数据结构-树的存储结构

树的存储结构：

利用链表组织树中的各个结点

链表中的前后关系不代表结点间的逻辑关系

结点的逻辑关系由 child 数据域描述

child 数据域保存其他结点的存储地址

树结点结构体

typedef struct _tag_GTreeNode GTreeNode;struct _tag_GTreeNode{    GTreeData* data;    GTreeNode* parent;    LinkList* child;};

链表结点结构体

typedef struct _tag_LinkList{    LinkListNode header;    int length;} TLinkList;

树结点在链表中的位置不代表树的任何逻辑关系。

下面给出代码：

首先是线性表的头文件LinkList.h

#ifndef _LINKLIST_H_#define _LINKLIST_H_typedef void LinkList;typedef struct _tag_LinkListNode LinkListNode;struct _tag_LinkListNode{    LinkListNode* next;};LinkList* LinkList_Create();void LinkList_Destroy(LinkList* list);void LinkList_Clear(LinkList* list);int LinkList_Length(LinkList* list);int LinkList_Insert(LinkList* list, LinkListNode* node, int pos);LinkListNode* LinkList_Get(LinkList* list, int pos);LinkListNode* LinkList_Delete(LinkList* list, int pos);#endif

线性表的实现文件LinkList.c

#include <stdio.h>#include <malloc.h>#include "LinkList.h"typedef struct _tag_LinkList{    LinkListNode header;    int length;} TLinkList;LinkList* LinkList_Create() // O(1){    TLinkList* ret = (TLinkList*)malloc(sizeof(TLinkList));        if( ret != NULL )    {        ret->length = 0;        ret->header.next = NULL;    }        return ret;}void LinkList_Destroy(LinkList* list) // O(1){    free(list);}void LinkList_Clear(LinkList* list) // O(1){    TLinkList* sList = (TLinkList*)list;        if( sList != NULL )    {        sList->length = 0;        sList->header.next = NULL;    }}int LinkList_Length(LinkList* list) // O(1){    TLinkList* sList = (TLinkList*)list;    int ret = -1;        if( sList != NULL )    {        ret = sList->length;    }        return ret;}int LinkList_Insert(LinkList* list, LinkListNode* node, int pos) // O(n){     TLinkList* sList = (TLinkList*)list;    int ret = (sList != NULL) && (pos >= 0) && (node != NULL);    int i = 0;        if( ret )    {        LinkListNode* current = (LinkListNode*)sList;                for(i=0; (i<pos) && (current->next != NULL); i++)        {            current = current->next;        }                node->next = current->next;        current->next = node;                sList->length++;    }        return ret;}LinkListNode* LinkList_Get(LinkList* list, int pos) // O(n){    TLinkList* sList = (TLinkList*)list;    LinkListNode* ret = NULL;    int i = 0;        if( (sList != NULL) && (0 <= pos) && (pos < sList->length) )    {        LinkListNode* current = (LinkListNode*)sList;                for(i=0; i<pos; i++)        {            current = current->next;        }                ret = current->next;    }        return ret;}LinkListNode* LinkList_Delete(LinkList* list, int pos) // O(n){    TLinkList* sList = (TLinkList*)list;    LinkListNode* ret = NULL;    int i = 0;        if( (sList != NULL) && (0 <= pos) && (pos < sList->length) )    {        LinkListNode* current = (LinkListNode*)sList;                for(i=0; i<pos; i++)        {            current = current->next;        }                ret = current->next;        current->next = ret->next;                sList->length--;    }        return ret;}

树定义头文件GTree.h

#ifndef _TREE_H_#define _TREE_H_typedef void Tree;typedef void TreeNode;/* 创建树 */Tree* Tree_Create();/* 销毁已存在的树 */void Tree_Destroy(Tree* tree);/* 将已存在的树清空为空树 */void Tree_Clear(Tree* tree);/* 将结点node插入到tree中的pos位置处 */int Tree_Insert(Tree* tree, TreeNode* node, int pos);/* 将tree中pos位置的结点删除并返回 */TreeNode* Tree_Delete(Tree* tree, int pos);/* 将tree中pos位置的结点返回 */TreeNode* Tree_Get(Tree* tree, int pos);/* 返回tree的根结点 */TreeNode* Tree_Root(Tree* tree);/* 返回tree的高度 */int Tree_Height(Tree* tree);/* 返回树的结点数 */int Tree_Count(Tree* tree);/* 返回树的度数 */int Tree_Degree(Tree* tree);#endif

