图的遍历（下）——邻接表

概述

在我的上一篇博客：图的遍历（上）——邻接矩阵 中主要介绍了邻接矩阵的BFS和递归的DFS与非递归的DFS这3种遍历算法。在这篇博客我将主要叙述邻接表的以上3中遍历算法。首先来看看邻接表的表示方法。

邻接表主要是针对稀疏图中邻接矩阵造成的空间浪费而提出的。下面我们来看看邻接表的表示。
1）无向图的表示

2）有向图

（说明：对于BFS，DFS的递归与非递归算法在这篇文章就不再重复，如有不了解请移步我的上一篇博客：图的遍历（上）——邻接矩阵 ）

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广度优先遍历（BFS）

//广度优先遍历(BFS)void BFS(int vertex){    EdgeList* cur = this->Find(vertex);     //找到当前结点        queue<int> queue;                   //初始化队列     queue.push(cur->getVertex(cur));            //当前结点入队    while(!queue.empty()){        int index = queue.front();      //队头元素出队        queue.pop();        isvisited[index] = 1;           //标记为已访问         cout<<index<<" ";        cur = this->Find(index);        while(cur){     //与当前结点相邻且未被访问的结点入队             index = cur->getVertex(cur);            if(isvisited[index] == 0){                queue.push(index);            }            cur = cur->getNext();           }     }}

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递归深度优先遍历（DFS）

//递归深度优先遍历(DFS)void DFS1(int vertex){    vector<int> node;    //找到当前结点     EdgeList* cur = this->Find(vertex);    while(cur){     //寻找当前结点的邻接点         node.push_back(cur->getVertex(cur));        cur = cur->getNext();    }    //打印当前结点     cur = this->Find(node[0]);    int index = cur->getVertex(cur);    this->isvisited[index] = 1;    cout<<index<<" ";    //一次堆当前结点的邻接点进行DFS     for(int i = 1 ; i < node.size() ; i++){        cur = this->Find(node[i]);        index = cur->getVertex(cur);        if(this->isvisited[index] == 0){            this->isvisited[index] = 1;            this->DFS1(index);        }    }}

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非递归深度优先遍历（DFS）

//非递归深度优先遍历(DFS)void DFS2(int vertex){    stack<int> stack;    EdgeList* cur = this->Find(vertex);     //查找当前元素     int index = cur->getVertex(cur);        //当前元素的顶点     stack.push(index);                      //顶点入栈     this->isvisited[index] = 1;             //标记为已访问     while(!stack.empty()){          //栈不空一直循环         index = stack.top();        //栈顶的顶点出栈         stack.pop();        cout<<index<<" ";           //打印当前顶点         cur = this->Find(index);         while(cur){         //把当前顶点的邻接点依次入栈             index = cur->getVertex(cur);            if(this->isvisited[index] == 0){                stack.push(index);                this->isvisited[index] = 1;            }            cur = cur->getNext();        }    }} 

