6-19 Count Connected Components（20 point(s)）-优快云博客

本文链接：https://blog.youkuaiyun.com/codeswarrior/article/details/78469571

本文介绍了一个函数CountConnectedComponents，该函数用于计算无向图中连通组件的数量。通过使用广度优先搜索（BFS）策略，遍历图的每个节点来确定其所属的连通组件。

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6-19 Count Connected Components（20 point(s)）

Write a function to count the number of connected components in a given graph.

Format of functions:

int CountConnectedComponents( LGraph Graph );

where LGraph is defined as the following:

typedef struct AdjVNode *PtrToAdjVNode; 
struct AdjVNode{
    Vertex AdjV;
    PtrToAdjVNode Next;
};

typedef struct Vnode{
    PtrToAdjVNode FirstEdge;
} AdjList[MaxVertexNum];

typedef struct GNode *PtrToGNode;
struct GNode{  
    int Nv;
    int Ne;
    AdjList G;
};
typedef PtrToGNode LGraph;

The function CountConnectedComponents is supposed to return the number of connected components in the undirectedGraph.

Sample program of judge:

#include <stdio.h>
#include <stdlib.h>

typedef enum {false, true} bool;
#define MaxVertexNum 10  /* maximum number of vertices */
typedef int Vertex;      /* vertices are numbered from 0 to MaxVertexNum-1 */

typedef struct AdjVNode *PtrToAdjVNode; 
struct AdjVNode{
    Vertex AdjV;
    PtrToAdjVNode Next;
};

typedef struct Vnode{
    PtrToAdjVNode FirstEdge;
} AdjList[MaxVertexNum];

typedef struct GNode *PtrToGNode;
struct GNode{  
    int Nv;
    int Ne;
    AdjList G;
};
typedef PtrToGNode LGraph;

LGraph ReadG(); /* details omitted */

int CountConnectedComponents( LGraph Graph );

int main()
{
    LGraph G = ReadG();
    printf("%d\n", CountConnectedComponents(G));

    return 0;
}

/* Your function will be put here */

Sample Input (for the graph shown in the figure):

Sample Output:

3
code：
 int CountConnectedComponents( LGraph Graph ){
    int counts = 0;//统计连通分支的个数
    int i,j;
    int vis[MaxVertexNum];//只标记这个点是否已经看过了
    for(i = 0; i < MaxVertexNum; i++)
           vis[i] = 0;//标记数组的初始化
    //用邻接表实现BFS
    for(i = 0; i < Graph->Nv; i++){
        if(vis[i]==0){
            counts++;
            vis[i] = 1;
            int q[MaxVertexNum];
            int tail = 0,head = 0;
            q[tail++] = i;//创建一个队列，并把第一个顶点入队
            PtrToAdjVNode t;//创建一个指针，用于遍历这个点的邻接表
            while(head<tail){//广搜
                t = Graph->G[q[head]].FirstEdge;//取出队首顶点的邻接表指针，实际上指向的是首顶点下一个连接的顶点
                while(t){
                    if(!vis[t->AdjV]){//如果下一个连接的点没有遍历过
                        vis[t->AdjV] = 1;//标记
                        q[tail++] = t->AdjV;//入队
                    }
                    t = t->Next;//下一个连接的顶点
                }
                head++;//队首pop
            }
        }
    }
    return counts;
}