第六章算法6.7-广度优先搜索遍历连通图

第六章算法6.7-广度优先搜索遍历连通图

代码实现

#pragma once
#include <iostream>

using namespace std;


//图的邻接表存储表示
#define MVNum 100 //最大顶点数

typedef int OtherInfo;
typedef char VerTexType;

//边（弧）的结点结构
typedef struct ArcNode 
{
	int adjvex;//存储与顶点vi相邻的顶点的位置 
	struct ArcNode* nextarc;//指向下一条边的指针 
	OtherInfo info;
}ArcNode;

//表头结点（顶点的结点结构）
typedef struct VexNode 
{
	VerTexType data;//顶点信息
	ArcNode* firstarc;//指向第一条依附于该顶点的边的指针 
}VexNode, AdjList[MVNum];//AdjList表示邻接表类型 
//邻接表 
typedef struct 
{
	AdjList vertices; //邻接表数组，存放所有结点
	int vexnum, arcnum;//图的当前顶点和边数 
}ALGraph;


//图G中查找顶点u，返回下标
int LocateVex(ALGraph G, VerTexType v)
{
	for (int i = 0; i < G.vexnum; i++)
	{
		if (v == G.vertices[i].data)
		{
			return i;
		}
			
	}
}

//采用邻接表表示法，创建无向图G
void CreateUDG(ALGraph& G)
{

	//输入总顶点数，总边数
	cout << "请输总顶点数：";
	cin >> G.vexnum;
	cout << "请输总边数：";
	cin >> G.arcnum;

	for (int i = 0; i < G.vexnum; i++)
	{
		cout << "输入顶点"<<i<<": ";
		cin >> G.vertices[i].data;//输入顶点值
		//初始化表头节点的指针域为空
		G.vertices[i].firstarc = NULL;

	}
	//构造邻接表(尾插法)
	VerTexType v1, v2;
	ArcNode* p1;
	ArcNode* p2;
	ArcNode* temp1;
	ArcNode* temp2;
	for (int k = 0; k < G.arcnum; k++)
	{
		cout << "输入一条边依附的两个顶点：";
		cin >> v1 >> v2;//输入一条边依附的两个顶点 
		//确定v1和v2在G中的位置，即 在G中的序号
		int i = LocateVex(G, v1);
		int j = LocateVex(G, v2);

		p1 = new ArcNode;//生成一个新的边结点p1 
		p1->adjvex = j;//邻接节点的序号是j
		p1->nextarc = NULL;
	
		//将第i个顶点的边表头指针赋值给表节点指针p
		temp1 = G.vertices[i].firstarc;
		if (temp1 == NULL)
		{
			//如果表头指针为空
			G.vertices[i].firstarc = p1;
		}
		else
		{
			while (temp1 ->nextarc != NULL)
			{
				//遍历到最后一个边结点
				temp1 = temp1->nextarc;
			}
			temp1->nextarc = p1;
		}

		p2 = new ArcNode;//生成一个新的边结点p2
		p2->adjvex = i;//邻接节点的序号是i
		//将新结点p2插入顶点vj的边表头部
		p2->nextarc = NULL;
		temp2 = G.vertices[j].firstarc;
		if (temp2 == NULL)
		{
			G.vertices[j].firstarc = p2;
		}
		else
		{
			while (temp2->nextarc != NULL)
			{
				//遍历到最后一个边结点
				temp2 = temp2->nextarc;
			}
			temp2->nextarc = p2;
		}
	}
}

//输出每个表头节点的值
void ShowGraph(ALGraph G)
{
	for (int i = 0; i < G.vexnum; i++)
	{
		cout << G.vertices[i].data << " ";
		ArcNode* temp = G.vertices[i].firstarc;
		while (temp!= NULL)
		{
			cout << temp->adjvex << " ";
			temp = temp->nextarc;
		}
		cout << endl;
	}
}





//顺序队类型定义
#define MAXQSIZE 100
typedef struct
{
	int *base;
	int front;// 队首指针
	int rear;// 队尾指针
} SqQueue;

//初始化队列
void initQueue(SqQueue& Q)
{
	Q.base = new int[MAXQSIZE];
	// 队首和队尾指针重合并指向0
	Q.front = Q.rear = 0;
}

//入队
void EnQueue(SqQueue& Q, int e)
{
	if ((Q.rear + 1) % MAXQSIZE == Q.front)
	{
		cout << "队列满！" << endl;
	}
	Q.base[Q.rear] = e;
	Q.rear = (Q.rear + 1) % MAXQSIZE;
}

//出队
void DeQueue(SqQueue& Q, int& e)
{
	if (Q.rear == Q.front)
	{
		cout << "队空！" << endl;
	}
	e = Q.base[Q.front];
	Q.front = (Q.front + 1) % MAXQSIZE;
}

//判断队列是否为空
bool QueueEmpty(SqQueue Q)
{
	if (Q.rear == Q.front)
	{
		return true;
	}
	return false;
}



//辅助数组
bool visited[MVNum];
//算法6.7 采用邻接表表示图的广度优先搜索遍历

void BFS(ALGraph G, int v)
{
	cout << G.vertices[v].data;
	visited[v] = true;

	SqQueue Q;
	initQueue(Q);
	//入队
	EnQueue(Q, v);
	int u;
	ArcNode* p;
	while (!QueueEmpty(Q))
	{
		//队列对头元素为每个表头结点的下标
		p = G.vertices[Q.base[Q.front]].firstarc;
		//出队
		DeQueue(Q, u);
		while (p != NULL)
		{
			int w = p->adjvex;
			if (!visited[w])
			{
				cout << G.vertices[w].data;
				visited[w] = true;
				EnQueue(Q, w);
			}
			p = p->nextarc;
		}

	}

}


int main()
{

	ALGraph G;
	//创建无向图的邻接表
	CreateUDG(G);
	//输出无向图的邻接表
	ShowGraph(G);

		//创建并初始化辅助数组
	for (int i = 0; i < G.vexnum; i++)
	{
		visited[i] = false;
	}
		
	cout << "从哪个顶点开始DFS?" << endl;
	int v;
	cin >> v;
	BFS(G, v);
	cout << endl;

	system("pause");
	return 0;
}

运行结果