树实现文件GTree.c

#include <stdio.h>#include <malloc.h>#include "GTree.h"#include "LinkList.h"typedef struct _tag_GTreeNode GTreeNode;struct _tag_GTreeNode{    GTreeData* data;    GTreeNode* parent;    LinkList* child;};typedef struct _tag_TLNode TLNode;struct _tag_TLNode{    LinkListNode header;    GTreeNode* node;};static void recursive_display(GTreeNode* node, GTree_Printf* pFunc, int format, int gap, char div){    int i = 0;        if( (node != NULL) && (pFunc != NULL) )    {        for(i=0; i<format; i++)        {            printf("%c", div);        }            pFunc(node->data);            printf("\n");            for(i=0; i<LinkList_Length(node->child); i++)        {            TLNode* trNode = (TLNode*)LinkList_Get(node->child, i);                        recursive_display(trNode->node, pFunc, format + gap, gap, div);        }    }}static void recursive_delete(LinkList* list, GTreeNode* node){    if( (list != NULL) && (node != NULL) )    {        GTreeNode* parent = node->parent;        int index = -1;        int i = 0;                for(i=0; i<LinkList_Length(list); i++)        {            TLNode* trNode = (TLNode*)LinkList_Get(list, i);                         if( trNode->node == node )            {                LinkList_Delete(list, i);                                free(trNode);                                index = i;                                break;            }        }                  if( index >= 0 )        {              if( parent != NULL )            {                 for(i=0; i<LinkList_Length(parent->child); i++)                 {                     TLNode* trNode = (TLNode*)LinkList_Get(parent->child, i);                                          if( trNode->node == node )                     {                         LinkList_Delete(parent->child, i);                                                  free(trNode);                                                  break;                     }                 }                           }                        while( LinkList_Length(node->child) > 0 )            {                TLNode* trNode = (TLNode*)LinkList_Get(node->child, 0);                                recursive_delete(list, trNode->node);            }                        LinkList_Destroy(node->child);                    free(node);        }    }}static int recursive_height(GTreeNode* node){    int ret = 0;        if( node != NULL )    {        int subHeight = 0;        int i = 0;                for(i=0; i<LinkList_Length(node->child); i++)        {            TLNode* trNode = (TLNode*)LinkList_Get(node->child, i);                        subHeight = recursive_height(trNode->node);                        if( ret < subHeight )            {                ret = subHeight;            }        }                ret = ret + 1;    }        return ret;}static int recursive_degree(GTreeNode* node){int ret = -1;        if( node != NULL )    {        int subDegree = 0;        int i = 0;                ret = LinkList_Length(node->child);                for(i=0; i<LinkList_Length(node->child); i++)        {            TLNode* trNode = (TLNode*)LinkList_Get(node->child, i);                        subDegree = recursive_degree(trNode->node);                        if( ret < subDegree )            {                ret = subDegree;            }        }    }        return ret;}GTree* GTree_Create(){    return LinkList_Create();}void GTree_Destroy(GTree* tree){    GTree_Clear(tree);    LinkList_Destroy(tree);}void GTree_Clear(GTree* tree){     GTree_Delete(tree, 0);}int GTree_Insert(GTree* tree, GTreeData* data, int pPos){    LinkList* list = (LinkList*)tree;    int ret = (list != NULL) && (data != NULL) && (pPos < LinkList_Length(list));        if( ret )    {        TLNode* trNode = (TLNode*)malloc(sizeof(TLNode));        TLNode* cldNode = (TLNode*)malloc(sizeof(TLNode));        TLNode* pNode = (TLNode*)LinkList_Get(list, pPos);        GTreeNode* cNode = (GTreeNode*)malloc(sizeof(GTreeNode));                ret = (trNode != NULL) && (cldNode != NULL) && (cNode != NULL);                if( ret )        {            cNode->data = data;            cNode->parent = NULL;            cNode->child = LinkList_Create();                        trNode->node = cNode;            cldNode->node = cNode;                        LinkList_Insert(list, (LinkListNode*)trNode, LinkList_Length(list));                        if( pNode != NULL )            {                cNode->parent = pNode->node;                                LinkList_Insert(pNode->node->child, (LinkListNode*)cldNode, LinkList_Length(pNode->node->child));            }        }        else        {            free(trNode);            free(cldNode);            free(cNode);        }    }        return ret;}GTreeData* GTree_Delete(GTree* tree, int pos){    TLNode* trNode = (TLNode*)LinkList_Get(tree, pos);    GTreeData* ret = NULL;        if( trNode != NULL )    {        ret = trNode->node->data;                recursive_delete(tree, trNode->node);    }        return ret;}GTreeData* GTree_Get(GTree* tree, int pos){    TLNode* trNode = (TLNode*)LinkList_Get(tree, pos);    GTreeData* ret = NULL;        if( trNode != NULL )    {        ret = trNode->node->data;    }        return ret;}GTreeData* GTree_Root(GTree* tree){    return GTree_Get(tree, 0);}int GTree_Height(GTree* tree){    TLNode* trNode = (TLNode*)LinkList_Get(tree, 0);    int ret = 0;        if( trNode != NULL )    {        ret = recursive_height(trNode->node);    }        return ret;}int GTree_Count(GTree* tree){    return LinkList_Length(tree);}int GTree_Degree(GTree* tree){    TLNode* trNode = (TLNode*)LinkList_Get(tree, 0);    int ret = -1;        if( trNode != NULL )    {        ret = recursive_degree(trNode->node);    }        return ret;}void GTree_Display(GTree* tree, GTree_Printf* pFunc, int gap, char div){    TLNode* trNode = (TLNode*)LinkList_Get(tree, 0);        if( (trNode != NULL) && (pFunc != NULL) )    {          recursive_display(trNode->node, pFunc, 0, gap, div);    }}

