数据结构-最小生成树的实现

// mygraph2.cpp : Defines the entry point for the console application.///*题目:用邻接表的形式表示图。

最小生成树编译器:visualc++ 6.0参考资料:《数据结构（用面向对象方法与c++语言描述）》尚未处理的边放在最小堆中，通过并査集的find运算，可以很快的判断任意一条边的两个端点是否来自同一个联通分量，是就舍去，不是就留下，通过并査集的union运算，将两棵树合二为一，直到成了一棵树P262-266并査集实现P235-239最小堆的实现P349-P350 图的模板基类P355-P356 用邻接表表示图P364-P366 图的广度优先和深度优先搜索P372 krusakal算法实现最小生成树*/#include "StdAfx.h"#include<iostream>#include<queue>#include <ASSERT.H>using namespace std;#define DefaultVertices 30//图的基类，主要包含初始化，虚函数，方便以后拓展template<class T,class E>class Graph{public:Graph(intsz=DefaultVertices){} //constructor~Graph(){} // destructorboolGraphEmpty(){ // isemptyif(numEdges==0)return true;elsereturn false;}boolGraphFull(){ //isfullif(numVertices==maxVertices||numEdges==maxVertices*(Vertices-1)/2)return true;elsereturn false;}intNumberOfVertices() // return the number of current vertices{returnnumVertices;}intNumberOfEdges() //return the number of current edges {returnnumEdges;}virtual T getValue(inti)=0;virtual E getWeight(int v1,int v2)=0;virtualintgetFirstNeighbor(int v)=0;virtualintgetNextNeighbor(intv,int w)=0;virtualboolinsertVertex(T& vertex)=0;virtualboolinsertEdge(int v1,int v2,E cost)=0;virtualboolremoveVertex(int v)=0;virtualboolremoveEdge(int v1,int v2)=0;intmaxVertices;intnumEdges;intnumVertices;virtualintgetVertexPos(T vertex)=0;};//边的结构体template<class T,class E>struct Edge{intdest; //存放的是指向那个E cost; //权值Edge<T,E> *link;Edge(){} //构造函数Edge(intnum,E weight):dest(num),cost(weight),link(NULL){}bool operator !=(Edge<T,E>& R){return (dest!=R.dest)?true:false;}};//顶点的结构体,包含数据，还有边template<class T,class E>struct Vertex{T data;Edge<T,E> *adj;};//用邻接矩阵表示的图的形式template<class T,class E>classGraphlnk:public Graph<T,E>{friendistream& operator>>(istream&in,Graphlnk<T,E>& G);friendostream& operator<<(ostream&out,Graphlnk<T,E>& G); public:Graphlnk(intsz=DefaultVertices); //构造函数~Graphlnk(); //析构函数T getValue(inti) //获得处于i位置的值{return (i>=0&&i<numVertices)?NodeTable[i].data:0;}E getWeight(int v1,int v2); //获得权值boolinsertVertex(T& vertex); //插入顶点boolremoveVertex(int v); //移除顶点boolinsertEdge(int v1,int v2,E cost); //插入边boolremoveEdge(int v1,int v2); //移除边intgetFirstNeighbor(int v);//获得第一个intgetNextNeighbor(intv,int w);//获得相邻的Vertex<T,E> *NodeTable;intgetVertexPos(T vertex){for(inti=0;i<numVertices;i++)if(NodeTable[i].data==vertex)returni;return -1;}};/**///建立空图template<class T,class E>Graphlnk<T,E>::Graphlnk(intsz){//thismaxVertices=sz;numVertices=0;numEdges=0;//创建顶点数组NodeTable=new Vertex<T,E>[maxVertices];if(NodeTable==NULL)cout<<"存储失败"<<endl;for(inti=0;i<maxVertices;i++)NodeTable[i].adj=NULL;};//destructor /template<class T,class E>Graphlnk<T,E>::~Graphlnk(){for(inti=0;i<numVertices;i++){Edge<T,E> *p=NodeTable[i].adj;while(p!