基于深度优先算法的有向图环路检测

１、digraph.h 

#ifndef _DIGRAPH_H_H#define _DIGRAPH_H_H#define ENABLE_DIGRAPH_TEST 0#define CHECK_NULL_AND_RET(x) { if((x) == NULL) return -1; }typedef struct _ADJ_ENTRY{    int                 adjoinPoint;    struct _ADJ_ENTRY*  pNext;} ADJ_ENTRY;typedef struct{    struct _ADJ_ENTRY*  entryHead;} ADJ_HEAD;typedef struct{    int         V;             //顶点数    int         E;             //边数    ADJ_HEAD*   adjTable;      //邻接表} DIGRAPH;int  digraphCreate(DIGRAPH *pDigraph, int V);int  reverseDigraphCreate(DIGRAPH* pSrcDigraph, DIGRAPH* pDstDigraph);int  digraphDestroy(DIGRAPH *pDigraph);int  V(DIGRAPH *pDigraph);int  E(DIGRAPH *pDigraph);int  addEdge(DIGRAPH *pDigraph, int x, int y);void showDigraph(DIGRAPH *pDigraph);#endif

２、digraph.c

#include <stdio.h>#include <stdlib.h>#include "digraph.h"//有向图的数据结构//当前图对象使用邻接表表示，大部分情况下，图中的所有顶点并非//都是关联的，这种叫作稀疏图，使用邻接表来做为稀疏图的数据结//构，可以节省很大的内存空间。如果以前了解过操作系统原理中内//存机制的一级页表、二级页表机制，就会很快明白，为什么使用邻//接表来表示稀疏图可以节省大部内存空间了。//创建图对象，其中Ｖ表示最大顶点个数int digraphCreate(DIGRAPH *pDigraph, int V){    if ( pDigraph == NULL )    {        return -1;     }    pDigraph->V = V;    pDigraph->E = 0;    pDigraph->adjTable = (ADJ_HEAD *)malloc(sizeof(ADJ_HEAD) * V);    CHECK_NULL_AND_RET(pDigraph->adjTable);    return 0;}//创建反向图int reverseDigraphCreate(DIGRAPH* pSrcDigraph, DIGRAPH* pDstDigraph){    int i = 0;    if ( pSrcDigraph == NULL || pDstDigraph == NULL )    {        return -1;     }    if ( digraphCreate(pDstDigraph, V(pSrcDigraph)) < 0 )    {        return -1;     }    for ( i = 0; i < V(pSrcDigraph); i++ )    {        ADJ_ENTRY* pCurAdjEntry = (pSrcDigraph->adjTable + i)->entryHead;        while ( pCurAdjEntry != NULL )        {            addEdge(pDstDigraph, pCurAdjEntry->adjoinPoint, i);            pCurAdjEntry = pCurAdjEntry->pNext;        }    }    return 0;}//销毁图对象int digraphDestroy(DIGRAPH *pDigraph){    int i = 0;    if ( pDigraph == NULL )    {        return -1;     }    for ( i = 0; i < V(pDigraph); i++ )    {        ADJ_ENTRY *pCurAdjEntry = (pDigraph->adjTable + i)->entryHead;        while ( pCurAdjEntry != NULL )        {            ADJ_ENTRY *pFreeAdjEntry = pCurAdjEntry;            pCurAdjEntry = pCurAdjEntry->pNext;            free(pFreeAdjEntry);        }    }    free(pDigraph->adjTable);    pDigraph->V = 0;    pDigraph->E = 0;    pDigraph->adjTable = NULL;    return 0;}//获取图对象的顶点个数int V(DIGRAPH *pDigraph){    if ( pDigraph == NULL )    {        return -1;     }    return pDigraph->V;}//获取图对象的边数int E(DIGRAPH *pDigraph){    if ( pDigraph == NULL )    {        return -1;     }    return pDigraph->E;}//邻接表添加条目static int adjAdd(DIGRAPH *pDigraph, int x, int y){    ADJ_HEAD  *pAdjHead = NULL;    ADJ_ENTRY *pNewAdjEntry = NULL;    if ( pDigraph == NULL )    {        return -1;     }    if ( x >= pDigraph->V || x < 0 || y >= pDigraph->V || y < 0 )    {        return -1;     }    pNewAdjEntry = (ADJ_ENTRY *)malloc(sizeof(ADJ_ENTRY));    CHECK_NULL_AND_RET(pNewAdjEntry);    memset(pNewAdjEntry, 0, sizeof(ADJ_ENTRY));    pNewAdjEntry->adjoinPoint = y;    pAdjHead = (pDigraph->adjTable + x);    pNewAdjEntry->pNext = pAdjHead->entryHead;    pAdjHead->entryHead = pNewAdjEntry;    return 0;}//向图对象中增加路径int addEdge(DIGRAPH *pDigraph, int x, int y){    if ( adjAdd(pDigraph, x, y) < 0 )    {        return -1;     }    pDigraph->E++;    return 0;}//显示图对象的信息void showDigraph(DIGRAPH *pDigraph){    int i = 0;    if ( pDigraph == NULL )    {        return;     }    printf("point count: %d\r\n", V(pDigraph));    printf("edge  count: %d\r\n", E(pDigraph));    printf("------------------\r\n");    for ( i = 0; i < V(pDigraph); i++ )    {        ADJ_ENTRY* pCurEntry = (pDigraph->adjTable + i)->entryHead;        while ( pCurEntry != NULL )         {            printf("%d --> %d\r\n", i, pCurEntry->adjoinPoint);             pCurEntry = pCurEntry->pNext;        }    }    printf("------------------\r\n");}#if ENABLE_DIGRAPH_TESTint main(){    DIGRAPH digraphObj = {0};    DIGRAPH reverseDigraphObj = {0};    digraphCreate(&digraphObj, 10);    addEdge(&digraphObj, 0, 1);    addEdge(&digraphObj, 0, 2);    addEdge(&digraphObj, 0, 3);    addEdge(&digraphObj, 0, 4);    showDigraph(&digraphObj);    reverseDigraphCreate(&digraphObj, &reverseDigraphObj);    showDigraph(&reverseDigraphObj);    digraphDestroy(&digraphObj);    digraphDestroy(&reverseDigraphObj);    return 0;}#endif