测试文件main.c

#include <stdio.h>#include "GTree.h"/* run this program using the console pauser or add your own getch, system("pause") or input loop */void printf_data(GTreeData* data){    printf("%c", (int)data);}int main(int argc, char *argv[]){    GTree* tree = GTree_Create();    int i = 0;        GTree_Insert(tree, (GTreeData*)'A', -1);    GTree_Insert(tree, (GTreeData*)'B', 0);    GTree_Insert(tree, (GTreeData*)'C', 0);    GTree_Insert(tree, (GTreeData*)'D', 0);    GTree_Insert(tree, (GTreeData*)'E', 1);    GTree_Insert(tree, (GTreeData*)'F', 1);    GTree_Insert(tree, (GTreeData*)'H', 3);    GTree_Insert(tree, (GTreeData*)'I', 3);    GTree_Insert(tree, (GTreeData*)'J', 3);        printf("Tree Height: %d\n", GTree_Height(tree));    printf("Tree Degree: %d\n", GTree_Degree(tree));    printf("Full Tree:\n");        GTree_Display(tree, printf_data, 2, ' ');        printf("Get Tree Data:\n");        for(i=0; i<GTree_Count(tree); i++)    {        printf_data(GTree_Get(tree, i));        printf("\n");    }        printf("Get Root Data:\n");        printf_data(GTree_Root(tree));        printf("\n");        GTree_Delete(tree, 3);         printf("After Deleting D:\n");        GTree_Display(tree, printf_data, 2, '-');        GTree_Clear(tree);        printf("After Clearing Tree:\n");        GTree_Display(tree, printf_data, 2, '.');            GTree_Destroy(tree);    return 0;}

运行结果：

总结：

本篇中的树结构是一种通用的数据结构

利用链表组织树结点

        能够便利的存取结点

        链表的维护具有一定复杂性