数据结构笔记-----二叉排序树和哈希表

二叉排序树

如何改进二分查找使其适应动态查找？

二分查找的过程

新的想法

二叉排序树

代码

BSTree.c

<strong><span style="font-size:18px;">#include <stdio.h>
#include <malloc.h>
#include "BSTree.h"

typedef struct _tag_BSTree TBSTree;
struct _tag_BSTree
{
    int count;
    BSTreeNode* root;
};

static void recursive_display(BSTreeNode* node, BSTree_Printf* pFunc, int format, int gap, char div) // O(n)
{
    int i = 0;
    
    if( (node != NULL) && (pFunc != NULL) )
    {
        for(i=0; i<format; i++)
        {
            printf("%c", div);
        }
        
        pFunc(node);
        
        printf("\n");
        
        if( (node->left != NULL) || (node->right != NULL) )
        {
            recursive_display(node->left, pFunc, format + gap, gap, div);
            recursive_display(node->right, pFunc, format + gap, gap, div);
        }
    }
    else
    {
        for(i=0; i<format; i++)
        {
            printf("%c", div);
        }
        printf("\n");
    }
}

static int recursive_count(BSTreeNode* root) // O(n)
{
    int ret = 0;
    
    if( root != NULL )
    {
        ret = recursive_count(root->left) + 1 + recursive_count(root->right);
    }
    
    return ret;
}

static int recursive_height(BSTreeNode* root) // O(n)
{
    int ret = 0;
    
    if( root != NULL )
    {
        int lh = recursive_height(root->left);
        int rh = recursive_height(root->right);
        
        ret = ((lh > rh) ? lh : rh) + 1;
    }
    
    return ret;
}

static int recursive_degree(BSTreeNode* root) // O(n)
{
    int ret = 0;
    
    if( root != NULL )
    {
        if( root->left != NULL )
        {
            ret++;
        }
        
        if( root->right != NULL )
        {
            ret++;
        }
        
        if( ret == 1 )
        {
            int ld = recursive_degree(root->left);
            int rd = recursive_degree(root->right);
            
            if( ret < ld )
            {
                ret = ld;
            }
            
            if( ret < rd )
            {
                ret = rd;
            }
        }
    }
    
    return ret;
}

static int recursive_insert(BSTreeNode* root, BSTreeNode* node, BSTree_Compare* compare)
{
    int ret = 1;
    int r = compare(node->key, root->key);
    
    if( r == 0 )
    {
        ret = 0;
    }
    else if( r < 0 )
    {
        if( root->left != NULL )
        {
            ret = recursive_insert(root->left, node, compare);
        }
        else
        {
            root->left = node;
        }
    }
    else if( r > 0 )
    {
        if( root->right != NULL )
        {
            ret = recursive_insert(root->right, node, compare);
        }
        else
        {
            root->right = node;
        }
    }
}

static BSTreeNode* recursive_get(BSTreeNode* root, BSKey* key, BSTree_Compare* compare)
{
    BSTreeNode* ret = NULL;
    
    if( root != NULL )
    {
        int r = compare(key, root->key);
        
        if( r == 0 )
        {
            ret = root;
        }
        else if( r < 0 )
        {
            ret = recursive_get(root->left, key, compare);
        }
        else if( r > 0 )
        {
            ret = recursive_get(root->right, key, compare);
        }
    }
    
    return ret;
}

static BSTreeNode* delete_node(BSTreeNode** pRoot)
{
    BSTreeNode* ret = *pRoot;
    
    if( (*pRoot)->right == NULL )
    {
        *pRoot = (*pRoot)->left;
    }
    else if( (*pRoot)->left == NULL )
    {
        *pRoot = (*pRoot)->right;
    }
    else
    {
        BSTreeNode* g = *pRoot;
        BSTreeNode* c = (*pRoot)->left;
        
        while( c->right != NULL )
        {
            g = c;
            c = c->right;
        }
        
        if( g != *pRoot )
        {
            g->right = c->left;
        }
        else
        {
            g->left = c->left;
        }

        c->left = (*pRoot)->left;
        c->right = (*pRoot)->right;
        
