graph.h

#ifndef GRAPH_H
#define GRAPH_H

#include<vector>

using namespace std;

class edge;

class vertex		//顶点
{
	friend void connect ( vertex& , vertex& , int );		//建立关系
	friend void bfs (const vertex& , int );					//广度遍历
	friend void bfs ( vertex& , vertex& , int n );
public:
	bool operator!=( const vertex& );
	vertex *pPre = nullptr;					//用于记录路径，指向第一个到达该顶点的顶点。
	int ID = 0;										//顶点的独一无二的序号，构造时给定。

private:
	int in_degree = 0;							//入度
	int out_degree = 0;						//出度
	vector<edge> incident_edge;		//关联边的集合

};

class edge				//边
{
	friend void connect ( vertex& , vertex& , int );
	friend void bfs ( const vertex& , int );
	friend void bfs ( vertex& , vertex& , int n );
public:
	edge ( vertex& , int );
private:
	int weight = 0;				//权重
	vertex* pNext = nullptr;		//指向的顶点
};

#endif

graph.cpp

#include"graph.h"

edge::edge ( vertex& v , int w )
{
	weight = w;
	pNext = &v;
}

void connect ( vertex& v1 , vertex& v2 , int w )
{
	v1.out_degree++;
	v2.in_degree++;
	edge e ( v2 , w );
	v1.incident_edge.push_back ( e );
}

bool vertex::operator!=( const vertex& v)
{
	return this->ID != v.ID;
}

main.cpp

#include<iostream>
#include<map>
#include<deque>

#include"graph.h"

using namespace std;

map<int , vertex> s;		//顶点的集合
deque<vertex> pre;			//顶点的集合，用于记录前一个顶点
deque<vertex> qv;			//顶点的队列
deque<int> qi;					//离顶点距离的队列
deque<vertex> path;		//记录路径的队列

void bfs ( const vertex& , int );		//第一次没有前驱的广度遍历
void bfs ( vertex& , vertex& , int n );		//广度遍历

int main ( void )
{
	//建立图
	int n;
	cout << "请输入边的数量" << endl;
	cin >> n;
	cout << "请输入边的弧尾、弧头和权重" << endl;
	for ( int i = 0; i < n; i++ )
	{
		int a , b , c;
		cin >> a >> b >> c;
		s [ a ].ID = a;
		s [ b ].ID = b;
		connect ( s [ a ] , s [ b ] , c );
	}
	cout << "请输入起始顶点和结束顶点" << endl;
	int a , b;
	cin >> a >> b;

	bfs ( s [ a ] , 0 );		//启动BFS

	//广度遍历直到到达终点
	while (s[b].pPre==nullptr)
	{
		bfs (pre[0], qv [ 0 ] , qi [ 0 ] );
		pre.pop_front ();
		qv.pop_front ();
		qi.pop_front ();
	}
	qv.clear ();
	qi.clear ();
	pre.clear ();
	for ( vertex * i = &s [ b ]; i != nullptr; i = i->pPre )
	{
		path.push_front ( *i );
	}
	for ( auto &i : path )
	{
		cout << i.ID << " ";
	}
	cout << endl;
	system ( "pause" );
	return 0;
}

void bfs ( const vertex& v , int n )
{
	if ( n == 0 )	//到达下一个顶点时
	{
		for ( auto &i : v.incident_edge )
		{
			qv.push_back ( *( i.pNext ) );
			qi.push_back ( i.weight );
			pre.push_back ( v );
		}
		return;
	}

	if ( n != 0 )	//未到达下一个顶点时
	{
		qv.push_back ( v );
		qi.push_back ( n - 1 );
		return;
	}
}

void bfs ( vertex& v1 , vertex& v2 , int n )
{
	if ( n == 0 )	//到达下一个顶点时
	{
		if ( s[v2.ID].pPre == nullptr )
		{
			s[ v2.ID ].pPre = &s[v1.ID];
		}

		for ( auto &i : v2.incident_edge )
		{
			qv.push_back ( *( i.pNext ) );
			pre.push_back ( v2 );
			qi.push_back ( i.weight );
		}
		return;
	}

	if ( n != 0 )	//未到达下一个顶点时
	{
		qv.push_back ( v2 );
		pre.push_back ( v1 );
		qi.push_back ( n - 1 );
		return;
	}
}