[数据结构]图基于邻接矩阵的BFS与DFS的C语言简单实现

Github:(https://github.com/FlameCharmander/DataStructure)

上次给大家看了一下图的邻接矩阵的存储。接下来来看下图的广度优先搜索和深度优先搜索。

为了更好的展示BFS和DFS，我把上次的图改了一个边，改成上图那样。
好了，贴代码
由于我们的图广度遍历时需要借助一个队列来实现
所以我们需要用到一个之前实现的队列
把下面这个代码写成queue.c，因为我们图的源文件需要对它导入

#define MAXSIZE 100
#define ElemType char
#define BOOL int
#define TRUE 1
#define FALSE 0

typedef struct{
    ElemType data[MAXSIZE];
    int front, rear;
}Queue;

static void InitQueue(Queue *queue);   //初始化队列
static BOOL IsEmpty(Queue *queue); //判断是否为空
static void EnQueue(Queue *queue, ElemType x); //入队
static void DeQueue(Queue *queue, ElemType *x);    //出队

void InitQueue(Queue *queue){
    queue->front = 0;
    queue->rear = 0;
}

void EnQueue(Queue *queue, ElemType e){
    queue->data[queue->rear] = e;
    queue->rear = (queue->rear + 1) % MAXSIZE;
}

void DeQueue(Queue *queue, ElemType *e){
    *e = queue->data[queue->front];
    queue->front = (queue->front + 1) % MAXSIZE;
}

BOOL IsEmpty(Queue *queue){
    if (queue->front == queue->rear) {
        return TRUE;
    } else {
        return FALSE;
    }
}

你可以拿上面的代码跟之前的代码做个比较。其实就是声明函数的那个部分加了static，加这个可以让别的源文件访问，然后main函数去掉了而已。
然后下面是图的代码。

#include 
#include 
#define INFINTE 65535
#define MAXSIZE 100
#include "queue.c"

typedef char VertexType;                //顶点类型应由用户定义
typedef int EdgeType;                   //边上的权值类型应由用户定义

typedef struct graph{
    VertexType vexs[MAXSIZE];            //顶点表
    EdgeType   arc[MAXSIZE][MAXSIZE];       //邻接矩阵
    int numNodes, numEdges;
}Graph;

int visited[200];

void CreateGraph(Graph* graph); //创建图
VertexType* FirstAdjVex(Graph graph, VertexType data);  //获取第一邻接点
VertexType* NextAdjVex(Graph graph, VertexType data, VertexType adj);   //获取下一邻接点
void DFSTraversal(Graph graph); //深度优先遍历
void BFSTraversal(Graph graph); //广度优先遍历
void DFS(Graph graph, VertexType data); //深度优先搜索
void BFS(Graph graph, VertexType data); //广度优先搜索

int main(){
    int i, j;
    Graph graph;
    CreateGraph(&graph);
    //打印邻接矩阵
    for (i = 0; i < graph.numNodes; ++i){
        for (j = 0; j < graph.numNodes; ++j){
            printf("%d ", graph.arc[i][j]);
        }
        printf("\n");
    }

    VertexType* adj = FirstAdjVex(graph, 'A');
    VertexType x = *adj;
    printf("%c ", x);
    adj = NextAdjVex(graph, 'A', x);
    x = *adj;
    printf("%c ", x);
    x = *adj;
    adj = FirstAdjVex(graph, 'D');
    printf("%c\n", *adj);
    for (i = 0; i < 200; ++i){
        visited[i] = 0;
    }
    BFSTraversal(graph);
    printf("\n");
    for (i = 0; i < 200; ++i){  //访问数组置空
        visited[i] = 0;
    }
    DFSTraversal(graph);
    return 0;
}

