6.3图的遍历
2.试设计一个算法，判断一个无向图G是否为一棵树。若是一棵树，则算法返回true，否则返回false。

#include <cstdio>
#include <cstring>

#define MaxVertexNum 100

typedef char VertexType;
typedef int EdgeType;
typedef struct {
    VertexType Vex[MaxVertexNum][MaxVertexNum];
    EdgeType Edge[MaxVertexNum][MaxVertexNum];
    int vexnum, arcnum;
} MGraph;

bool visited[MaxVertexNum];

int getIndex(MGraph &G, char *s)
{
    for (int i = 0; i < G.vexnum; i++) {
        if (strcmp(s, G.Vex[i]) == 0)
            return i;
    }
    return -1;
}

void CreateGraph(MGraph &G)
{
    scanf("%d%d", &G.vexnum, &G.arcnum);
    for (int i = 0; i < G.vexnum; i++)
        scanf("%s", G.Vex[i]);
    for (int i = 0; i < G.vexnum; i++)
        for (int j = 0; j < G.vexnum; j++)
            G.Edge[i][j] = 0;
    char a[5], b[5];
    int k = 0, u, v;
    while (k < G.arcnum) {
        scanf("%s%s", a, b);
        u = getIndex(G, a);
        v = getIndex(G, b);
        G.Edge[u][v] = 1;
        G.Edge[v][u] = 1;
        k++;
    }
}

void PrintGraph(MGraph G)
{
    for (int i = 0; i < G.vexnum; i++) {
        for (int j = -1; j < G.vexnum; j++) {
            printf("%4d", G.Edge[i][j]);
        }
        printf("\n");
    }
}

void visit(int n)
{
    printf("%d ", n);
}

int FirstNeighbor(MGraph G, int v)
{
    for (int i = 0; i < G.vexnum; i++)
        if (G.Edge[v][i] == 1) return i;
    return -1;
}

int NextNeighbor(MGraph G, int v, int w)
{
    for (int i = w + 1; i < G.vexnum; i++)
        if (G.Edge[v][i] == 1) return i;
    return -1;
}

void DFS(MGraph &G, int v, int &Vnum, int &Enum, bool *visited)
{
    visited[v] = true;
    Vnum++;
    int w = FirstNeighbor(G, v);
    while (w != -1) {
        Enum++;
        if (!visited[w])
            DFS(G, w, Vnum, Enum, visited);
        w = NextNeighbor(G, v, w);
    }
}

bool isTree(MGraph &G)
{
    for (int i = 1; i < G.vexnum; i++) visited[i] = false;
    int Vnum = 0, Enum = 0;
    DFS(G, 1, Vnum, Enum, visited);
    if (Vnum == G.vexnum && Enum == 2 * (G.vexnum - 1)) return true;
    else return false;
}

int main()
{
    MGraph G;
    CreateGraph(G);
    PrintGraph(G);
    if (isTree(G)) printf("yes\n");
    else printf("no\n");
    return 0;
}

/*
8 7
v1 v2 v3 v4 v5 v6 v7 v8
v1 v2
v1 v3
v2 v4
v2 v5
v3 v6
v3 v7
v5 v8
*/