图的一系类操作，邻接表创建图，邻接矩阵创建图，连通图，非连通图，深度优先，广度优先，

采用邻接矩阵表示法创建无向网

//采用邻接矩阵表示法创建无向网
#include 
using namespace std;

#define MaInt 32767
#define MVNum 100
#define OK 1

typedef char VerTextType;
typedef int ArcType;

typedef struct {
    VerTextType Vexs[MVNum];
    ArcType arcs[MVNum][MVNum];
    int vexnum, arcnum;
}AMGrach;

int LocateVex(AMGrach G, VerTextType v) {
    for (int i = 0;i < G.vexnum;i++) {
        if (G.Vexs[i] == v)
            return i;
    }
    return -1;
}

int CreateUDN(AMGrach& G) {
    int i, j, k;
    cout << "请输入总顶点数，总边数，以空格隔开：";
    cin >> G.vexnum >> G.arcnum;
    cout << endl;

    cout << "输入点的名称，如a" << endl;
        for (i = 0;i < G.vexnum;i++) {
            cout << "input the " << i << " name";
            cin >> G.Vexs[i];
        }
    cout << endl;

    for (i = 0;i < G.vexnum;i++)
        for (j = 0;j < G.vexnum;++j)
            G.arcs[i][j] = MaInt;
    cout << "输入边依附的顶点及权值，如 a b 5" << endl;

    for (k = 0;k < G.arcnum;++k) {
        VerTextType v1, v2;
        ArcType w;
        cout << "input the" << (k + 1) << " side of weigth";
        cin >> v1 >> v2 >> w;
        i = LocateVex(G, v1);
        j = LocateVex(G, v2);
        G.arcs[i][j] = w;
        G.arcs[j][i] = G.arcs[i][j];
    }
    return 0;
}

int main() {
    cout << "采用邻接矩阵表示法创建无向网";
    AMGrach G;
    int i, j;
    CreateUDN(G);
    cout << endl;
    for (i = 0;i < G.vexnum;i++) {
        for (j = 0;j < G.vexnum;++j) {

            if (j != G.vexnum - 1) {

                if (G.arcs[i][j] != MaInt) {
                    cout << G.arcs[i][j] << "\t";
                }
                else {
                    cout << "~" << "\t";
                }

            }
            else {

                if (G.arcs[i][j] != MaInt)
                    cout << G.arcs[i][j] << endl;
                else
                    cout << "~" << endl;
            }

        }
    }
    cout << endl;
    return 0;
}

采用邻接表表示法创建无向图

//采用邻接表表示法创建无向图
#include 
using namespace std;

#define MVNnm 100
#define OK 1

typedef char VerTexType;
typedef int OtherInfo;

typedef struct ArcNode {
    int adjvex;
    struct ArcNode* nextarc;
    OtherInfo info;
}ArcNode;

typedef struct VNode {
    VerTexType data;
    ArcNode* firstarc;
}VNode, adjList[MVNnm];

typedef struct {
    adjList vertices;
    int vexnum, arcnum;
}ALGraph;


int LocateVex(ALGraph G, VerTexType v) {
    for (int i = 0;i < G.vexnum;++i) {
        if (G.vertices[i].data == v) {
            return i;
        }
    }
    return -1;
}

int CreatUDG(ALGraph& G) {
    int i, k;
    cout << "请输入总顶点数，总边数中间以空格隔开:";
    cin >> G.vexnum >> G.arcnum;
    cout << endl;

    for (i = 0;i < G.vexnum;++i) {
        cout << "请输入第" << (i + 1) << "个点的名称:";
        cin >> G.vertices[i].data;
        G.vertices[i].firstarc = NULL;
    }
    cout << endl;

    cout << "请输入一条边依附的顶点,如 a b" << endl;
    for (k = 0;k < G.arcnum;++k) {
        VerTexType v1, v2;
        int i, j;
        cout << "请输入第" << (k + 1) << "条边依附的顶点:";
        cin >> v1 >> v2;
        i = LocateVex(G, v1);
        j = LocateVex(G, v2);

        ArcNode* p1 = new ArcNode;
        p1->adjvex = j;
        p1->nextarc = G.vertices[i].firstarc;
        G.vertices[i].firstarc = p1;

