图(Graph)的常用代码集合

图的相关概念请查阅离散数学图这一章或者数据结构中对图的介绍。代码来自课本。

/*Graph存储结构*/
//邻接矩阵表示法
#define MAX_VERTEX_NUM 20    /*最多顶点个数*/
#define INFINITY 32768       /*表示极大值，即∞*/

/*图的种类：DG表示有向图，DN表示有向网，DUG表示无向图，UDN表示无向网*/
typedef enum {DG, DN, UDG, UDN} GraphKind;  /*枚举类型*/
typedef char VertexData     /*假设顶点数据为字符型*/
typedef struct ArcNode {
    AdjType adj;            /*对于无权图，用1或0表示是否相邻；对带权图，则为权值类型*/
    OtherInfo info;
} ArcNode;
typedef struct {
    VertexData vertex[MAX_VERTEX_NUM];    /*顶点向量*/
    ArcNode arcs[MAX_VERTEX_NUM][MAX_VERTEX_NUM];    /*邻接矩阵*/
    int vexnum,arcnum;
    GraphKind kind;
} AdjMartrix;     /*(AdjMartrix Matrix Graph)*/
/*采用邻接矩阵表示法创建有向图*/
int LocateVertex(AdjMartrix *G, VertexData v) {     /*定位顶点位置函数*/
    int j = ERROR, k;
    for(k = 0; k < G->vexnum; k++) {
        if(G->vertex[k] == v) {
            j = k; break;
        }
    }
    return j;
}

int CreateDN(AdjMartrix *G) {
    int i,j,k,weight; VertexData v1,v2;
    scanf("%d,%d", &G->arcnum; &G->vexnum);     /*输入图的顶点数和弧数*/
    for(i = 0; i < G->vexnum; i++) {            /*初始化邻接矩阵*/
        for(j = 0; j < G->vexnum; j++) {
            G->arcs[i][j].adj = INFINITY;
        }
    }
    for(i = 0; i < G->vertex; i++) {      /*输入图的顶点*/
        scanf("%c", &G->vertex)[i];
    }
    for(k = 0; k < G->arcnum; k++) {      /*输入一条弧的两个顶点和权值*/
        scanf("%c,%c,%d", &v1,&v2,&weight);
        i = LocateVertex_M(G, v1);
        j = LocateVertex_M(G, v2);
        G->arcs[i][j].adj = weight;      /*建立弧*/
    }
    return OK;
}
//邻接表表示法
#define MAX_VERTEX_NUM 20
typedef enum {DG, DN, UDG, UDN} GraphKind;
typedef struct ArcNode {
    int adjvex;                   /*该弧指向顶点的位置*/
    struct ArcNode *nextarc;      /*指向下一条弧的指针*/
    OtherInfo;
} ArcNode;
typedef struct VerNode {
    VertexData data;
    ArcNode *firstarc;
} VerNode;
typedef struct {
    VertexNode vertex[MAX_VERTEX_NUM];
    int vexnum,arcnum;
    GraphKind kind;
} AdjList;     /*Adjacency List Graph*/
//十字链表
#define MAX_VERTEX_NUM 20
typedef enum {DG, NG, UDG, UDN} GraphKind;
typedef struct ArcNode {
    int tailvex,headvex;
    struct ArcNode *hlink, *tlink;
} ArcNode;
typedef struct VertexNode {
    VertexData data;
    ArcNode *firstin, *firstout;
} VertexNode;
typedef struct {
    VertexNode vertex[MAX_VERTEX_NUM];
    int vexnum,arcnum;     //图的顶点数和弧数
    GraphKind kind;
} OrthList;
/*创建图的十字链表*/
void CrtOrthList(OrthList *g) {
/*从终端输入n个顶点的信息和e条弧的信息，以建立一个有向图的十字链表*/
    scanf("%d,%d", &n,&e);    /*从键盘输入图的顶点个数和弧的个数*/
    g->vertex = n;
    g->vertex = e;
    for(i = 0; i < n; i++) {     /*初始化顶点结点*/
        scanf("%c", &(g->vertex[i].data));
        g->vertex[i].firstin = NULL;
        g->vertex[i].firstout = NULL;
    }
    for(k = 0; k < e; k++) {     /*创建弧结点,建立弧结点个顶点的连接*/
        scanf("%c,%c", &vt,&vh);
        i = LocateVertex(g, vt);
        j = LocateVertex(g, vh);
        p = (ArcNode *)malloc(sizeof(ArcNode));
        p->tailvex = i; p->headvex = j;
        p->tlink = g->vertex[i].firstout;
        g->vertex[i].firstout = p;
        p->hlink = g->vertex[j];
        g->vertex[j].firstin = p;
    }
}    /*CrtOrthList*/
/*邻接多重表*/
#define MAX_VERTEX_NUM 20
typedef struct EdgeNode {
    int mark,ivex,jvex;
    struct EdgeNode *ilink, *jlink;
} EdgeNode;
typedef struct {
    VertexData data;
    EdgeNode *firstedge;
} VertexNode;
typedef struct {
    VertexNode vertexp[MAX_VERTEX_NUM];
    int vernum,arcnum;
    GraphKind kind;
} AdjMultiList;

