(value, buffer_size);
        int i = 0;
        while (arr[h1] != nullptr && i < buffer_size)
        {
            if (arr[h1]->value == value && arr[h1]->state)
            {
                arr[h1]->state = false;
                --size;
                return true;
            }
            h1 = (h1 + h2) % buffer_size;
            ++i;
        }
        return false;
    }
    bool Find(const T& value, const THash1& hash1 = THash1(), const THash2& hash2 = THash2())
    {
        int h1 = hash1(value, buffer_size);
        int h2 = hash2(value, buffer_size);
        int i = 0;
        while (arr[h1] != nullptr && i < buffer_size)
        {
            if (arr[h1]->value == value && arr[h1]->state)
                return true;
            h1 = (h1 + h2) % buffer_size;
            ++i;
        }
        return false;
    }
};