        ArcNode* p2 = new ArcNode;
        p2->adjvex = j;
        p2->nextarc = G.vertices[j].firstarc;
        G.vertices[j].firstarc = p2;
    }
    return OK;
}

int main() {
    cout << "采用邻接表表示法创建无向图" << endl;
    ALGraph G;
    CreatUDG(G);
    int i;

    cout << endl;
    cout << "邻接表表示法创建的无向图" << endl;

    for (i = 0;i < G.vexnum;i++) {
        VNode temp = G.vertices[i];
        ArcNode* p = temp.firstarc;
        if (p == NULL) {
            cout << G.vertices[i].data;
            cout << endl;
        }
        else {
            cout << temp.data;
            while (p) {
                cout << "->";
                cout << p->adjvex;
                p = p->nextarc;
            }
        }
        cout << endl;
    }
    return 0;
}

深度优先搜索遍历连通图的递归算法

//深度优先搜索遍历连通图的递归算法
#include 
using namespace std;

#define MVNun 100
typedef char VerTexType;
typedef int ArcType;

typedef struct {
    VerTexType vexs[MVNun];
    ArcType arcs[MVNun][MVNun];
    int vexnum, arcnum;
}Graph;

bool visited[MVNun];
int FirstAdjVex(Graph G, int v);
int NextAdjVex(Graph G, int v, int w);

int LocateVex(Graph G, VerTexType v) {
    for (int i = 0;i < G.vexnum;++i) {
        if (G.vexs[i] == v)
            return i;
    }
    return -1;
}

void CreateUDN(Graph& G) {
    int i, j, k;
    cout << "请输入总顶点数，总边数 , 以空格隔开:";
    cin >> G.vexnum >> G.arcnum;
    cout << endl;
    cout << "输入点的名称，如 a：" << endl;

    for (i = 0;i < G.vexnum;++i) {
        cout << "请输入第" << (i + 1) << "请输入第";
        cin >> G.vexs[i];
    }
    cout << endl;

    for (i = 0;i < G.vexnum;++i)
        for (j = 0;j < G.vexnum;++j)
            G.arcs[i][j] = 0;
    cout << "输入边依附的顶点，如：a b" << endl;
    for (k = 0;k < G.arcnum;++k) {
        VerTexType v1, v2;
        cout << "请输入第" << (k + 1) << "条边依附的顶点:";
        cin >> v1 >> v2;
        i = LocateVex(G, v1);
        j = LocateVex(G, v2);
        G.arcs[j][i] = G.arcs[i][j] = 1;
    }
}

void DFS(Graph G, int v) {
    cout << G.vexs[v] << "    ";  visited[v] = true;
    int w;
    for (w = FirstAdjVex(G, v); w >= 0; w = NextAdjVex(G, v, w))
        if (!visited[w]) DFS(G, w);
}

int FirstAdjVex(Graph G, int v) {
    int i;
    for (i = 0;i < G.vexnum;++i) {
        if (G.arcs[v][i] == 1 && visited[i] == false)
            return i;
    }
    return -1;
}

int NextAdjVex(Graph G, int v, int w) {
    int i;
    for (i = w;i < G.vexnum;++i) {
        if (G.arcs[v][i] == 1 && visited[i] == false)
            return i;
    }
    return -1;
}

int main() {
    cout << "深度优先搜索遍历连通图的递归算法";
    Graph G;
    CreateUDN(G);
    cout << endl;
    cout << "无向连通图G创建完成！" << endl;

    cout << "请输入遍历连通图的起始点：";
    VerTexType c;
    cin >> c;

    int i;
    for (i = 0;i < G.vexnum;++i) {
        if (c == G.vexs[i])
            break;
    }
    cout << endl;
    while (i >= G.vexnum) {
        cout << "该点不存在，请重新输入！" << endl;
        cout << "请输入遍历连通图的起始点：";
        cin >> c;
        for (i = 0;i < G.vexnum;++i) {
            if (c == G.vexs[i]) {
                break;
            }
        }
    }
    cout << "深度优先搜索遍历连通图结果：" << endl;
    DFS(G, i);

    cout << endl;
    return 0;
}

深度优先搜索遍历非连通图

//深度优先搜索遍历非连通图
#include 
using namespace std;

