数据结构封装之《LGraph邻接表式图》

说明：

1. 邻接表是图的另一种有效的存储表示方法. 每个顶点u建立一个单链表, 链表中每个结点代表一条边《u, v》,为边结点，每个单链表相当于邻接矩阵的一行；
2. 通过复用LinkList和LinkQueue的方法封装的LGraph，请看：
   数据结构封装之《LinkList单向链表》
   数据结构封装之《LinkQueue链式队列》

下面将给出该数据结构的代码，每个函数的结构分析 ，以及个别主要函数的汇编分析

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代码：

TGraph.h

#ifndef _LGRAPH_H_
#define _LGRAPH_H_

typedef void LGraph;
typedef void LVertex;
typedef void (LGraph_Printf)(LVertex*);

//创建并返回有n个顶点的图
LGraph* LGraph_Create(LVertex** v, int n);

//销毁graph
void LGraph_Destroy(LGraph* graph);

//将graph所值图的边集合清空
void LGraph_Clear(LGraph* graph);

//在graph所值的v1和v2之间加上边，且边的权为w
int LGraph_AddEdge(LGraph* graph, int v1, int v2, int w);

//将graph所指图中v1和v2之间的边删除，返回权值
int LGraph_RemoveEdge(LGraph* graph, int v1, int v2);

//将graph所值图中v1和v2之间的权值返回
int LGraph_GetEdge(LGraph* graph, int v1, int v2);

//将graph所指图中v顶点的度数返回
int LGraph_TD(LGraph* graph, int v);

//将graph所值图中的定点数返回
int LGraph_VertexCount(LGraph* graph);

//将graph所指图中的边数返回
int LGraph_EdgeCount(LGraph* graph);

//深度优先遍历
void LGraph_DFS(LGraph* graph, int v, LGraph_Printf* pFunc);

//广度优先遍历
void LGraph_BFS(LGraph* graph, int v, LGraph_Printf* pFunc);

void LGraph_Display(LGraph* graph, LGraph_Printf* pFunc);

#endif

TGraph.c

#include <malloc.h>
#include <stdio.h>
#include "LGraph.h"
#include "LinkList.h"
#include "LinkQueue.h"

typedef struct _tag_LGraph
{
    int count;
    LVertex** v;
    LinkList** la;
} TLGraph;

typedef struct _tag_ListNode
{
    LinkListNode header;
    int v;
    int w;
} TListNode;

//深度优先递归遍历
static void recursive_dfs(TLGraph* graph, int v, int visited[], LGraph_Printf* pFunc)
{
    int i = 0;

    pFunc(graph->v[v]);//打印当前元素数据

    visited[v] = 1;//已访问的元素下标，要做标志

    printf(", ");

    //当前元素的下级元素访问
    for(i=0; i<LinkList_Length(graph->la[v]); i++)
    {
        TListNode* node = (TListNode*)LinkList_Get(graph->la[v], i);

        //检查是否被访问过，若无则进入该元素的深度遍历
        if( !visited[node->v] )
        {
            recursive_dfs(graph, node->v, visited, pFunc);
        }
    }
}

//广度优先遍历
static void bfs(TLGraph* graph, int v, int visited[], LGraph_Printf* pFunc)
{
    LinkQueue* queue = LinkQueue_Create();

    if( queue != NULL )
    {
        LinkQueue_Append(queue, graph->v + v);//将当前元素入队

        visited[v] = 1;//已访问的元素下标，要做标志

        while( LinkQueue_Length(queue) > 0 )
        {
            int i = 0;

            v = (LVertex**)LinkQueue_Retrieve(queue) - graph->v;//当前元素出队

            pFunc(graph->v[v]);//打印当前访问的元素

            printf(", ");

            //检查当前元素是否有下级元素
            for(i=0; i<LinkList_Length(graph->la[v]); i++)
            {
                TListNode* node = (TListNode*)LinkList_Get(graph->la[v], i);//逐一获取其下级元素

                if( !visited[node->v] )//检查该下级元素是否被访问过
                {
                    LinkQueue_Append(queue, graph->v + node->v);//将该没被访问的元素入队

                    visited[node->v] = 1;//入队的元素，标记已访问
                }
            }
        }
    }

