C++ dijkstra 最短路径算法、top排序、DFS、BFS 示例 C++11

好一段时间前写的了。。。正好现在在复习数据结构，重构了一下代码

首先先是 图、点Vertex和边AdjACent的定义

class JpGraph    {    public:        class Vertex;        class AdjAcent        {        public:            int cost;            Vertex* ptr;            explicit AdjAcent(int newCost = 0,Vertex* newPtr = nullptr):cost(newCost),ptr(newPtr){}        };        class Vertex        {        public:            int index;            int inDegree;            vector<AdjAcent>degree;            Vertex(int data, int in_degree)                : index(data),                  inDegree(in_degree)                             {            }        };        JpGraph(){}        void lowestCost(const Vertex& v);        void buildGraph(vector<Vertex> vertexs);        void BFS(int index);        void DFS(int index);        void topSort();    private:        vector<Vertex>vertexs;    };

下面是最短路径的实现，也就是dijkstra算法的实现inline void JpGraph::lowestCost(const Vertex& v) //形参既是从哪个点开始算    {        vector<pair<bool, int>> status;        for (int i = 0; i < vertexs.size(); ++i)        {            status.push_back(pair<bool, int>(false, INT32_MAX));        }        //建立与相应点集对应的集合。        status[v.index].second = 0;        auto findMin = [&]() //lambda表达式，反正我就这个函数用就没单独写个私有函数                             //目的是找到当前权重最小的点的下标        {            int min = INT32_MAX;            int minIndx = 0;            for (int i = 0; i < status.size(); ++i)                if (status[i].second < min && status[i].first == false)                {                    min = status[i].second;                    minIndx = i;                }            return minIndx;        };        auto isAllTrue = [&]() //检查所有的点是不是都已标记为true        {            for (const auto& i : status)            {                if (i.first == false)                    return false;            }            return true;        };        //以前写的实现，这次重构发现完全没必要全部遍历。。dijkstra算法的思想可不就是贪心么。。不知道以前咋想的        //for (;;)        //{        //  status[findMin()].first = true; //每次都将未知的点集中的最小值设为已知        //  for (int i = 0; i < status.size(); ++i)        //  {        //      if (status[i].first == true)        //      {        //          for (const auto& adj : vertexs[i].degree)        //          {        //              auto desV = (*(adj.ptr)).index;        //              if (status[i].second + adj.cost < status[desV].second) //对与已知点相连接的点的cost进行更新        //                  status[desV].second = status[i].second + adj.cost;        //          }        //      }        //  }        //  if (isAllTrue()) //如果所有点都已知，则退出循环        //      break;        //}        while(!isAllTrue())        {            auto minIndex = findMin();            status[minIndex].first = true; //每次都将未知的点集中的最小值设为已知                    for (const auto& adj : vertexs[minIndex].degree)                    {                        auto desV = (*(adj.ptr)).index;                        if (status[minIndex].second + adj.cost < status[desV].second) //对与已知点相连接的点的cost进行更新                            status[desV].second = status[minIndex].second + adj.cost;                    }        }        for (int i = 0; i < status.size(); ++i)        {            cout << "vertexIndex :" << i << "   cost: " << status[i].second << endl;        }    }

以下为测试代码

    inline void testDijkstra()    {        std::cout << "testDijkstra :" << std::endl;        vector<int>vec;        //sort(vec.begin(), vec.end(), less<int>());        typedef JpGraph::Vertex  vertex;        typedef JpGraph::AdjAcent adj;        vertex v0(0, 0);        vertex v1(1, 1);        vertex v2(2, 1);        vertex v3(3, 2);        vertex v4(4, 2);        vertex v5(5, 3);        vertex v6(6, 2);        v0.degree = vector<adj>{ adj(1,&v3),adj{ 2,&v1 } };        v1.degree = vector<adj>{ adj{ 3,&v3 },adj{ 2,&v4 } };        v2.degree = vector<adj>{ adj{ 5,&v5 },adj{ 4,&v0 } };        v3.degree = vector<adj>{ adj{ 8,&v5 },adj{ 2,&v2 },adj{ 2,&v4 },adj{ 4,&v6 } };        v4.degree = vector<adj>{ adj{ 6,&v6 }, };        v5.degree = vector<adj>();        v6.degree = vector<adj>{ adj{ 1,&v5 } };        JpGraph graph;        graph.buildGraph(vector<vertex>{v0, v1, v2, v3, v4, v5, v6});        graph.lowestCost(v0);    }