#define MVNum 100
typedef char VerTexType;
typedef int ArcType;

typedef struct {
    VerTexType vexs[MVNum];
    ArcType arcs[MVNum][MVNum];
    int vexnum, arcnum;
}Graph;

bool visited[MVNum];
int FirstAdjVex(Graph G, int v);
int NextAdjVex(Graph G, int v, int w);

int LocateVex(Graph G, VerTexType v) {
    for (int i = 0;i < G.vexnum;++i) {
        if (G.vexs[i] == v)
            return i;
    }
    return -1;
}

void CreateUDN(Graph &G) {
    int i, j, k;
    cout << "请输入总顶点数，总边数，以空格隔开:";
    cin >> G.vexnum >> G.arcnum;
    cout << endl;

    cout << "输入点的名称，如a" << endl;
    for (i = 0;i < G.vexnum;++i) {
        cout << "请输入第" << (i + 1) << "个数的名称";
        cin >> G.vexs[i];
    }
    cout << endl;
    for (i = 0;i < G.vexnum;++i) {
        for (j = 0;j < G.vexnum;++j) {
            G.arcs[i][j] = 0;
        }
    }
    cout << "输入边依附的顶点，如a b" << endl;
    for (k = 0;k < G.arcnum;k++) {
        VerTexType v1, v2;
        cout << "请输入第" << (k + 1) << "条边依附的顶点:";
        cin >> v1 >> v2;
        i = LocateVex(G, v1);
        j = LocateVex(G, v2);
        G.arcs[j][i] = G.arcs[i][j]=1;
    }
}

void DFS(Graph G, int v) {
    cout << G.vexs[v] << "    ";
    visited[v] = true;
    int w;;
    for (w = FirstAdjVex(G, v);w >= 0;w = NextAdjVex(G, v, w))
        if (visited[w]) DFS(G, w);
}

//key
void DFSTraverse(Graph G) {
    int v;
    for (v = 0;v < G.vexnum;++v)
        visited[v] = false;
    for (v = 0;v < G.vexnum;++v)
        if (!visited[v]) DFS(G, v);
}

int FirstAdjVex(Graph G, int v) {
    int i;
    for (i = 0;i < G.vexnum;++i) {
        if (G.arcs[v][i] == 1 && visited[i] == false)
            return i;
    }
    return -1;
}

int NextAdjVex(Graph G, int v, int w) {
    int i;
    for (i = w; i < G.vexnum; ++i) {
        if (G.arcs[v][i] == 1 && visited[i] == false)
            return i;
    }
    return -1;
}

int main() {
    cout << "深度优先搜索遍历非连通图";
    Graph G;
    CreateUDN(G);
    cout << endl;
    cout << "无向图G创建完成！" << endl;
    cout << "深度优先搜索遍历非连通图结果：" << endl;
    DFSTraverse(G);
    cout << endl;
    return 0;
}

采用邻接矩阵表示图的深度优先搜索遍历(与深度优先搜索遍历连通图的递归算法仅仅是DFS的遍历方式变了)

//采用邻接矩阵表示图的深度优先搜索遍历(与深度优先搜索遍历连通图的递归算法仅仅是DFS的遍历方式变了)
#include 
using namespace std;

#define MVNun 100
typedef char VerTexType;
typedef int ArcType;

typedef struct {
    VerTexType vexs[MVNun];
    ArcType arcs[MVNun][MVNun];
    int vexnum, arcnum;
}Graph;

bool visited[MVNun];
int FirstAdjVex(Graph G, int v);
int NextAdjVex(Graph G, int v, int w);

int LocateVex(Graph G, VerTexType v) {
    for (int i = 0;i < G.vexnum;++i) {
        if (G.vexs[i] == v)
            return i;
    }
    return -1;
}

void CreateUDN(Graph& G) {
    int i, j, k;
    cout << "请输入总顶点数，总边数 , 以空格隔开:";
    cin >> G.vexnum >> G.arcnum;
    cout << endl;
    cout << "输入点的名称，如 a：" << endl;

    for (i = 0;i < G.vexnum;++i) {
        cout << "请输入第" << (i + 1) << "请输入第";
        cin >> G.vexs[i];
    }
    cout << endl;

    for (i = 0;i < G.vexnum;++i)
        for (j = 0;j < G.vexnum;++j)
            G.arcs[i][j] = 0;
    cout << "输入边依附的顶点，如：a b" << endl;
    for (k = 0;k < G.arcnum;++k) {
        VerTexType v1, v2;
        cout << "请输入第" << (k + 1) << "条边依附的顶点:";
        cin >> v1 >> v2;
        i = LocateVex(G, v1);
        j = LocateVex(G, v2);
        G.arcs[j][i] = G.arcs[i][j] = 1;
    }
}