=NULL){NodeTable[i].adj=p->link;delete p;p=NodeTable[i].adj;}}delete[] NodeTable;}//获取边的权值template<class T,class E>E Graphlnk<T,E>::getWeight(int v1,int v2) {if(v1!=-1&&v2!=-1){Edge<T,E> *p=NodeTable[v1].adj;while(p!=NULL&&p->dest!=v2){p=p->link;}if(p!=NULL)return p->cost;}return 0;}//插入顶点的函数实现template<class T,class E>boolGraphlnk<T,E>::insertVertex(T& vertex) {if(numVertices==maxVertices)return false;NodeTable[numVertices].data=vertex;numVertices++;return true;};//删除顶点的实现template<class T,class E>boolGraphlnk<T,E>::removeVertex(int v){if(numVertices==1||v<0||v>=numVertices)return false;Edge<T,E>*p,*s,*t;int k;//删除第v个边链表的顶点while(NodeTable[v].adj!=NULL){cout<<"测试顶点的数值"<<NodeTable[v].data<<endl;//cout<<"test"<<endl;p=NodeTable[v].adj;cout<<"p的权值"<<p->cost<<endl;k=p->dest;cout<<"k是邻接节点"<<k<<endl;//找对称存放的边结点s=NodeTable[k].adj;cout<<"s->cost 测试"<<s->cost<<endl;t=NULL;while(s!=NULL&&s->dest!=v){//cout<<t-<<"弄懂t算法"<<endl;t=s;s=s->link;cout<<"s->dest"<<s->dest<<endl;cout<<s->link<<"能显示吗"<<endl;cout<<"在while循环测"<<s->cost<<endl;}//删除堆存放的边结点cout<<"删除堆存放的边结点"<<endl;if(s!=NULL){if(t==NULL){cout<<"s->link的权值"<<s->link->cost<<endl;NodeTable[k].adj=s->link;cout<<"NodeTable[k].adjifceshi"<<NodeTable[k].adj->cost<<endl;}else{cout<<t->link->cost<<"之前"<<endl;cout<<s->link<<endl;t->link=s->link;//cout<<t->link->cost<<"之后"<<endl;}delete s;}//清除顶点v的边链表结点NodeTable[v].adj=p->link;delete p;numEdges--;}// cout<<"执行出来"<<endl;numVertices--;//填补cout<<"NodeTable[v].data"<<NodeTable[v].data<<endl;NodeTable[v].data=NodeTable[numVertices].data;p=NodeTable[v].adj=NodeTable[numVertices].adj;cout<<"p=NodeTable[v].adj=NodeTable[numVertices].adj "<<NodeTable[v].adj->cost<<endl;while(p!=NULL){// cout<<"死循环？？"<<endl;// cout<<NodeTable[p->dest].data<<endl;s=NodeTable[p->dest].adj;while(s!=NULL)if(s->dest==numVertices){s->dest=v;break;}elses=s->link;p=p->link;}return true;};//移除边的函数的实现template<class T,class E>boolGraphlnk<T,E>::removeEdge(int v1,int v2){if(v1!=-1&&v2!=-1){Edge<T,E> *p=NodeTable[v1].adj,*q=NULL,*s=p;while(p!=NULL&&p->dest!=v2){q=p;p=p->link;}if(p!=NULL){if(p==s)NodeTable[v1].adj=p->link;elseq->link=p->link;delete p;}elsereturn false;p=NodeTable[v2].adj;q=NULL,s=p;while(p->dest!=v1){q=p;p=p->link;}if(p==s)NodeTable[v2].adj=p->link;elseq->link=p->link;delete p;return true;}return false;};//插入边的函数实现template<class T,class E>boolGraphlnk<T,E>::insertEdge(int v1,int v2,E weight){if(v1>=0&&v1<numVertices&&v2>=0&&v2<numVertices) {//v1对应边链表头指针Edge<T,E> *q,*p=NodeTable[v1].adj;//寻找邻接顶点v2while(p!=NULL&&p->dest!=v2)p=p->link;//找到此边不插入if(p!=NULL)return false;// 否则，创建新结点p=new Edge<T,E>;q=new Edge<T,E>;p->dest=v2;p->cost=weight;p->link=NodeTable[v1].adj;//链入v1边链表NodeTable[v1].adj=p;q->dest=v1;q->cost=weight;q->link=NodeTable[v2].adj;//链入v2边链表NodeTable[v2].adj=q;numEdges++;return true;}return 0;};//获得第一个邻接定点的位置template<class T,class E>intGraphlnk<T,E>::getFirstNeighbor(int v){//对应边链表第一个边节点if(v!