        *pRoot = c;
    }
    
    return ret;
}

static BSTreeNode* recursive_delete(BSTreeNode** pRoot, BSKey* key, BSTree_Compare* compare)
{
    BSTreeNode* ret = NULL;
    
    if( (pRoot != NULL) && (*pRoot != NULL) )
    {
        int r = compare(key, (*pRoot)->key);
        
        if( r == 0 )
        {
            ret = delete_node(pRoot);
        }
        else if( r < 0 )
        {
            ret = recursive_delete(&((*pRoot)->left), key, compare);
        }
        else if( r > 0 )
        {
            ret = recursive_delete(&((*pRoot)->right), key, compare);
        }
    }
    
    return ret;
}

BSTree* BSTree_Create() // O(1)
{
    TBSTree* ret = (TBSTree*)malloc(sizeof(TBSTree));
    
    if( ret != NULL )
    {
        ret->count = 0;
        ret->root = NULL;
    }
    
    return ret;
}

void BSTree_Destroy(BSTree* tree) // O(1)
{
    free(tree);
}

void BSTree_Clear(BSTree* tree) // O(1)
{
    TBSTree* btree = (TBSTree*)tree;
    
    if( btree != NULL )
    {
        btree->count = 0;
        btree->root = NULL;
    }
}

int BSTree_Insert(BSTree* tree, BSTreeNode* node, BSTree_Compare* compare) 
{
    TBSTree* btree = (TBSTree*)tree;
    int ret = (btree != NULL) && (node != NULL) && (compare != NULL);
    
    if( ret )
    {
        node->left = NULL;
        node->right = NULL;
        
        if( btree->root == NULL )
        {
            btree->root = node;
        }
        else
        {
            ret = recursive_insert(btree->root, node, compare);
        }
        
        if( ret )
        {
            btree->count++;
        }
    }
    
    return ret;
}

BSTreeNode* BSTree_Delete(BSTree* tree, BSKey* key, BSTree_Compare* compare)
{
    TBSTree* btree = (TBSTree*)tree;
    BSTreeNode* ret = NULL; 
    
    if( (btree != NULL) && (key != NULL) && (compare != NULL) )
    {
        ret = recursive_delete(&btree->root, key, compare);
        
        if( ret != NULL )
        {
            btree->count--;
        }
    }
    
    return ret;
}

BSTreeNode* BSTree_Get(BSTree* tree, BSKey* key, BSTree_Compare* compare)
{
    TBSTree* btree = (TBSTree*)tree;
    BSTreeNode* ret = NULL; 
    
    if( (btree != NULL) && (key != NULL) && (compare != NULL) )
    {
        ret = recursive_get(btree->root, key, compare);
    }
    
    return ret;
}

BSTreeNode* BSTree_Root(BSTree* tree) // O(1)
{
    TBSTree* btree = (TBSTree*)tree;
    BSTreeNode* ret = NULL;
    
    if( btree != NULL )
    {
        ret = btree->root;
    }
    
    return ret;
}

int BSTree_Height(BSTree* tree) // O(n)
{
    TBSTree* btree = (TBSTree*)tree;
    int ret = 0;
    
    if( btree != NULL )
    {
        ret = recursive_height(btree->root);
    }
    
    return ret;
}

int BSTree_Count(BSTree* tree) // O(1)
{
    TBSTree* btree = (TBSTree*)tree;
    int ret = 0;
    
    if( btree != NULL )
    {
        ret = btree->count;
    }
    
    return ret;
}

int BSTree_Degree(BSTree* tree) // O(n)
{
    TBSTree* btree = (TBSTree*)tree;
    int ret = 0;
    
    if( btree != NULL )
    {
        ret = recursive_degree(btree->root);
    }
    
    return ret;
}

void BSTree_Display(BSTree* tree, BSTree_Printf* pFunc, int gap, char div) // O(n)
{
    TBSTree* btree = (TBSTree*)tree;
    
    if( btree != NULL )
    {
        recursive_display(btree->root, pFunc, 0, gap, div);
    }
}</span></strong>