void DFS(Graph G, int v){                
    int w;
    cout << G.vexs[v] << "    ";  visited[v] = true;        
    for(w = 0; w < G.vexnum; w++)                       
        if((G.arcs[v][w] != 0)&& (!visited[w]))  DFS(G, w);
}

int FirstAdjVex(Graph G, int v) {
    int i;
    for (i = 0;i < G.vexnum;++i) {
        if (G.arcs[v][i] == 1 && visited[i] == false)
            return i;
    }
    return -1;
}

int NextAdjVex(Graph G, int v, int w) {
    int i;
    for (i = w;i < G.vexnum;++i) {
        if (G.arcs[v][i] == 1 && visited[i] == false)
            return i;
    }
    return -1;
}

int main() {
    cout << "深度优先搜索遍历连通图的递归算法";
    Graph G;
    CreateUDN(G);
    cout << endl;
    cout << "无向连通图G创建完成！" << endl;

    cout << "请输入遍历连通图的起始点：";
    VerTexType c;
    cin >> c;

    int i;
    for (i = 0;i < G.vexnum;++i) {
        if (c == G.vexs[i])
            break;
    }
    cout << endl;
    while (i >= G.vexnum) {
        cout << "该点不存在，请重新输入！" << endl;
        cout << "请输入遍历连通图的起始点：";
        cin >> c;
        for (i = 0;i < G.vexnum;++i) {
            if (c == G.vexs[i]) {
                break;
            }
        }
    }
    cout << "深度优先搜索遍历连通图结果：" << endl;
    DFS(G, i);

    cout << endl;
    return 0;
}

采用邻接表表示图的深度优先搜索遍历

//采用邻接表表示图的深度优先搜索遍历
#include 
using namespace std;

#define MVNum 100
typedef char VerTexType;

typedef char VerTexType;

typedef struct ArcNode {
    int adjvex;
    struct ArcNode* nextarc;
}ArcNode;

typedef struct VNode {
    VerTexType data;
    ArcNode* firstarc;
}VNode, AdjList[MVNum];

typedef struct {
    AdjList vertices;
    int vexnum, arcnum;
}ALGraph;

bool visited[MVNum];

int LocateVex(ALGraph G, VerTexType v) {
    for (int i = 0;i < G.vexnum;++i)
        if (G.vertices[i].data == v)
            return i;
    return -1;
}

void CreateUDG(ALGraph& G) {
    int i, k;
    cout << "请输入总顶点数，总边数，以空格隔开:";
    cin >> G.vexnum >> G.arcnum;
    cout << endl;

    cout << "输入点的名称，如a" << endl;

    for (i = 0;i < G.vexnum;++i) {
        cout << "请输入第" << (i + 1) << "个点的名称:";
        cin >> G.vertices[i].data;
        G.vertices[i].firstarc = NULL;
    }
    cout << endl;

    cout << "输入边依附的顶点，如a b" << endl;

    for (k = 0;k < G.arcnum;++k) {
        VerTexType v1, v2;
        int i, j;
        cout << "请输入第" << (k + 1) << "条边依附的顶点:";
        cin >> v1 >> v2;
        i = LocateVex(G, v1);
        j = LocateVex(G, v2);

        ArcNode* p1 = new ArcNode;
        p1->adjvex = j;
        p1->nextarc = G.vertices[j].firstarc;
        G.vertices[j].firstarc = p1;

        ArcNode* p2 = new ArcNode;
        p1->adjvex = j;
        p1->nextarc = G.vertices[j].firstarc;
        G.vertices[j].firstarc = p2;
    }
}

void DFS(ALGraph G, int v) {
    cout << G.vertices[v].data << "   ";
    visited[v] = true;
    ArcNode* p = G.vertices[v].firstarc;
    while (p != NULL) {
        int w = p->adjvex;
        if (!visited[w]) DFS(G, w);
        p = p->nextarc;
    }
}

int main() {
    cout << "采用邻接表表示图的深度优先搜索遍历";
    ALGraph G;
    CreateUDG(G);
    cout << endl;
    cout << "无向连通图G创建完成！" << endl;

    cout << "请输入其实的点";
    VerTexType c;
    cin >> c;

    int i;
    for (i = 0;i < G.vexnum;++i) {
        if (c == G.vertices[i].data)
            break;
    }
    cout << endl;
    while (i >= G.vexnum) {
        cout << "该点不存在，请重新输入！" << endl;
        cout << "请输入遍历连通图的起始点：";
        cin >> c;
        for (i = 0;i < G.vexnum;++i) {
            if (c == G.vertices[i].data)
                break;
        }
    }
    cout << "深度优先搜索遍历图结果：" << endl;
    DFS(G, i);

    cout << endl;
    return 0;
}

广度优先搜索遍历连通图

//广度优先搜索遍历连通图
#include 
using namespace std;