=-1){//存在，返回第一个邻接顶点Edge<T,E> *p=NodeTable[v].adj;if(p!=NULL)//第一个邻接顶点不存在return p->dest;}return -1;};//输出某邻接顶点w的下一邻接顶点，思路同上template<class T,class E>intGraphlnk<T,E>::getNextNeighbor(intv,int w) {if(v!=-1){Edge<T,E> *p=NodeTable[v].adj;while(p!=NULL&&p->dest!=w)p=p->link;if(p!=NULL&&p->link!=NULL)return p->link->dest;}return -1;};//重载运算符template<class T,class E>istream& operator>>(istream&in,Graphlnk<T,E>& G){ int choose;cout<<"what do you want to do"<<endl;in>>choose;switch(choose){case 0: break;}}//重载运算template<class T,class E>ostream& operator<<(ostream&out,Graphlnk<T,E>& G) {for(inti=0;i<G.numVertices;i++)out<<G.NodeTable[i].data<<endl;return out;}//深度优先搜索template<class T,class E>void DFS(Graph<T,E>& G,T& v){inti,n=G.NumberOfVertices();intloc;bool *visited=new bool[n];for(i=0;i<n;i++)visited[i]=false;loc=G.getVertexPos(v);DFS(G,loc,visited);delete[] visited;}//深度优先具体实现template<class T,class E>void DFS(Graph<T,E>&G,intv,bool visited[]){//深度优先，cout<<G.getValue(v)<<" ";visited[v]=true;int w=G.getFirstNeighbor(v);while(w!=-1){if(visited[w]==false)DFS(G,w,visited);w=G.getNextNeighbor(v,w);}}//广度优先=函数template<class T,class E>void BFS(Graph<T,E>& G,T& v){inti,w,n=G.NumberOfVertices();bool *visited=new bool[n];for(i=0;i<n;i++)visited[i]=false;intloc=G.getVertexPos(v);cout<<G.getValue(loc)<<" ";visited[loc]=true;queue<int> q;q.push(loc);while(!q.empty()){intloc=q.front();q.pop();w=G.getFirstNeighbor(loc);while(w!=-1){if(visited[w]==false){cout<<G.getValue(w)<<" ";visited[w]=true;q.push(w);}w=G.getNextNeighbor(loc,w);}}delete[] visited;}//并査集intDefaultSize=10;classUFSets{public:UFSets(intsz=DefaultSize);~UFSets(){delete[] parent;}UFSets& operator=(UFSets& R);void Union(int Root1,int Root2);int Find(int x);voidWeightUnion(int Root1,int Root2);int *parent;int size;};//并査集构造函数UFSets::UFSets(intsz){size=sz;parent=new int[size];for(inti=0;i<size;i++)parent[i]=-1;}//并査集查找intUFSets::Find(int x){while(parent[x]>=0)x=parent[x];return x;}//union简单，但是好容易出现退化树的情况voidUFSets::Union(int Root1,int Root2){parent[Root1]+=parent[Root2];parent[Root2]=Root1;}//P265，为了避免出现退化的树，而用的算法，用加权的原则来改进union算法voidUFSets::WeightUnion(int Root1,int Root2){int r1=Find(Root1),r2=Find(Root2),temp;if(r1!=r2){temp=parent[r1]+parent[r2];if(parent[r1]>parent[r2]){parent[r1]=r2;parent[r2]=temp;}else{parent[r2]=r1;parent[r1]=temp;}}elseUnion(Root1,Root2);}//最小生成树边节点的类声明template<class T,class E> structMSTEdgeNode{//顶点的位置以及权值inttail,head;E key;//构造函数MSTEdgeNode():tail(-1),head(-1),key(0){}bool operator<=(MSTEdgeNode<T,E>& R){return key<=R.key;}bool operator>(MSTEdgeNode<T,E>& R){return key>R.key;}};//最小生成树template<class