《数据结构与算法分析——C语言描述》ADT实现(NO.05) : 散列（Hash）

散列（Hash）是一种以常数复杂度实现查找功能的数据结构。它将一个关键词Key，通过某种映射（哈希函数）转化成索引值直接定位到相应位置。

实现散列有两个关键，一是哈希函数的选择，二是冲突的处理。

对于哈希函数，例程中以“Key为int型，操作为取（关于表长的）模”为例。事实上，可以直接将其换成任何一个哈希函数，不会影响实现。

对于冲突处理，有两大类处理方案，一是分离链接法，二是开放定址法。开放定址法包括线性探测法、平方探测法、双散列法等，本文给出分离链接法和平方探测法的实现。

1. 分离链接法：

// HashSep.h

#include <stdio.h>
#include <stdlib.h>

struct ListNode;
typedef struct ListNode *Position;
struct HashTbl;
typedef struct HashTbl *HashTable;

typedef Position List;

HashTable InitializeTable(int TableSize);
void DestroyTable(HashTable H);
Position Find(ElementType Key, HashTable H);
void Insert(ElementType Key, HashTable H);

// HashSep.c

#include "HashSep.h"

struct ListNode
{
    ElementType Key;
    Position Next;
};

struct HashTbl
{
    int TableSize;
    List *TheLists;
};

int NextPrime(int N)
{
    if (N % 2 == 0)
        N++;
    int i;
    int NotPrime = 0;
    for (;; N += 2)
    {
        NotPrime = 0;
        for (i = 3; i * i <= N; i += 2)
            if (N % i == 0)
            {
                NotPrime = 1;
                break;
            }
        if (!NotPrime)
            return N;
    }
}

int Hash(ElementType Key, int TableSize)
{
    return Key * Key % 10;
}

HashTable InitializeTable(int TableSize)
{
    HashTable H;
    int i;
    if ((H = (HashTable)malloc(sizeof(struct HashTbl))) == NULL)
    {
        printf("Error! Out of memory! \n");
        return NULL;
    }
    H->TableSize = NextPrime(TableSize);
    H->TheLists = (Position *)malloc(H->TableSize * sizeof(Position));
    for (i = 0; i < H->TableSize; i++)
    {
        if ((H->TheLists[i] = (List)malloc(sizeof(struct ListNode))) == NULL)
        {
            printf("Error! Out of memory! \n");
            return NULL;
        }
        H->TheLists[i]->Next = NULL;
    }
    return H;
}

void DestroyTable(HashTable H)
{
    int i;
    for (i = 0; i < H->TableSize; i++)
    {
        Position p, q;
        q = H->TheLists[i];
        p = q->Next;
        while(p)
        {
            free(q);
            q = p;
            p = p->Next;
        }
    }
    free(H);
}

int Same(ElementType e1, ElementType e2)
{
    return e1 == e2;
}

Position Find(ElementType Key, HashTable H)
{
    Position p;
    p = H->TheLists[Hash(Key, H->TableSize)]->Next;
    while(p)
    {
        if(Same(p->Key, Key))
            break;
        p = p->Next;
    }
    return p;
}

void Insert(ElementType Key, HashTable H)
{
    Position p;
    List L;
    if(Find(Key, H) != NULL)
        return;
    if((p = (Position)malloc(sizeof(struct ListNode))) == NULL)
    {
        printf("Error! Out of memory! \n");
        return;
    }
    p->Key = Key;
    L = H->TheLists[Hash(Key, H->TableSize)];
    p->Next = L->Next;
    L->Next = p;
}

2. 平方探测法

// HashQuad.h

#include <stdio.h>
#include <stdlib.h>

typedef unsigned int Index;
typedef Index Position;

struct HashTbl;
typedef struct HashTbl *HashTable;

typedef struct HashEntry Cell;

HashTable InitializeTable(int TableSize);
void DestroyTable(HashTable H);
Position Find(ElementType Key, HashTable H);
void Insert(ElementType Key, HashTable H);
ElementType Retrieve(Position P, HashTable H);
HashTable ReHash(HashTable H);

// HashQuad.c

#include "HashQuad.h"

enum KindOfEntry
{
    Legitimate,
    Empty,
    Deleted
};

struct HashEntry
{
    ElementType Element;
    enum KindOfEntry Info;
};

struct HashTbl
{
    int TableSize;
    Cell *TheCells;
};

int NextPrime(int N)
{
    if (N % 2 == 0)
        N++;
    int i;
    int NotPrime = 0;
    for (;; N += 2)
    {
        NotPrime = 0;
        for (i = 3; i * i <= N; i += 2)
            if (N % i == 0)
            {
                NotPrime = 1;
                break;
            }
        if (!NotPrime)
            return N;
    }
}

Index Hash(ElementType Key, int TableSize)
{
    return Key % TableSize;
}

HashTable InitializeTable(int TableSize)
{
    HashTable H;
    int i;
    if ((H = (HashTable)malloc(sizeof(struct HashTbl))) == NULL)
    {
        printf("Error!\n");
        return NULL;
    }
    H->TableSize = NextPrime(TableSize);
    if ((H->TheCells = (Cell *)malloc(sizeof(Cell) * H->TableSize)) == NULL)
    {
        printf("Error!\n");
        return NULL;
    }
    for (i = 0; i < H->TableSize; i++)
        H->TheCells[i].Info = Empty;
    return H;
}

void DestroyTable(HashTable H)
{
    free(H->TheCells);
    free(H);
}

Position Find(ElementType Key, HashTable H)
{
    Index id = Hash(Key, H->TableSize);
    int i = 0;
    while (H->TheCells[id].Info == Legitimate && H->TheCells[id].Element != Key)
    {
        id += (++i << 1) - 1;
        if (id >= H->TableSize)
            id -= H->TableSize;
    }
    return id;
}

void Insert(ElementType Key, HashTable H)
{
    Position p = Find(Key, H);
    if (H->TheCells[p].Info != Legitimate)
    {
        H->TheCells[p].Element = Key;
        H->TheCells[p].Info = Legitimate;
    }
}

ElementType Retrieve(Position P, HashTable H)
{
    return H->TheCells[P].Element;
}

HashTable ReHash(HashTable H)
{
    int i;
    int OldSize;
    Cell *OldCells;
    OldCells = H->TheCells;
    OldSize = H->TableSize;
    H = InitializeTable(2 * OldSize);
    for(i = 0; i < H->TableSize; i++)
        if(OldCells[i].Info == Legitimate)
            Insert(OldCells[i].Element, H);
    free(OldCells);
    return H;
}

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