#define MVNum 100
#define MAXQSIZE 100

typedef char VerTexType;
typedef int ArcType;
bool visited[MVNum];

typedef struct {
    VerTexType vexs[MVNum];
        ArcType arcs[MVNum][MVNum];
    int vexnum, arcnum;
}Graph;

typedef struct {
    ArcType* base;
    int front;
    int rear;
}sqQueue;

void InitQueue(sqQueue& Q) {
    Q.base = new ArcType[MAXQSIZE];
    if (!Q.base)
        exit(1);
    Q.front = Q.rear = 0;
}

void EnQueue(sqQueue& Q, ArcType e) {
    if ((Q.rear + 1) % MAXQSIZE == Q.front)
        return;
    Q.base[Q.rear] = e;
    Q.rear = (Q.rear + 1) % MAXQSIZE;
}

bool QueueEmpty(sqQueue Q) {
    if (Q.rear == Q.front)
        return true;
    return false;
}

void Dequeue(sqQueue& Q, ArcType& u) {
    u = Q.base[Q.front];
    Q.front = (Q.front + 1) % MAXQSIZE;
}

int LocateVex(Graph G, VerTexType v) {
    for (int i = 0;i < G.vexnum;++i)
        if (G.vexs[i] == v)
            return i;
    return -1;
}

void CreateUDN(Graph& G) {
    int i, j, k;
    cout << "请输入总顶点数，总边数，以空格隔开:";
    cin >> G.vexnum >> G.arcnum;
    cout << endl;
    cout << "输入点的名称，如a" << endl;
    for (i = 0;i < G.vexnum;++i) {
        cout << "请输入第" << (i + 1) << "个点的名称:";
        cin >> G.vexs[i];
    }
    cout << endl;
    for (i = 0;i < G.vexnum;++i) {
        for (j = 0;j < G.vexnum;++i)
            G.arcs[i][j] = 0;
    }
    cout << "输入边依附的顶点，如a b" << endl;
    for (k = 0;k < G.vexnum;k++) {
        VerTexType v1, v2;
        cout << "请输入第" << (k + 1) << "条边依附的顶点:";
        cin >> v1 >> v2;
        i = LocateVex(G, v1);
        j = LocateVex(G, v2);
        G.arcs[i][j] = 1;
        G.arcs[j][i] = G.arcs[i][j];
    }
}

int FirstAdjVex(Graph G, int v) {
    int i;
    for (i = 0;i < G.vexnum;++i) {
        if (G.arcs[v][i] == 1 && visited[i] == false)
            return i;
    }
    return -1;
}

int NextAdjVex(Graph G, int u, int w) {
    int i;
    for (i = w;i < G.vexnum;++i) {
        if (G.arcs[u][i] == 1 && visited[i] == false)
            return i;
    }
    return -1;
}

void BFS(Graph G, int v) {
    sqQueue Q;
    ArcType u;
    ArcType w;

    cout << G.vexs[v] << "  ";
    visited[v] = true;
    InitQueue(Q);
    EnQueue(Q, v);
    while (!QueueEmpty(Q)) {
        Dequeue(Q, u);
        for (w = FirstAdjVex(G, u);w >= 0;w = NextAdjVex(G, u, w)) {
            if (!visited[w]) {
                cout << G.vexs[w] << "   ";
                visited[w] = true;
                EnQueue(Q, w);
            }
        }
    }
}

int main() {
    cout << "广度优先搜索遍历连通图";
    Graph G;
    CreateUDN(G);
    cout << endl;
    cout << "无向连通图G创建完成！" << endl;

    cout << "请输入遍历连通图的起始点：";
    VerTexType c;
    cin >> c;

    int i;
    for (i = 0;i < G.vexnum;++i) {
        if (c == G.vexs[i])
            break;
    }
    cout << endl;
    while (i >= G.vexnum) {
        cout << "该点不存在，请重新输入！" << endl;
        cout << "请输入遍历连通图的起始点：";
        cin >> c;
        for (i = 0;i < G.vexnum;++i) {
            if (c == G.vexs[i])
                break;
        }
    }
    cout << "广度优先搜索遍历连通图结果：" << endl;
    BFS(G, i);

    cout << endl;
    return 0;
}