数据结构实验6-图算法 最小生成树 BFS与DFS

实验要求

编写一个程序，实现图的相关运算，并在此基础上设计一个主程序，完成如下功能：

1. 建立如教材图7.所示的有向图G的邻接矩阵，并分别输出顶点表和邻接矩阵。
2. 在图G的邻接矩阵存储表示基础上，实现深度优先遍历算法，输出从顶点V1开始的深度优先遍历序列。
3. 实现广度优先遍历算法，输出从顶点V1开始的广度优先遍历序列。
4. 建立如教材图7.16(a)所示的无向带权图G的邻接矩阵，实现普里姆算法，输出从顶点V1出发的最小生成树（按照求解出的边的顺序）

程序代码

#include 
#include 
#include 
#include 
using namespace std;
#define TRUE 1
#define FALSE 0
#define OK 1
#define ERROR 0
#define INFEASIBLE -1
#define OVERFLOW -2
#define MAXSIZE 100
#define INFINITY INT_MAX
#define MAX_VERTEX_NUM 20
#define VRtype int
#define Status int
#define VertexType int
typedef enum{DG,DN,UDG,UDN} GraphKind;
typedef struct ArcCell {
    VRtype adj;
}ArcCell, AdjMatrix[MAX_VERTEX_NUM][MAX_VERTEX_NUM];
typedef struct {
    VertexType vex[MAX_VERTEX_NUM];
    AdjMatrix arcs;
    int vexnum, arcnum;
    int kind;
}MGraph;
bool visited[MAX_VERTEX_NUM + 5];
Status CreatUDN(MGraph &G)
{
    printf("请输入图的顶点个数和边的个数\n");
    scanf("%d %d",&G.vexnum,&G.arcnum);
    printf("%d %d\n",G.vexnum,G.arcnum);
    for(int i = 1; i<=G.vexnum;++i) G.vex[i] = i;
    for(int i = 1; i<=G.vexnum;++i){
        for(int j = 1; j<=G.vexnum;++j){
            G.arcs[i][j] = {INFINITY};
        }
    }
    printf("请输入%d条边的信息，格式为起点，终点，权值\n",G.arcnum);
    for(int i = 0; iint v1,v2,w;
        scanf("%d %d %d",&v1,&v2,&w);
        G.arcs[v1][v2].adj = w;
        G.arcs[v2][v1] = G.arcs[v1][v2];
    }
    return OK;
}
Status CreatGraph( MGraph &G)
{
    printf("请输入图的种类 3代表无向网\n");
    scanf("%d",&G.kind);
    printf("%d\n",G.kind);
    switch(G.kind){
        //case DG: return CreateDG(G);
        //case DN: return CreateDN(G);
       // case UGD: return CreatUDG(G);
        case UDN: return CreatUDN(G);
        default : return ERROR;
    }
}
void DFS(MGraph G, int v)
{
    visited[v] = TRUE;
    printf("%d ",v);
    for(int i = 1; i <= G.vexnum;++i){
        if(G.arcs[v][i].adj != INFINITY && !visited[i])
            DFS(G,i);
    }
}
void DFSTraverse(MGraph G)
{
    for(int i = 1; i<=G.vexnum;++i) visited[i] = false;
    for(int i = 1; i<=G.vexnum;++i)
        if(!visited[i]) DFS(G,i);
    printf("\n");
}
void BFSTraverse(MGraph G)
{
    for(int i = 1; i<=G.vexnum;++i) visited[i] =FALSE;
    int Queue[1000],fro = 0,rear = 0;
    for(int i = 1; i<=G.vexnum ;++i){
        if(!visited[i]){
            visited[i] = TRUE;
            printf("%d ",i);
        }
        Queue[rear++] = i;
        while(fro != rear){
            int temp = Queue[fro++];
            for(int k = 1;k<=G.vexnum;++k){
                if(G.arcs[temp][k].adj != INFINITY && !visited[k]){
                    visited[k] = TRUE;
                    // shuchu
                    printf("%d ",k);
                    Queue[rear++] = k;
                }
            }
        }
    }
    printf("\n");
}
void MiniSpanTree_PRIM(MGraph G, VertexType u)
{
    printf("最小生成树的边生成顺序为：\n");
    struct {
        VertexType adjvex;
        VRtype lowcost;
    }closedge[MAX_VERTEX_NUM];
    int k = u;
    for( int j = 1; j<=G.vexnum; ++j){
        if(j != k){
            closedge[j].adjvex = k;
            closedge[j].lowcost = G.arcs[k][j].adj;
            //printf("%d %d %d\n",closedge[j].adjvex,j,closedge[j].lowcost);
        }
    }
    closedge[k].lowcost = 0;
    for(int i = 2; i<=G.vexnum;++i){
        //findmin
        int id = 0,cost = INFINITY;
        for(int l = 1; l<=G.vexnum;++l){
                //printf("%d %d %d \n",l,closedge[l].lowcost,cost);
            if(closedge[l].lowcost!= 0 &&closedge[l].lowcost < cost ){
                id = l;
                cost = closedge[l].lowcost;
            }
        }
        //printf("id %d\n",id);
        k = id;
        printf("%d %d\n",closedge[k].adjvex, k);
        closedge[k].lowcost = 0;
        for(int j = 1; j<=G.vexnum ;++j){
            if(G.arcs[k][j].adj < closedge[j].lowcost && closedge[j].lowcost != 0  ){
                closedge[j].adjvex = G.vex[k];
                closedge[j].lowcost = G.arcs[k][j].adj;
            }
        }
    }
}
void output(MGraph G)
{
    printf("顶点表为\n");
    for(int i =1; i<=G.vexnum;++i){
        printf("%d %d\n",i,G.vexnum);
    }
    printf("邻接矩阵为\n");
    for(int i = 1; i<=G.vexnum;++i){
        for(int j = 1; j<=G.vexnum;++j){
            if(G.arcs[i][j].adj != INFINITY){
                printf("%d ",G.arcs[i][j].adj);
            }else{
                printf("# ");
            }
        }
        printf("\n");
    }
}
int main()
{
    freopen("in.txt","r",stdin);
    MGraph G;
    CreatGraph(G);
    output(G);
    DFSTraverse(G);
    BFSTraverse(G);
    MiniSpanTree_PRIM(G,1);
    return 0;
}

运行结果

数据

3
6 10
1 2 6
1 4 5
1 3 1
2 3 5
3 4 5
2 5 3
5 3 6
6 4 2
3 6 4 
5 6 6