T,class E> classMinSpanTree{protected:MSTEdgeNode<T,E> *edgevalue;intmaxSize,n;public:MinSpanTree(intsz=DefaultSize-1):maxSize(sz),n(0){edgevalue=new MSTEdgeNode<T,E>[sz];}int Insert(MSTEdgeNode<T,E>& item);};//最小生成树的插入template<class T,class E>intMinSpanTree<T,E>::Insert(MSTEdgeNode<T,E>& item){cout<<item.tail<<" "<<item.head<<endl;return 0;}//P124~P125优先队列constintDefaultPQSize=50;template<class T>classPQueue{public:PQueue(intsz=DefaultPQSize); //构造函数~PQueue(){delete[] pqelements;} //析构函数bool Insert(T& x); //插入函数boolRemoveMin(T& x); //移除最小元素boolgetFront(T& x); //取出最小元素void makeEmpty(){count=0;} //制空队列boolIsEmpty() //判断是队列否为空{return (count==0)?true:false;}boolIsFull() //判断队列是否已满{return (count==maxSize)?true:false;}intgetSize() //获得队列目前大小{return count;}protected:T *pqelements; //dataint count; //当前队列个数intmaxSize; //队列最大值void adjust(); //调整函数};//最小优先级最烈的构造函数P125template<class T>PQueue<T>::PQueue(intsz):maxSize(sz),count(0){pqelements=new T[maxSize];assert(pqelements!=NULL);}//插入函数，插入到队尾P125template<class T>boolPQueue<T>::Insert(T& x){if(count==maxSize)return false;pqelements[count++]=x;adjust();return true;}//删除优先权值最小元素P126template<class T>boolPQueue<T>::RemoveMin(T& x){if(count==0)return false;x=pqelements[0];for(inti=1;i<count;i++)pqelements[i-1]=pqelements[i];count--;return true;}//取得最小优先权函数的值P126template<class T>boolPQueue<T>::getFront(T& x){if(count==0)return false;else{x=pqelements[0];return true;}}//P125~P126 将队尾元素按优先权调整到适当的位置，保持优先权不变template<class T>voidPQueue<T>::adjust(){T temp=pqelements[count-1];int j;for(j=count-2;j>=0;j--)if(pqelements[j]<=temp)break;elsepqelements[j+1]=pqelements[j];pqelements[j+1]=temp;}//P236 最小堆的类template<class E>classMinHeap:publicPQueue<E>{public:MinHeap(intsz=DefaultSize); //构造函数MinHeap(E arr[],int n); //重载构造函数~MinHeap(){delete[] heap;} //析构函数bool Insert(E& x); //插入函数boolRemoveMin(E& x); //移除最小值函数boolIsEmpty() //查看是否是空{return (currentSize==0)?true:false;}boolIsFull() //查看是否是满的{return (currentSize==maxHeapSize)?true:false;}void MakeEmpty() //将最小堆置成空{currentSize=0;}E getMin(); // 获取最小值void output(); //输出最小堆的元素，进行验证private:E* heap; //存放最小堆元素的数组intcurrentSize; //最小堆当前元素的个数intmaxHeapSize; //最小堆最多元素个数void siftDown(intstart,int m); //下滑调整为最小堆void siftUp(int start); //上滑调整为最小堆};//构造函数P237template<class E>MinHeap<E>::MinHeap(intsz){maxHeapSize=(DefaultSize<sz)?sz:DefaultSize;heap=new E[maxHeapSize];if(heap==NULL){cerr<<"123"<<endl;exit(1);}currentSize=0;}//最小堆的构造函数P237template<class E>MinHeap<E>::MinHeap(E arr[],int n){maxHeapSize=(DefaultSize<n)?n:DefaultSize;heap=new E[maxHeapSize];if(heap==NULL){cerr<<"123"<<endl;exit(1);}for(inti=0;i<n;i++)heap[i]=arr[i];currentSize=n;intcurrentPos=(currentSize-2)/2;while(currentPos>=0){siftDown(currentPos,currentSize-1);currentPos--;}}//最小堆的下滑调整P238template<class