以下为top排序，top排序的思想我也不说了，网上一搜都有，以下仅实现

    inline void JpGraph::topSort()    {        deque<Vertex>q;        for(const Vertex& vertex : vertexs)        {            if (vertex.inDegree == 0)//将所有入度为0的点加入                q.push_back(vertex);        }        while(q.size()!=0)//依次将与入度为0的点相连的点加入，并将入度0的点pop掉，此处既是一个DFS        {            auto i = q.front(); q.pop_front();            cout<<i.index << " "; //通过简单的cout代表访问点            for(auto& adj : i.degree)             {                auto ptr = adj.ptr;                --(ptr->inDegree);                if (ptr->inDegree == 0)                    q.push_back(*ptr);            }        }    }

以下为测试代码

        inline void testTopSort()    {        vector<int>vec;        //sort(vec.begin(), vec.end(), less<int>());        typedef JpGraph::Vertex  vertex;        typedef JpGraph::AdjAcent adj;        vertex v0(0, 0);        vertex v1(1, 1);        vertex v2(2, 1);        vertex v3(3, 2);        vertex v4(4, 2);        vertex v5(5, 3);        vertex v6(6, 2);        v0.degree = vector<adj>{ adj(1,&v3),adj{ 2,&v1 } };        v1.degree = vector<adj>{ adj{ 3,&v3 },adj{ 2,&v4 } };        v2.degree = vector<adj>{ adj{ 5,&v5 },adj{4,&v0} };        v3.degree = vector<adj>{ adj{ 8,&v5 },adj{ 2,&v2 },adj{2,&v4},adj{ 4,&v6 } };        v4.degree = vector<adj>{ adj{ 6,&v6 },};        v5.degree = vector<adj>();        v6.degree = vector<adj>{ adj{ 1,&v5 } };        JpGraph graph;        graph.buildGraph(vector<vertex>{v0, v1, v2, v3, v4, v5, v6});        graph.topSort();    }

DFS和BFS我也不说废话，直接上代码，DFS和BFS的思想网上随便找

inline void JpGraph::BFS(int index)    {        map<int, bool>hasVisited;        deque<int>checkLine;        for (int i = 0; i < vertexs.size(); ++i)            hasVisited[i] = false;        checkLine.push_back(index);        while(!checkLine.empty())        {            int toTravel = checkLine.front();            checkLine.pop_front();            if (!hasVisited[toTravel])            {                hasVisited[toTravel] = true;                cout << vertexs[toTravel].index + 1 << " ";                for(const auto& i : vertexs[toTravel].degree)                {                    auto toPAt = *(i.ptr);                    if(!hasVisited[toPAt.index])                    {                        checkLine.push_back(toPAt.index);                    }                }            }            else;        }    }    inline void JpGraph::DFS(int index)    {        map<int, bool>hasVisited;        for (int i = 0; i < vertexs.size(); ++i)        {            hasVisited[i] = false;        }        stack<int>stk;        stk.push(index);        while (!stk.empty())        {            int toTravel = stk.top();            stk.pop();            if (hasVisited[toTravel] == false)             {                hasVisited[toTravel] = true;                cout << vertexs[toTravel].index + 1 << " ";                for (const auto& i : vertexs[toTravel].degree)                {                    auto toPAt = *(i.ptr);                    if (!hasVisited[toPAt.index])                    {                        stk.push(toPAt.index);                    }                }            }            else;        }    }

测试代码

inline void testDFSAndBFS()    {        vector<int>vec;        //sort(vec.begin(), vec.end(), less<int>());        typedef JpGraph:: Vertex  vertex;        typedef JpGraph:: AdjAcent adj;        vertex v0(0, 0);        vertex v1(1, 1);        vertex v2(2, 1);        vertex v3(3, 2);        vertex v4(4, 2);        vertex v5(5, 3);        vertex v6(6, 2);        v0.degree = vector<adj>{ adj(1,&v3),adj{ 2,&v1 } };        v1.degree = vector<adj>{ adj{ 3,&v3 },adj{ 2,&v4 } };        v2.degree = vector<adj>{ adj{ 5,&v5 },adj{ 4,&v0 } };        v3.degree = vector<adj>{ adj{ 8,&v5 },adj{ 2,&v2 },adj{ 2,&v4 },adj{ 4,&v6 } };        v4.degree = vector<adj>{ adj{ 6,&v6 }, };        v5.degree = vector<adj>();        v6.degree = vector<adj>{ adj{ 1,&v5 } };        JpGraph graph;        graph.buildGraph(vector<vertex>{v0, v1, v2, v3, v4, v5, v6});        std::cout << "testDFS :" << std::endl;        graph.DFS(0);        cout << "test BFS" << endl;        graph.BFS(0);    }