    LinkQueue_Destroy(queue);
}

LGraph* LGraph_Create(LVertex** v, int n)  // O(n)
{
    TLGraph* ret = NULL;
    int ok = 1;

    if( (v != NULL ) && (n > 0) )
    {
        ret = (TLGraph*)malloc(sizeof(TLGraph));

        if( ret != NULL )
        {
            ret->count = n;

            ret->v = (LVertex**)calloc(n, sizeof(LVertex*));

            ret->la = (LinkList**)calloc(n, sizeof(LinkList*));

            ok = (ret->v != NULL) && (ret->la != NULL);

            if( ok )
            {
                int i = 0;

                for(i=0; i<n; i++)
                {
                    ret->v[i] = v[i];
                }

                for(i=0; (i<n) && ok; i++)
                {
                    ok = ok && ((ret->la[i] = LinkList_Create()) != NULL);
                }
            }

            if( !ok )
            {
                if( ret->la != NULL )
                {
                    int i = 0;

                    for(i=0; i<n; i++)
                    {
                        LinkList_Destroy(ret->la[i]);
                    }
                }

                free(ret->la);
                free(ret->v);
                free(ret);

                ret = NULL;
            }
        }
    }

    return ret;
}

void LGraph_Destroy(LGraph* graph) // O(n*n)
{
    TLGraph* tGraph = (TLGraph*)graph;

    LGraph_Clear(tGraph);

    if( tGraph != NULL )
    {
        int i = 0;

        for(i=0; i<tGraph->count; i++)
        {
            LinkList_Destroy(tGraph->la[i]);
        }

        free(tGraph->la);
        free(tGraph->v);
        free(tGraph);
    }
}

void LGraph_Clear(LGraph* graph) // O(n*n)
{
    TLGraph* tGraph = (TLGraph*)graph;

    if( tGraph != NULL )
    {
        int i = 0;

        for(i=0; i<tGraph->count; i++)
        {
            while( LinkList_Length(tGraph->la[i]) > 0 )
            {
                free(LinkList_Delete(tGraph->la[i], 0));
            }
        }
    }
}

int LGraph_AddEdge(LGraph* graph, int v1, int v2, int w) // O(1)
{
    TLGraph* tGraph = (TLGraph*)graph;
    TListNode* node = NULL;
    int ret = (tGraph != NULL);

    ret = ret && (0 <= v1) && (v1 < tGraph->count);
    ret = ret && (0 <= v2) && (v2 < tGraph->count);
    ret = ret && (0 < w) && ((node = (TListNode*)malloc(sizeof(TListNode))) != NULL);

    if( ret )
    {
       node->v = v2;
       node->w = w;

       LinkList_Insert(tGraph->la[v1], (LinkListNode*)node, 0);
    }

    return ret;
}

int LGraph_RemoveEdge(LGraph* graph, int v1, int v2) // O(n*n)
{
    TLGraph* tGraph = (TLGraph*)graph;
    int condition = (tGraph != NULL);
    int ret = 0;

    condition = condition && (0 <= v1) && (v1 < tGraph->count);
    condition = condition && (0 <= v2) && (v2 < tGraph->count);

    if( condition )
    {
        TListNode* node = NULL;
        int i = 0;

        for(i=0; i<LinkList_Length(tGraph->la[v1]); i++)
        {
            node = (TListNode*)LinkList_Get(tGraph->la[v1], i);

            if( node->v == v2)
            {
                ret = node->w;

                LinkList_Delete(tGraph->la[v1], i);

                free(node);

                break;
            }
        }
    }

    return ret;
}

int LGraph_GetEdge(LGraph* graph, int v1, int v2) // O(n*n)
{
    TLGraph* tGraph = (TLGraph*)graph;
    int condition = (tGraph != NULL);
    int ret = 0;

    condition = condition && (0 <= v1) && (v1 < tGraph->count);
    condition = condition && (0 <= v2) && (v2 < tGraph->count);

    if( condition )
    {
        TListNode* node = NULL;
        int i = 0;

        for(i=0; i<LinkList_Length(tGraph->la[v1]); i++)
        {
            node = (TListNode*)LinkList_Get(tGraph->la[v1], i);

            if( node->v == v2)
            {
                ret = node->w;

                break;
            }
        }
    }

    return ret;
}

int LGraph_TD(LGraph* graph, int v) // O(n*n*n)
{
    TLGraph* tGraph = (TLGraph*)graph;
    int condition = (tGraph != NULL);
    int ret = 0;

    condition = condition && (0 <= v) && (v < tGraph->count);

    if( condition )
    {
        int i = 0;
        int j = 0;

        for(i=0; i<tGraph->count; i++)
        {
            for(j=0; j<LinkList_Length(tGraph->la[i]); j++)
            {
                TListNode* node = (TListNode*)LinkList_Get(tGraph->la[i], j);

                if( node->v == v )
                {
                    ret++;
                }
            }
        }

        ret += LinkList_Length(tGraph->la[v]);
    }

    return ret;
}

int LGraph_VertexCount(LGraph* graph) // O(1)
{
    TLGraph* tGraph = (TLGraph*)graph;
    int ret = 0;

    if( tGraph != NULL )
    {
        ret = tGraph->count;
    }

    return ret;
}

int LGraph_EdgeCount(LGraph* graph) // O(n)
{
    TLGraph* tGraph = (TLGraph*)graph;
    int ret = 0;