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例子

下面的程序所基于的图结构够如下：

#include <iostream>#include <vector> #include <queue> #include <stack>#include <cstring> using namespace std;//边表类 class EdgeList{    private:        int vertex;        EdgeList* next;    public:        EdgeList* Create(int vertex){            EdgeList* list = new EdgeList;            list->vertex = vertex;            list->next = NULL;            return list;        }        //寻找最后一个结点        EdgeList* getLast(EdgeList* list){            EdgeList* cur = list;            while(cur){                if(cur->next == NULL){                    return cur;                }                cur = cur->next;            }        }        //插入函数         EdgeList* Attach(EdgeList* list,int vertex){            EdgeList* last = this->getLast(list);            EdgeList* insert = insert->Create(vertex);            last->next = insert;            return list;        }        int getVertex(EdgeList* list){            return list->vertex;        }        void Print(EdgeList* list){            EdgeList* cur = list;            while(cur){                cout<<cur->vertex<<" ";                cur = cur->next;            }        }        EdgeList* getNext(){            return this->next;        }}; class Graph{    private:        vector<EdgeList*> Edgelist;     //邻接表         int* isvisited;                 //访问数组         int Nv;         //顶点数        int Ne;         //边数     public:         //构造函数         Graph(int nv ,int ne){            this->Ne = ne;            this->Nv = nv;            this->Edgelist.reserve(nv);            this->isvisited = new int[nv+1];            memset(this->isvisited,0,sizeof(this->isvisited[0])*(this->Nv+1));            cout<<"请输入顶点："<<endl;            //依次构造图的结点             for(int i = 0 ; i < this->Nv ; i++){                int vertex;                cin>>vertex;                this->Edgelist[i] = new EdgeList;                this->Edgelist[i] = this->Edgelist[i]->Create(vertex);            }            cout<<"请输入边："<<endl;            //依次构造无向图的边             for(int i = 0 ; i < this->Ne ; i++){                int start,end;                cin>>start>>end;                //找到一条边的两个顶点                 EdgeList* s1 = this->Find(start);                       EdgeList* s2 = this->Find(end);                s1->Attach(s1,end);                s2->Attach(s2,start);            }         }        //按指定结点查找        EdgeList* Find(int vertex){            for(int i = 0 ; i < this->Nv ; i++){                if(this->Edgelist[i]->getVertex(this->Edgelist[i]) == vertex){                    return this->Edgelist[i];                }            }         }        //打印邻接表函数         void Print(){            for(int i = 0 ; i < this->Nv ; i++){                EdgeList* list = this->Edgelist[i];                list->Print(list);                cout<<endl;            }        }        //广度优先遍历(BFS)        void BFS(int vertex){            EdgeList* cur = this->Find(vertex);     //找到当前结点                queue<int> queue;                   //初始化队列             queue.push(cur->getVertex(cur));            //当前结点入队            while(!queue.empty()){                int index = queue.front();      //队头元素出队                queue.pop();                isvisited[index] = 1;               //标记为已访问                 cout<<index<<" ";                cur = this->Find(index);                while(cur){     //与当前结点相邻且未被访问的结点入队                     index = cur->getVertex(cur);                    if(isvisited[index] == 0){                        queue.push(index);                    }                    cur = cur->getNext();                   }             }        }        //重置访问数组         void reset(){            memset(this->isvisited,0,sizeof(this->isvisited[0])*(this->Nv+1));        }         //递归深度优先遍历(DFS)        void DFS1(int vertex){            vector<int> node;            //找到当前结点             EdgeList* cur = this->Find(vertex);            while(cur){     //寻找当前结点的邻接点                 node.push_back(cur->getVertex(cur));                cur = cur->getNext();            }            //打印当前结点             cur = this->Find(node[0]);            int index = cur->getVertex(cur);            this->isvisited[index] = 1;            cout<<index<<" ";            //一次堆当前结点的邻接点进行DFS             for(int i = 1 ; i < node.size() ; i++){                cur = this->Find(node[i]);                index = cur->getVertex(cur);                if(this->isvisited[index] == 0){                    this->isvisited[index] = 1;                    this->DFS1(index);                }            }        }        //非递归深度优先遍历(DFS)        void DFS2(int vertex){            stack<int> stack;            EdgeList* cur = this->Find(vertex);     //查找当前元素             int index = cur->getVertex(cur);        //当前元素的顶点             stack.push(index);                      //顶点入栈             this->isvisited[index] = 1;             //标记为已访问             while(!stack.empty()){          //栈不空一直循环                 index = stack.top();        //栈顶的顶点出栈                 stack.pop();                cout<<index<<" ";           //打印当前顶点                 cur = this->Find(index);                 while(cur){         //把当前顶点的邻接点依次入栈                     index = cur->getVertex(cur);                    if(this->isvisited[index] == 0){                        stack.push(index);                        this->isvisited[index] = 1;                    }                    cur = cur->getNext();                }            }        } };int main(){    cout<<"请输入顶点数与边数:"<<endl;    int nv,ne;    cin>>nv>>ne;    Graph graph(nv,ne);    cout<<"邻接表为："<<endl;    graph.Print();    cout<<"请输入结点:"<<endl;    int vertex;    cin>>vertex;     cout<<"广度优先遍历（BFS）序列为："<<endl;    graph.BFS(vertex);    cout<<endl;    cout<<"递归深度优先遍历（DFS）序列为："<<endl;    graph.reset();     graph.DFS1(vertex);    cout<<endl;     cout<<"非递归深度优先遍历（DFS）序列为："<<endl;    graph.reset();     graph.DFS2(vertex);    cout<<endl;     return 0;}

截图：