E>voidMinHeap<E>::siftDown(intstart,int m){inti=start,j=2*i+1;E temp=heap[i];while(j<=m){if(j<m&&heap[j]>heap[j+1])j++;if(temp<=heap[j])break;else{heap[i]=heap[j];i=j;j=2*j+1;}}heap[i]=temp;}//最小堆的上滑调整P238~P239template<class E>voidMinHeap<E>::siftUp(int start) {int j=start,i=(j-1)/2;E temp=heap[j];while(j>0){if(heap[i]<=temp)break;else{heap[j]=heap[i];j=i;i=(i-1)/2;}}heap[j]=temp;}//最小堆移除最小值也就是根P239 template<class E>boolMinHeap<E>::RemoveMin(E& x) {if(!currentSize){cout<<"Heap Empty"<<endl;return false;}x=heap[0];heap[0]=heap[currentSize-1];currentSize--;siftDown(0,currentSize-1);return true;}//最小堆的插入P239template<class E>boolMinHeap<E>::Insert(E& x){if(currentSize==maxHeapSize){cerr<<"Heap Full"<<endl;return false;}heap[currentSize]=x;siftUp(currentSize);currentSize++;return true;}//获得最小堆的根template<class E>E MinHeap<E>::getMin(){return heap[0];}//最小堆的输出template<class E>voidMinHeap<E>::output(){for(inti=0;i<currentSize;i++)cout<<heap[i]<<" ";cout<<endl;}//krusal算法，逐步寻找最小权值的边，然后连接template<class T,class E>voidKruskal(Graph<T,E>&G,MinSpanTree<T,E>& MST){MSTEdgeNode<T,E>ed;intu,v,count;//n是顶点的数目int n=G.NumberOfVertices();//m是边的数目int m=G.NumberOfEdges();MinHeap<MSTEdgeNode<T,E>> H(m);UFSets F(n);//并査集for(u=0;u<n;u++)for(v=u+1;v<n;v++)if(G.getWeight(u,v)!=0){// cout<<"u"<<u<<"v"<<v<<endl;// cout<<G.getWeight(u,v)<<"进行测试全知"<<endl;ed.tail=u;ed.head=v;ed.key=G.getWeight(u,v);H.Insert(ed);}count=1;//最小生成树加入边数计算cout<<"这是分割线"<<endl;while(count<n){//反复执行，取N-1条边H.RemoveMin(ed);//从最小对中退出具有最小值的边edu=F.Find(ed.tail);v=F.Find(ed.head);// cout<<"u"<<u<<"v"<<v<<endl;//取两定点所在党的根U,Vif(u!=v){cout<<"u"<<u<<"v"<<v<<endl;//合并，联通他们F.Union(u,v);MST.Insert(ed);count++;}}}//----------------------------------主函数----------------------//大多数测试都在step6中完成的，这一步主要完成最小生成树int main(){MinSpanTree<int,int>mst;Graphlnk<int,int> graph(7);int a[7]={0,1,2,3,4,5,6};for(inti=0;i<7;i++)graph.insertVertex(a[i]);//前面构建书上树已经成功，现在构建自己的树graph.insertEdge(0,1,100);graph.insertEdge(1,3,110);graph.insertEdge(3,4,60);graph.insertEdge(4,6,70);graph.insertEdge(5,6,80);graph.insertEdge(2,0,10);graph.insertEdge(2,5,30);graph.insertEdge(2,3,20);graph.insertEdge(2,4,50);graph.insertEdge(2,6,40);graph.insertEdge(5,0,90);//广度优先搜索cout<<"这是广度优先"<<endl;BFS(graph,a[0]);cout<<endl;//深度优先搜索，depth,是往下一直找cout<<"这是深度优先"<<endl;DFS(graph,a[0]);cout<<endl;//MSTEdgeNode<int,int>//根据书上的图所做的，kruskal算法Kruskal(graph,mst);cout<<"节点的数目"<<graph.NumberOfVertices()<<endl;cout<<"边的数目"<<graph.NumberOfEdges()<<endl;// if (graph.removeVertex(6))// cout<<"删除成功"<<endl;/* if (graph.removeVertex(3)){cout<<"删除成功"<<endl;}*/if (graph.removeVertex(1))cout<<"删除成功"<<endl;cout<<"节点的数目"<<graph.NumberOfVertices()<<endl;cout<<"边的数目"<<graph.NumberOfEdges()<<endl;//cout<<graph;return 0;}。