邻接矩阵无向图的广度优先遍历C/C++代码实现

广度优先遍历：

与深度优先遍历不同，广度优先遍历还需要一个辅助队列，用来按顺序存储遍历过的顶点以便出队的顶点总是先被遍历的顶点。

以该图为例：

代码如下：

#include<stdio.h>

#define MaxInt 0
#define MVNum 100
typedef char VerTexType;    //顶点类型
typedef int ArcType;		//边权值类型

//邻接矩阵存储结构
typedef struct
{
	VerTexType vexs[MVNum];				//顶点表
	ArcType arcs[MVNum][MVNum];			//邻接矩阵

	int vexnum, arcnum;					//图的当前点数和边数
}AMGraph;
void printGraph(AMGraph G);
int LocateVex(AMGraph G, char v);


//创建无向网
void CreateUDN(AMGraph &G)
{
	G.vexnum = 8;						//输入总顶点数和边数
	G.arcnum = 9;
	G.vexs[0] = 'v1';					//输入顶点信息
	G.vexs[1] = 'v2';
	G.vexs[2] = 'v3';
	G.vexs[3] = 'v4';
	G.vexs[4] = 'v5';
	G.vexs[5] = 'v6';
	G.vexs[6] = 'v7';
	G.vexs[7] = 'v8';

	for (int i = 0; i < G.vexnum; i++)			//初始化邻接矩阵为极大值
	{
		for (int j = 0; j < G.vexnum; j++)
		{
			G.arcs[i][j] = MaxInt;
		}
	}

	//建立边
	int i, j;
	i = LocateVex(G, 'v1');
	j = LocateVex(G, 'v2');
	G.arcs[i][j] = G.arcs[j][i] = 1;
	i = LocateVex(G, 'v1');
	j = LocateVex(G, 'v3');
	G.arcs[i][j] = G.arcs[j][i] = 1;
	i = LocateVex(G, 'v2');
	j = LocateVex(G, 'v4');
	G.arcs[i][j] = G.arcs[j][i] = 1;
	i = LocateVex(G, 'v2');
	j = LocateVex(G, 'v5');
	G.arcs[i][j] = G.arcs[j][i] = 1;
	i = LocateVex(G, 'v5');
	j = LocateVex(G, 'v8');
	G.arcs[i][j] = G.arcs[j][i] = 1;
	i = LocateVex(G, 'v4');
	j = LocateVex(G, 'v8');
	G.arcs[i][j] = G.arcs[j][i] = 1;
	i = LocateVex(G, 'v3');
	j = LocateVex(G, 'v6');
	G.arcs[i][j] = G.arcs[j][i] = 1;
	i = LocateVex(G, 'v3');
	j = LocateVex(G, 'v7');
	G.arcs[i][j] = G.arcs[j][i] = 1;
	i = LocateVex(G, 'v6');
	j = LocateVex(G, 'v7');
	G.arcs[i][j] = G.arcs[j][i] = 1;

	printGraph(G);
}

//确定顶点在顶点表数组中的下边，并返回
int LocateVex(AMGraph G, char v)
{
	for (int i = 0; i < G.vexnum; i++)
	{
		if (G.vexs[i] == v)
		{
			return i;
		}
	}

}

//输出打印
void printGraph(AMGraph G)
{

	for (int i = 0; i < G.vexnum; i++)
	{
		printf("v%d :", i + 1);

		for (int j = 0; j < G.vexnum; j++)
		{
			printf("%d ", G.arcs[i][j]);
		}
		printf("\n");
	}
}



//邻接矩阵广度优先遍历
//创建队列
typedef struct
{
	int base[MVNum];
	int front;
	int rear;
}SqQueue;
//初始化
int InitQueue(SqQueue &Q)
{
	Q.front = Q.rear = 0;
	return 1;
}
//入队
int EnQueue(SqQueue &Q, int e)
{
	if ((Q.rear + 1) % MVNum == Q.front) return 0;
	Q.base[Q.rear] = e;
	Q.rear = (Q.rear + 1) % MVNum;
}
//出队
int DeQueue(SqQueue &Q, int &e)
{
	if (Q.front == Q.rear)  return 0;
	e = Q.base[Q.front];
	Q.front = (Q.front + 1) % MVNum;
	return 1;
}




bool visited[MVNum];			//辅助数组
void BFS_AM(AMGraph G, int v)
{
	int u;

	printf("v%c->", G.vexs[v]);
	visited[v] = true;

	SqQueue Q;
	InitQueue(Q);
	EnQueue(Q, v);

	while (Q.front != Q.rear)
	{
		DeQueue(Q, u);						//出队列并放入u中

		for (int j = 0; j < G.vexnum; j++)
		{
			if (G.arcs[u][j] == 1 && !visited[j])			//查询与u有边的顶点时候被访问
			{
				printf("v%c->", G.vexs[j]);
				visited[j] = true;
				EnQueue(Q, j);
			}
		}
	}
}

int main()
{
	AMGraph G;
	CreateUDN(G);

	int v = 0;
	BFS_AM(G, v);
}

运行结果：