BSTree.h

<strong><span style="font-size:18px;">#ifndef _BSTREE_H_
#define _BSTREE_H_

typedef void BSTree;
typedef void BSKey;

typedef struct _tag_BSTreeNode BSTreeNode;
struct _tag_BSTreeNode
{
    BSKey* key;
    BSTreeNode* left;
    BSTreeNode* right;
};

typedef void (BSTree_Printf)(BSTreeNode*);
typedef int (BSTree_Compare)(BSKey*, BSKey*);

BSTree* BSTree_Create();

void BSTree_Destroy(BSTree* tree);

void BSTree_Clear(BSTree* tree);

int BSTree_Insert(BSTree* tree, BSTreeNode* node, BSTree_Compare* compare);

BSTreeNode* BSTree_Delete(BSTree* tree, BSKey* key, BSTree_Compare* compare);

BSTreeNode* BSTree_Get(BSTree* tree, BSKey* key, BSTree_Compare* compare);

BSTreeNode* BSTree_Root(BSTree* tree);

int BSTree_Height(BSTree* tree);

int BSTree_Count(BSTree* tree);

int BSTree_Degree(BSTree* tree);

void BSTree_Display(BSTree* tree, BSTree_Printf* pFunc, int gap, char div);

#endif
</span></strong>

main.c

<strong><span style="font-size:18px;">#include <stdio.h>
#include <stdlib.h>
#include "BSTree.h"

/* run this program using the console pauser or add your own getch, system("pause") or input loop */

struct Node
{
    BSTreeNode header;
    char v;
};

void printf_data(BSTreeNode* node)
{
    if( node != NULL )
    {
        printf("%c", ((struct Node*)node)->v);
    }
}

int compare_key(BSKey* k1, BSKey* k2)
{
    return (int)k1 - (int)k2;
}

int main(int argc, char *argv[])
{
    BSTree* tree = BSTree_Create();
    
    struct Node n1 = {{(BSKey*)1, NULL, NULL}, 'A'};
    struct Node n2 = {{(BSKey*)2, NULL, NULL}, 'B'};
    struct Node n3 = {{(BSKey*)3, NULL, NULL}, 'C'};
    struct Node n4 = {{(BSKey*)4, NULL, NULL}, 'D'};
    struct Node n5 = {{(BSKey*)5, NULL, NULL}, 'E'};
    struct Node n6 = {{(BSKey*)6, NULL, NULL}, 'F'};
    
    BSTree_Insert(tree, (BSTreeNode*)&n4, compare_key);
    BSTree_Insert(tree, (BSTreeNode*)&n1, compare_key);
    BSTree_Insert(tree, (BSTreeNode*)&n3, compare_key);
    BSTree_Insert(tree, (BSTreeNode*)&n6, compare_key);
    BSTree_Insert(tree, (BSTreeNode*)&n2, compare_key);
    BSTree_Insert(tree, (BSTreeNode*)&n5, compare_key);
    
    printf("Height: %d\n", BSTree_Height(tree));
    printf("Degree: %d\n", BSTree_Degree(tree));
    printf("Count: %d\n", BSTree_Count(tree));
    printf("Search Key 5: %c\n", ((struct Node*)BSTree_Get(tree, (BSKey*)5, compare_key))->v);
    printf("Full Tree: \n");
    
    BSTree_Display(tree, printf_data, 4, '-');
    
    BSTree_Delete(tree, (BSKey*)4, compare_key);
    
    printf("After Delete Key 4: \n");
    printf("Height: %d\n", BSTree_Height(tree));
    printf("Degree: %d\n", BSTree_Degree(tree));
    printf("Count: %d\n", BSTree_Count(tree));
    printf("Full Tree: \n");
    
    BSTree_Display(tree, printf_data, 4, '-');
    
    BSTree_Clear(tree);
    
    printf("After Clear: \n");
    printf("Height: %d\n", BSTree_Height(tree));
    printf("Degree: %d\n", BSTree_Degree(tree));
    printf("Count: %d\n", BSTree_Count(tree));
    
    BSTree_Display(tree, printf_data, 4, '-');
    
