《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-->aOutvoid 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0std::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;elsestd::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：