用C语言解决问题:1.创建图(邻接矩阵和邻接表两种方法) 2.图的深度和广度优先搜索结果 3.判断图是否为连通图,并打印其连通分量 4.判断图中是否存在顶点Vi到顶点Vj的简单路径 并输出该路径上的顶点 5.打印图中各顶点的度。
时间: 2025-01-05 14:38:11 浏览: 27
好的,我来为您解答如何使用C语言解决这些问题:
1. 创建图(邻接矩阵和邻接表两种方法):
邻接矩阵:
```c
#define MAX_VERTEX_NUM 100
typedef struct {
int vexs[MAX_VERTEX_NUM];
int arcs[MAX_VERTEX_NUM][MAX_VERTEX_NUM];
int vexnum, arcnum;
} MGraph;
```
邻接表:
```c
#define MAX_VERTEX_NUM 100
typedef struct ArcNode {
int adjvex;
struct ArcNode *next;
} ArcNode;
typedef struct VNode {
int data;
ArcNode *first;
} VNode, AdjList[MAX_VERTEX_NUM];
typedef struct {
AdjList vertices;
int vexnum, arcnum;
} ALGraph;
```
2. 图的深度优先搜索(DFS)和广度优先搜索(BFS):
DFS:
```c
void DFS(Graph G, int v, int visited[]) {
printf("%d ", v);
visited[v] = 1;
for (int i = 0; i < G.vexnum; i++) {
if (G.arcs[v][i] && !visited[i]) {
DFS(G, i, visited);
}
}
}
```
BFS:
```c
void BFS(Graph G, int v, int visited[]) {
int queue[MAX_VERTEX_NUM], front = 0, rear = 0;
printf("%d ", v);
visited[v] = 1;
queue[rear++] = v;
while (front < rear) {
int u = queue[front++];
for (int i = 0; i < G.vexnum; i++) {
if (G.arcs[u][i] && !visited[i]) {
printf("%d ", i);
visited[i] = 1;
queue[rear++] = i;
}
}
}
}
```
3. 判断图是否为连通图,并打印其连通分量:
```c
void ConnectedComponents(Graph G) {
int visited[MAX_VERTEX_NUM] = {0};
for (int i = 0; i < G.vexnum; i++) {
if (!visited[i]) {
printf("Component %d: ", i);
DFS(G, i, visited);
printf("\n");
}
}
}
```
4. 判断图中是否存在顶点Vi到顶点Vj的简单路径,并输出该路径上的顶点:
```c
int found = 0;
void FindPath(Graph G, int vi, int vj, int path[], int len) {
path[len] = vi;
visited[vi] = 1;
if (vi == vj) {
found = 1;
for (int i = 0; i <= len; i++) {
printf("%d ", path[i]);
}
printf("\n");
} else {
for (int i = 0; i < G.vexnum; i++) {
if (G.arcs[vi][i] && !visited[i]) {
FindPath(G, i, vj, path, len + 1);
}
}
}
visited[vi] = 0;
}
```
5. 打印图中各顶点的度:
```c
void PrintDegrees(Graph G) {
for (int i = 0; i < G.vexnum; i++) {
int degree = 0;
for (int j = 0; j < G.vexnum; j++) {
if (G.arcs[i][j]) degree++;
}
printf("Vertex %d: degree %d\n", i, degree);
}
}
```
这些代码片段提供了基本的实现框架,您可能需要根据具体的图结构和需求进行调整和完善。
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