/*图的深度遍历算法*/
#define True  1
#define False 0
#define Error -1
#define OK    1
int visited[MAX_VERTEX_NUM];     /*初始化标准数组*/

void TraverseGraph(Graph g) {
/*在图g中寻找未访问的顶点作为起始点，并调用深度优先搜索过程进行遍历。Graph表示图的
一种存储结构，如邻接矩阵或者邻接表等*/
    for(vi = 0; vi < g.vexnum; vi++) Visited[vi] = False;    /*访问标志数组*/
    for(vi = 0; vi < g.vexnum; vi++) {    //循环调用深度优先遍历连通子图，若g是连通图，则此
        if(!visted[vi]) DepthFirstSearch(g,vi);    //仅调用一次
    }                                     
} /*TraverseGraph*/
/*深度优先遍历v0所在的连通子图*/
void DepthFirstSearch(Graph g, int v0) {
    visit(v0); visit[v0] = True;     /*访问顶点v0，修改访问变量*/

    w = FirstAdjVertex(g, v0);
    while(w != -1) {
        if(!visited[w]) DepthFirstSearch(g, w);    /*递归调用DepthFirstSearch*/
        w = NextAdjVertex(g, v0, w);     /*找下一个邻接点*/ 
    }
}     /*DepthFirstSearch*/
/*采用邻接矩阵的DepthFirstSearch*/
void DepthFirstSearch(AdjMartrix g, int v0) {
    visit(v0); visited[vo] = True;
    for(vj = 0; vj < g.vexnum; vj++) {
        if(!visited[vj] && g.arcs[v0][vj].adj  == 1) {    //未访问过且路径存在
            DepthFirstSearch(g, vj);
        }
    }
}     /*DepthFirstSearch*/
/*采用邻接表的DepthFiirstSearch*/
void DepthFirstSearch(AdjList g, int v0) {
    visit(v0); visited[v0] = True;
    p = g.vertex[v0].firstarc;
    while(p != NULL) {
        if(!visited[p->adjvex]) DepthFirstSearch(g, p->adjvex);
        p = p->nextarc;
    }
}     /*DepthFirstSearch*/
/*非递归形式的DepthFirstSearch*/
void DepthFirstSearch(Graph g, int v0) {
/*从v0出发深度优化搜索图g*/
    InitStack(&s);
    Push(&S, v0);
    while(!is Empty(S)) {
        Pop(&S, &v);
        if(!visited[v]) {
            visit(v);
            visited[v] = True;
            w = FirstAdjVertex(g, v);
            while(w != -1) {
                if(!visted[w]) {
                    Push(&S, w);
                }
                w = NextAdjVertex(g, v, w);     /*求v相对于w的下一个邻接点*/
            }
        }
    }
}
/*广度优先搜索图g中v0所在的连通子图*/
void BreadthFirstSearch(Graph g, int v0) {
    visit(v0); visited[v0] = True;
    InitQueue(&Q);
    EnterQueue(&Q, v0);
    while(Empty(&Q, v0)) {
        DeleteQueue(&Q, &v);
        w = FirstAdjVertex(g, v);
        while(w != -1) {
            if(!visited[w]) {
                visit(w); visited[w] = True;
                EnterQueue(&Q, w);
            }
            w = NextAdjVertex(g, v, w);
        }
    }
}
/*图的应用*/
/*深度优先找出从顶点u到v的简单路径*/
int *pre;
void one_path(Graph *G, int u, int v) {
    int i;
    pre = (int *)malloc(G->vexnum * sizeof(int));
    for(i = 0; i < G->vexnum; i++) {     /*初始化，置-1*/
        pre[i] = -1;
    }
    pre[u] = -2;           /*将pre[u]置-2，表示已访问过，且没有前驱*/
    DFS_path(G, u, v);     /*用深度优先算法找出一条从u到v的简单路径*/
    free(pre);
}
int DFS_path(Graph *G, int u, int v) {
    int j;
    for(j = firstadj(G, u)); j >= 0; j = nextadj(G, u, j)) {
        if(pre[j] == -1) {     //不等于-1则参数有误
            pre[j] = u;
            if(j == v) {
                print_path(pre, v);   //从v0开始，沿着pre[]中保留的前驱指针输出路径(直到-2)
            }
            else if(DFS_path(G, j, v)); return 1;
        }
    }
    return 0;
}
/*求图的最小生成树*/
/*prim算法(加点法)*/
struct {
    int adjvex;
    int lowcost;
} closedge[MAX_VERTEX_NUM];    /*求最小生成树时的辅助数组*/

MiniSpanTree_Prim(AdjMartrix gn, int u) {
/*从顶点u出发，按prim算法构造连通网gn的最小生成树，并输出生成时的每条边*/
    closedge[u].lowcost = 0;     /*初始化*， U = {u}*/
    for(i = 0; i < gn.vexnum; i++) {
        if(i != u) {             /*对V-U的顶点i，初始化closedge[i]*/
            closedge[i].adjvex = u;
            closedge[i].lowcost = gn.arcs[u][i].adj;    
        }
    }
    for(e = 1; e < gn.vexnum - 1; e++) {    /*找n-1条边*/
        v = Mimium(closedge);     /*closedge中存有当前最小边(u，v)的信息*/
        printf(u, v);     /*输出生成树的当前最小边(u，v)*/
        closedge[v].lowcost = 0;     /*将顶点v纳入U集合*/
        for(i = 0; i < gn.vexnum; i++) {     /*顶点v纳入U集合后,更新closedge[i]*/
            if(gn.arcs[v][i].adj < closedge[i].lowcost) {
                closedge[i].lowcost = gn.arcs[v][i].adj;
                closedge[i].adj = v;
            }
        }
    }

}