    BSTree_Destroy(tree);
    
	return 0;
}</span></strong>

小结

哈希表及其实现

最常见的代码需求：

再论数组

一个常见的情形

解决方案

代码

Hash.c

<strong><span style="font-size:18px;">#include <stdio.h>
#include <malloc.h>
#include "Hash.h"
#include "BSTree.h"

typedef struct _tag_HashNode HashNode;
struct _tag_HashNode
{
    BSTreeNode header;
    HashValue* value;
};

void recursive_clear(BSTreeNode* node)
{
    if( node != NULL )
    {
        recursive_clear(node->left);
        recursive_clear(node->right);
        
        free(node);
    }
}

Hash* Hash_Create()
{
    return BSTree_Create();
}

void Hash_Destroy(Hash* hash)
{
    Hash_Clear(hash);
    BSTree_Destroy(hash);
}

void Hash_Clear(Hash* hash)
{
    recursive_clear(BSTree_Root(hash));
    BSTree_Clear(hash);
}

int Hash_Add(Hash* hash, HashKey* key, HashValue* value, Hash_Compare* compare)
{
    int ret = 0;
    HashNode* node = (HashNode*)malloc(sizeof(HashNode));
    
    if( ret = (node != NULL) )
    {
        node->header.key = key;
        node->value = value;
        
        ret = BSTree_Insert(hash, (BSTreeNode*)node, compare);
        
        if( !ret )
        {
            free(node);
        }
    }
    
    return ret;
}

HashValue* Hash_Remove(Hash* hash, HashKey* key, Hash_Compare* compare)
{
    HashValue* ret = NULL;
    HashNode* node = (HashNode*)BSTree_Delete(hash, key, compare);
    
    if( node != NULL )
    {
        ret = node->value;
        
        free(node);
    }
    
    return ret;
}

HashValue* Hash_Get(Hash* hash, HashKey* key, Hash_Compare* compare)
{
    HashValue* ret = NULL;
    HashNode* node = (HashNode*)BSTree_Get(hash, key, compare);
    
    if( node != NULL )
    {
        ret = node->value;
    }
    
    return ret;
}

int Hash_Count(Hash* hash)
{
    return BSTree_Count(hash);
}</span></strong>

Hash.h

<strong><span style="font-size:18px;">#ifndef _HASH_H_
#define _HASH_H_

typedef void Hash;
typedef void HashKey;
typedef void HashValue;

typedef int (Hash_Compare)(HashKey*, HashKey*);

Hash* Hash_Create();
void Hash_Destroy(Hash* hash);
void Hash_Clear(Hash* hash);
int Hash_Add(Hash* hash, HashKey* key, HashValue* value, Hash_Compare* compare);
HashValue* Hash_Remove (Hash* hash, HashKey* key, Hash_Compare* compare);
HashValue* Hash_Get(Hash* hash, HashKey* key, Hash_Compare* compare);
int Hash_Count(Hash* hash);


#endif</span></strong>

main.c

<strong><span style="font-size:18px;">#include <stdio.h>
#include <stdlib.h>
#include "Hash.h"

/* run this program using the console pauser or add your own getch, system("pause") or input loop */

struct Student
{
    char* id;
    char* name;
    int age;
};

int compare_id(HashKey* k1, HashKey* k2)
{
    return strcmp((char*)k1, (char*)k2);
}

int main(int argc, char *argv[]) 
{
    Hash* hash = Hash_Create();
    
    struct Student s1 = {"9001201", "Delphi", 30};
    struct Student s2 = {"0xABCDE", "Java", 20};
    struct Student s3 = {"koabc", "C++", 40};
    struct Student s4 = {"!@#$%^", "C#", 10};
    struct Student s5 = {"Python", "Python", 10};
    struct Student* ps = NULL;
    
    Hash_Add(hash, s1.id, &s1, compare_id);
    Hash_Add(hash, s2.id, &s2, compare_id);
    Hash_Add(hash, s3.id, &s3, compare_id);
    Hash_Add(hash, s4.id, &s4, compare_id);
    Hash_Add(hash, s5.id, &s5, compare_id);
    
    ps = Hash_Get(hash, "koabc", compare_id);
    
    printf("ID: %s\n", ps->id);
    printf("Name: %s\n", ps->name);
    printf("Age: %d\n", ps->age);
    
    Hash_Destroy(hash);
    
	return 0;
}</span></strong>

小结

整个数据结构总结

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