图的表示

矩阵表示法：不能表示平行边，可以表示自环
空间复杂度V^2，时间复杂度，寻找和某个顶点相邻边的复杂度为V
边表示法：空间复杂度V，时间复杂度 寻找和某个顶点相邻边复杂度为E
邻接表 空间复杂度V+E，用V个头结点表示所有顶点，每个头结点下面连着和它相邻的顶点。可以表示自环和平行边
实现方式

#include <iostream>#include <vector>#include <algorithm>#include <string>using namespace std;struct Node{    int who;    //int weight;    Node*next;};struct HeadNode{    //int nodeName;    int inDegree;    Node*link;};class Graph{private:    int V;    int E;    vector<HeadNode*> vec;private:    bool connected(int v){ return vec[v]->link != NULL;}    Node* rear(int v){        Node* current = vec[v]->link;        for(int i = 1; i < vec[v]->inDegree ; i++){            current = current->next;        }        return current;    }public:    Graph(int V);    int Vs(){ return V;};    int Es(){ return E;};    void addEdge(int v,int w);    int degree(int v){ return vec[v]->inDegree;}    int maxDegree();    int numOfSelfLoops();    void Print();};Graph::Graph(int V){    this->V = V;    this->E = 0;    for(int i = 0 ; i <= V ; i++){        HeadNode* newone= new HeadNode;        newone->inDegree = 0;        newone->link = NULL;        vec.push_back(newone);    }}void Graph::addEdge(int v,int w){    E++;    Node* newone = new Node;    newone->who = w;    newone->next = NULL;    if(connected(v)){        Node* last = rear(v);        last->next = newone;    }    else vec[v]->link = newone;    vec[v]->inDegree++;    Node* newone2 = new Node;    newone2->who = v;    newone2->next = NULL;    if(connected(w)){        Node* last = rear(w);        last->next = newone2;    }    else vec[w]->link = newone2;    vec[w]->inDegree++;}int Graph::maxDegree(){    int max = vec[1]->inDegree;    for(int i = 2 ; i <= V ; i++){        if(vec[i]->inDegree>max) max = vec[i]->inDegree;    }    return max;}int Graph::numOfSelfLoops(){    int cnt = 0;    for(int v = 1 ; v <= V; v++){        Node* current = vec[v]->link;        while(current->next != NULL){            if(current->who == v) cnt++;            current = current->next;        }    }    return cnt;}void Graph::Print(){    cout<<V<<" vertices and "<<E<<" edges"<<endl;    for(int i = 1 ; i <= V ; i++){        cout<<"vertices "<<i<<" link: ";        if(!connected(i)) {            cout<<" null"<<endl;            continue;        }        Node* current = vec[i]->link;        while(current != NULL){            cout<<current->who<<", ";            current = current->next;        }        cout<<endl;    }}int main(){    Graph a(5);    a.addEdge(2,1);    a.addEdge(2,3);    a.addEdge(3,4);    a.addEdge(3,5);    a.Print();    return 0;}