    if( tGraph != NULL )
    {
        int i = 0;

        for(i=0; i<tGraph->count; i++)
        {
            ret += LinkList_Length(tGraph->la[i]);
        }
    }

    return ret;
}

void LGraph_DFS(LGraph* graph, int v, LGraph_Printf* pFunc)
{
    TLGraph* tGraph = (TLGraph*)graph;
    int* visited = NULL;
    int condition = (tGraph != NULL);

    condition = condition && (0 <= v) && (v < tGraph->count);
    condition = condition && (pFunc != NULL);
    condition = condition && ((visited = (int*)calloc(tGraph->count, sizeof(int))) != NULL);

    if( condition )
    {
        int i = 0;

        //以深度优先方式，打印当前顶点的所有内容
        recursive_dfs(tGraph, v, visited, pFunc);

        //检查未访问的顶点
        for(i=0; i<tGraph->count; i++)
        {
            if( !visited[i] )
            {
                recursive_dfs(tGraph, i, visited, pFunc);
            }
        }

        printf("\n");
    }

    free(visited);
}

void LGraph_BFS(LGraph* graph, int v, LGraph_Printf* pFunc)
{
    TLGraph* tGraph = (TLGraph*)graph;
    int* visited = NULL;
    int condition = (tGraph != NULL);

    condition = condition && (0 <= v) && (v < tGraph->count);
    condition = condition && (pFunc != NULL);
    condition = condition && ((visited = (int*)calloc(tGraph->count, sizeof(int))) != NULL);

    if( condition )
    {
        int i = 0;

        //以广度优先方式，打印当前顶点的所有内容
        bfs(tGraph, v, visited, pFunc);

        //检查未访问的顶点
        for(i=0; i<tGraph->count; i++)
        {
            if( !visited[i] )
            {
                bfs(tGraph, i, visited, pFunc);
            }
        }

        printf("\n");
    }

    free(visited);
}

void LGraph_Display(LGraph* graph, LGraph_Printf* pFunc) // O(n*n*n)
{
    TLGraph* tGraph = (TLGraph*)graph;

    if( (tGraph != NULL) && (pFunc != NULL) )
    {
        int i = 0;
        int j = 0;

        for(i=0; i<tGraph->count; i++)
        {
            printf("%d:", i);
            pFunc(tGraph->v[i]);
            printf(" ");
        }

        printf("\n");

        for(i=0; i<tGraph->count; i++)
        {
            for(j=0; j<LinkList_Length(tGraph->la[i]); j++)
            {
                TListNode* node = (TListNode*)LinkList_Get(tGraph->la[i], j);

                printf("<");
                pFunc(tGraph->v[i]);
                printf(", ");
                pFunc(tGraph->v[node->v]);
                printf(", %d", node->w);
                printf(">");
                printf(" ");               
            }
        }

        printf("\n");
    }
}

main.c

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


void print_data(LVertex* v)
{
    printf("%s", (char*)v);
}

int main(int argc, char *argv[])
{
    LVertex* v[] = {"A", "B", "C", "D", "E", "F"};
    LGraph* graph = LGraph_Create(v, 6);

    LGraph_AddEdge(graph, 0, 1, 1);
    LGraph_AddEdge(graph, 0, 2, 1);
    LGraph_AddEdge(graph, 0, 3, 1);
    LGraph_AddEdge(graph, 1, 5, 1);
    LGraph_AddEdge(graph, 1, 4, 1);
    LGraph_AddEdge(graph, 2, 1, 1);
    LGraph_AddEdge(graph, 3, 4, 1);
    LGraph_AddEdge(graph, 4, 2, 1);

    LGraph_Display(graph, print_data);

    LGraph_RemoveEdge(graph, 0, 1, 1);
    int edgeW = LGraph_GetEdge(graph,0,2);
    int td = LGraph_TD(graph,0);
    int vc = LGraph_VertexCount(graph);
    int ec = LGraph_EdgeCount(graph);


    LGraph_DFS(graph, 0, print_data);
    LGraph_BFS(graph, 0, print_data);

    LGraph_Destroy(graph);

    return 0;
}

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函数结构分析：

1.tGraph_Create

2.LGraph_Destroy

3.LGraph_Clear

4.LGraph_AddEdge

5.LGraph_RemoveEdge

6.LGraph_GetEdge

7.LGraph_TD

8.LGraph_VertexCount

9.LGraph_EdgeCount

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汇编分析：

main

1.tGraph_Create

2.LGraph_Destroy

3.LGraph_Clear

4.LGraph_AddEdge

5.LGraph_RemoveEdge

6.LGraph_GetEdge

7.LGraph_TD

8.LGraph_VertexCount

9.LGraph_EdgeCount