《数据结构实战》-------------------------------------------图论 无加权最短路径算法

该代码是用于计算无加权的最短路径算法：

#ifndef __CDIRECTEDGRAPH__H
#define __CDIRECTEDGRAPH__H
#include <iostream>
#include <list>

// 邻接表表示有向图 拓扑排序 无权最短路径

const int NERVER_ATTACH = 9999;

struct VertexNode // 顶点
{
	std::string cName; // 顶点名字
	int  nInDegree; // 入度
	int  nDistance; // 最短路径
	std::list<struct VertexNode*> listNodes; // 邻接点
	VertexNode()
	{
		cName = "";
		nInDegree = NERVER_ATTACH; // 未分配的顶点
		nDistance = NERVER_ATTACH;
		listNodes.clear();
	}
};

class CDirectedGraph
{
public:
	CDirectedGraph(int nNodes);
	~CDirectedGraph();

public:
	bool InsertEdge(std::string aIn, std::string bOut); // 插入有向边 aIn-->aOut
	void TopologicalSort(); // 拓扑排序
	void ShortedPath(std::string sVertex); // 无权最短路径算法
private:
	void FindIndexInsert(std::string aIn, int& nInsertIndex, bool& bFindInsert, bool& bFindIn);
private:
	struct VertexNode* m_pNodes; // 所有点的集合
	int    m_nNodes; // 顶点数量
};

#endif

#include "DirectedGraph.h"
#include <algorithm>
#include <queue>
#include <string>

CDirectedGraph::CDirectedGraph(int nNodes) : m_nNodes(nNodes)
{
	if (!m_pNodes)
		m_pNodes = new VertexNode[nNodes];
}


CDirectedGraph::~CDirectedGraph()
{
	delete[] m_pNodes;
}

void CDirectedGraph::FindIndexInsert(std::string aIn, int& nInsertIndex, bool& bFindInsert, bool& bFindIn)
{
	nInsertIndex = 0;
	bFindInsert = false;
	bFindIn = false;
	for (int i = 0; i < m_nNodes; i++)
	{
		if ((m_pNodes + i)->cName != aIn && (m_pNodes + i)->nInDegree == NERVER_ATTACH && !bFindInsert)
		{
			nInsertIndex = i;
			bFindInsert = true;
		}
		if ((m_pNodes + i)->cName == aIn)
		{
			bFindIn = true;
			nInsertIndex = i;
			break;
		}
	}
}

bool CDirectedGraph::InsertEdge(std::string aIn, std::string bOut)
{
	int nInsertIndex = 0;
	bool bFindInsert = false;
	bool bFindIn = false;
	int nInsertIndexOut = 0;
	bool bFindInsertOut = false;
	bool bFindInOut = false;
	FindIndexInsert(aIn, nInsertIndex, bFindInsert, bFindIn);
	if (bFindInsert && !bFindIn) // 还未分配
	{
		(m_pNodes + nInsertIndex)->cName = aIn;
		(m_pNodes + nInsertIndex)->nInDegree = 0; // 入度为0
	}
	FindIndexInsert(bOut, nInsertIndexOut, bFindInsertOut, bFindInOut);
	if (bFindInsertOut && !bFindInOut) // 还未分配
	{
		(m_pNodes + nInsertIndexOut)->cName = bOut;
		(m_pNodes + nInsertIndexOut)->nInDegree = 0; // 入度为0
	}
	(m_pNodes + nInsertIndexOut)->nInDegree += 1; // 入度加1
	(m_pNodes + nInsertIndex)->listNodes.push_back(m_pNodes + nInsertIndexOut); // 改变邻接表
	return true;
}

void CDirectedGraph::TopologicalSort() // 拓扑排序 注意一次排序后就更改了所有节点的度
{
	std::queue<VertexNode*> queueVertex; // 度为0的顶点
	for (int i = 0; i < m_nNodes; i++)
		if ((m_pNodes + i)->nInDegree == 0)
			queueVertex.push(m_pNodes + i);
	while (!queueVertex.empty())
	{
		VertexNode* pNode = queueVertex.front();
		queueVertex.pop();
		std::cout << pNode->cName << "\t";
		// 更新邻接点的度
		for (auto& iter : pNode->listNodes)
		{
			iter->nInDegree -= 1;
			if (iter->nInDegree == 0)
				queueVertex.push(iter);
		}
	}
}

void CDirectedGraph::ShortedPath(std::string sVertex) // 无权最短路径算法
{
	std::cout << std::endl;

	int nInsertIndex = 0;
	bool bFindInsert = false;
	bool bFindIn = false;
	FindIndexInsert(sVertex, nInsertIndex, bFindInsert, bFindIn);
	if (!bFindIn) // 没有该顶点
		return;
	for (int i = 0; i < m_nNodes; i++) // 初始化到所有顶点的路径长度
		(m_pNodes + i)->nDistance = NERVER_ATTACH;
	(m_pNodes + nInsertIndex)->nDistance = 0; // 自己到自己的路径为0
	std::queue<VertexNode*> queueDistance;
	queueDistance.push(m_pNodes + nInsertIndex);
	while (!queueDistance.empty())
	{
		VertexNode* pNode = queueDistance.front();
		queueDistance.pop();
		if (!pNode->listNodes.empty())
		{
			for (auto iter = pNode->listNodes.begin(); iter != pNode->listNodes.end(); iter++)
			{
				if ((*iter)->nDistance == NERVER_ATTACH)
					(*iter)->nDistance = pNode->nDistance + 1; // 更新长度
				queueDistance.push(*iter);
			}
		}
	}

	// 打印到所有顶点的无权路径
	for (int i = 0; i < m_nNodes; i++)
	{
		std::cout << sVertex << " 到顶点" << (m_pNodes + i)->cName << "的最短距离为: ";
		if ((m_pNodes + i)->nDistance == NERVER_ATTACH)
			std::cout << "无法到达" << std::endl;
		else
			std::cout << (m_pNodes + i)->nDistance << std::endl;
	}
}

#include "DirectedGraph.h"

int main()
{
	CDirectedGraph directedGraph(7);
	directedGraph.InsertEdge("v1", "v2");
	directedGraph.InsertEdge("v1", "v4");
	directedGraph.InsertEdge("v1", "v3");
	directedGraph.InsertEdge("v2", "v4");
	directedGraph.InsertEdge("v2", "v5");
	directedGraph.InsertEdge("v3", "v6");
	directedGraph.InsertEdge("v4", "v3");
	directedGraph.InsertEdge("v4", "v6");
	directedGraph.InsertEdge("v4", "v7");
	directedGraph.InsertEdge("v5", "v4");
	directedGraph.InsertEdge("v5", "v7");
	directedGraph.InsertEdge("v7", "v6");
	directedGraph.TopologicalSort();
	directedGraph.ShortedPath("v1");
	directedGraph.ShortedPath("v6");
	std::cin.get();
	return 0;
}

用到的图如下：