void CreateGraph(Graph* graph){
    int i, j;
    //先把图的邻接矩阵置为0(0表示没边，1表示有边)
    for (i = 0; i < graph->numNodes; ++i){
        for (j = 0; j < graph->numNodes; ++j){
            graph->arc[i][j] = 0;
        }
    }
    //printf("请输入顶点数, 边数：");
    //scanf("%d %d", &graph->numNodes, &graph->numEdges);
    //getchar();
    graph->numNodes = 6;
    graph->numEdges = 6;
    /*
    for (i = 0; i < graph->numNodes; ++i){
        printf("请输入顶点：");
        scanf("%c", &graph->vexs[i]);
        getchar();  //消除空白符
    }
    */
    graph->vexs[0] = 'A';
    graph->vexs[1] = 'B';
    graph->vexs[2] = 'C';
    graph->vexs[3] = 'D';
    graph->vexs[4] = 'E';
    graph->vexs[5] = 'F';
    VertexType start, end;
    /*
    for (i = 0; i < graph->numEdges; ++i){
        printf("请输入起点， 终点：");
        scanf("%c %c", &start, &end);
        getchar();  //消除空白符
        int startIndex, endIndex;
        for (j = 0; j < graph->numNodes; ++j){  //找到起始点,终点
            if (start == graph->vexs[j]){
                startIndex = j;
            }
            if (end == graph->vexs[j]){
                endIndex = j;
            }
        }
        graph->arc[startIndex][endIndex] = 1;
        //如果是无向图，需要双向保存
        graph->arc[endIndex][startIndex] = 1;
    }
    */
    graph->arc[0][2] = 1;
    graph->arc[0][3] = 1;
    graph->arc[3][1] = 1;
    graph->arc[2][4] = 1;
    graph->arc[3][5] = 1;
    graph->arc[4][5] = 1;
    //如果是无向图，需要保存两个边
    /*
    graph->arc[2][0] = 1;
    graph->arc[3][0] = 1;
    graph->arc[1][3] = 1;
    graph->arc[4][2] = 1;
    graph->arc[5][3] = 1;
    graph->arc[5][4] = 1;
    */

}


VertexType* FirstAdjVex(Graph graph, VertexType vex){
    //先找到data这个结点
    int i, j;
    for (i = 0; i < graph.numNodes; ++i){
        if (graph.vexs[i] == vex){
            for (j = 0; j < graph.numNodes; ++j){
                if (graph.arc[i][j] == 1){  //找到第一个邻接点
                    return &(graph.vexs[j]);
                }
            }
        }
    }
    return NULL;    //这步说明没找到
}


VertexType* NextAdjVex(Graph graph, VertexType vex, VertexType adj){
    int vexIndex, adjIndex, i;
    for (i = 0; i < graph.numNodes; ++i){
        if (graph.vexs[i] == vex){
            vexIndex = i;
        }
        if (graph.vexs[i] == adj){
            adjIndex = i;
        }
    }
    for (i = adjIndex + 1; i < graph.numNodes; ++i){  //从当前邻接点的后面寻找
        if (graph.arc[vexIndex][i] == 1){
            return &(graph.vexs[i]);
        }
    }
    return NULL;    //这步说明没找到
}

/* 深度优先遍历 */
void DFSTraversal(Graph graph){
    int i;
    for (i = 0; i < graph.numNodes; ++i){
        if (visited[graph.vexs[i]] != 1) {
            DFS(graph, graph.vexs[i]);
        }
    }
}

/* 广度优先遍历 */
void BFSTraversal(Graph graph){
    int i;
    for (i = 0; i < graph.numNodes; ++i){
        if (visited[graph.vexs[i]] != 1) {
            DFS(graph, graph.vexs[i]);
        }
    }
}

/*
    广度优先搜索
*/
void BFS(Graph graph, VertexType vetex){
    Queue queue;
    InitQueue(&queue);
    EnQueue(&queue, vetex);
    VertexType adj;
    VertexType *p;
    visited[vetex] = 1;
    while (!IsEmpty(&queue)){
        DeQueue(&queue, &vetex);
        printf("%c ", vetex);
        for (p = FirstAdjVex(graph, vetex); p != NULL; p=NextAdjVex(graph, vetex, adj)){
            adj = *p; //应该可以写成*p，但是不行
            if (visited[adj] != 1){
                EnQueue(&queue, adj);
                visited[adj] = 1;
            }
        }
    }
}

/*
    深度优先搜索
*/
void DFS(Graph graph, VertexType vex){
    visited[vex] = 1;
    printf("%c ", vex);
    VertexType *p;
    VertexType x;
    for (p = FirstAdjVex(graph, vex); p != NULL; p=NextAdjVex(graph, vex, x)){
        x = *p;
        if (visited[x] != 1){    //没访问过
            DFS(graph, x);
        }
    }
}