３、digraphCycle.c

#include "stdio.h"#include "digraph.h"#define CHECK_NULL_RET(x) { if ( (x) == NULL ) return -1; }enum{    FALSE,    TRUE} E_BOOL;int* gMarked = NULL;int* gOnStack = NULL;int  gIsCycle = FALSE;//基于深度优先算法实现的有向图环路检测void dfs(DIGRAPH* pDigraph, int s){    ADJ_ENTRY* pCurAdjEntry = NULL;    if ( s < 0 || s >= V(pDigraph) )    {        printf("invalid s %d\r\n", s);        return;     }    gMarked[s] = TRUE;    gOnStack[s] = TRUE;    pCurAdjEntry = (pDigraph->adjTable + s)->entryHead;    while ( pCurAdjEntry != NULL )    {        if ( !gMarked[pCurAdjEntry->adjoinPoint] )         {            dfs(pDigraph, pCurAdjEntry->adjoinPoint);         }        else if ( gOnStack[pCurAdjEntry->adjoinPoint] )        {            gIsCycle = TRUE;            return;        }        pCurAdjEntry = pCurAdjEntry->pNext;     }    //注意这里gOnStack与gMarked的区别，gMarked是深度优先算法所使用的    //标记，记录当前该点是否走过，如果走过就选择其它点进行尝试。    //而gOnStack表示从源点到当前点的路径，如果在遇到每条路不通的情况下，    //需要退回到上个点，这时候gOnStack中就要撤销标记，如下示例，当走到    //3的时候，此时gOnStack和gMarked一样，0～3的数组索引都标为TRUE，    //但这时候已经没有路，需要退回到2，此时gOnStack[3]则为FALSE，这时候    //发现２也没有其它可走的路，则退回到1，此时gOnStack[2]则为FALSE，    //当从1走到4的时候，gOnStack只有索引0、１、４为TRUE，而gMarked则    //索引0~4都为TRUE。    //    //示例：    //0 --> 1 --> 2 --> 3    //      |    //      |---> 4 --> 5     gOnStack[s] = FALSE;}int main(){    int size = 0;    DIGRAPH digraphObj = {0};    //创建有向图对象    digraphCreate(&digraphObj, 5);    #if 0    addEdge(&digraphObj, 0, 1);    addEdge(&digraphObj, 0, 2);    addEdge(&digraphObj, 1, 3);    addEdge(&digraphObj, 2, 3);    addEdge(&digraphObj, 3, 4);    #else    addEdge(&digraphObj, 0, 1);    addEdge(&digraphObj, 0, 2);    addEdge(&digraphObj, 1, 3);    addEdge(&digraphObj, 2, 3);    addEdge(&digraphObj, 3, 0);    #endif    showDigraph(&digraphObj);    //资源分配    size = sizeof(int) * V(&digraphObj);    gMarked = (int *)malloc(size);    CHECK_NULL_RET(gMarked);    memset(gMarked, 0, size);    gOnStack = (int *)malloc(size);    CHECK_NULL_RET(gOnStack);    memset(gOnStack, 0, size);    //基于深度优先算法实现的有向图环路检测    dfs(&digraphObj, 0);    printf("Cycle: %s\r\n", gIsCycle ? "TRUE" : "FALSE" );    //资源销毁    free(gMarked);    free(gOnStack);    digraphDestroy(&digraphObj);    return 0;}