Vorwort

Ich habe viele Male im Internet gesucht, viele interessante Artikel über Hash-Tabellen gefunden, aber ich habe keine verständliche und vollständige Beschreibung ihrer Implementierung gefunden. In dieser Hinsicht konnte ich es kaum erwarten, einen Beitrag zu diesem so interessanten Thema zu schreiben.

Es mag für erfahrene Programmierer nicht so nützlich sein, aber es wird für Studenten technischer Universitäten und angehende autodidaktische Programmierer interessant sein.

Motivation zur Verwendung von Hash-Tabellen

Berücksichtigen Sie aus Gründen der Übersichtlichkeit Standardbehälter und die Asymptotik ihrer am häufigsten verwendeten Methoden.

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. , . () . O(1) .

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( ) -, .

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

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

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-, . - , . , , -.

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;
    }
};