邻接表实现Dijkstra算法以及DFS与BFS算法

Posted 2020-06-18

//============================================================================
// Name        : ListDijkstra.cpp
// Author      : fffff
// Version     :
// Copyright   : Your copyright notice
// Description : Hello World in C++, Ansi-style
//============================================================================

#include<iostream>
#include<cstdlib>
#include<queue>

using namespace std;

#define MAXSIZE 100
#define INF (~(0x1<<31)) //最大值 0x7FFFFFFF

class ListUDG{
    /*
     * 内部类
     */
private:
    /*
     * 邻接表中的边节点
     * ivex:下一个节点的编号
     * nextEdge:指向下一个边节点的指针
     */
    class Enode{
    public:
        int ivex;
        int weight;
        Enode *nextEdge;
    };
    /*
     * 邻接表中的顶点节点
     * data:顶点节点的数据
     * firstEdge:顶点节点的第一条边
     */
    class Vnode{
    public:
        char data;
        Enode *firstEdge;
    };
private:
    int mVexNum;//顶点个数
    int mEdgNum;//边的条数
    Vnode mVexs[MAXSIZE];
    bool visited[MAXSIZE];
public:
    ListUDG();
    ListUDG(char vexs[],int vlen,char edge[][2],int elen,int weigh[]);
    ~ListUDG();
    char rChar();
    int getPost(char ch);
    int getmVexNum();
    int getmEdgNum();
    Vnode getVexs(int i){
        return mVexs[i];
    };
    int getWeight(int v,int u);
    void print();
    void BFS();
    void DFS();
    void DFSK(int k);
    void Dijkstra(ListUDG *listudg,int v,int pre[],int dist[]);
    void trace(ListUDG *listudg,int v,int u,int pre[]);
private:
    char readChar();
    int getPosition(char ch);
    void LinkLast(Enode *list,Enode *node);
};
ListUDG::ListUDG(char vexs[],int vlen,char edge[][2],int elen,int weigh[]){
    /*
     * 初始化顶点数与边的条数
     */
    mVexNum = vlen;
    mEdgNum = elen;
    /*
     * 初始化邻接表中的顶点节点
     */
    for(int i=0;i<mVexNum;i++){
        mVexs[i].data = vexs[i];
        mVexs[i].firstEdge = NULL;
    }
    /*
     * 初始化邻接表中的边节点
     */
    for(int i=0;i<mEdgNum;i++){
        char first = edge[i][0];
        char second = edge[i][1];
        int start = getPosition(first);
        int end = getPosition(second);

        Enode *enode1 = new Enode;
        enode1->ivex = end;
        enode1->weight = weigh[i];
        enode1->nextEdge = NULL;
        if(mVexs[start].firstEdge==NULL)
            mVexs[start].firstEdge = enode1;
        else
            LinkLast(mVexs[start].firstEdge,enode1);

        Enode *enode2 = new Enode;
        enode2->ivex = start;
        enode2->weight = weigh[i];
        enode2->nextEdge = NULL;
        if(mVexs[end].firstEdge==NULL)
            mVexs[end].firstEdge=enode2;
        else
            LinkLast(mVexs[end].firstEdge,enode2);
    }
};
ListUDG::ListUDG(){
    /*
     * 初始化顶点数与边的条数
     */
    cout<<"input num of Vexs and Edges : ";
    cin>>mVexNum>>mEdgNum;
    /*
     * 初始化邻接表中的顶点节点
     */
    for(int i=0;i<mVexNum;i++){
        cout<<"input data of "<<i<<" Vex:";
        mVexs[i].data = readChar();
        mVexs[i].firstEdge = NULL;
    }
    /*
     * 初始化邻接表中的边节点
     */
    for(int i=0;i<mEdgNum;i++){
            cout<<"input edge("<<i<<"):";
            char first = readChar();
            char second = readChar();
            int start = getPosition(first);
            int end = getPosition(second);

            cout<<"input weight of the edge:";
            int weight;
            cin>>weight;

            Enode *enode1 = new Enode;
            enode1->ivex = end;
            enode1->weight = weight;

            /********************-----ERROR-----********************
             * 两个构造方法都忘掉此句,导致出错,
             * 出错地方在调用方法LinkLast的时候无法判断nextEdge是否为空
             * 因为nextEdge没有被赋值
             *******************************************************/
            enode1->nextEdge = NULL;
            if(mVexs[start].firstEdge==NULL)
                mVexs[start].firstEdge = enode1;
            else
                LinkLast(mVexs[start].firstEdge,enode1);

            Enode *enode2 = new Enode;
            enode2->ivex = start;
            enode2->weight = weight;
            enode2->nextEdge = NULL;
            if(mVexs[end].firstEdge==NULL)
                mVexs[end].firstEdge = enode2;
            else
                LinkLast(mVexs[end].firstEdge,enode2);
    }
};
ListUDG::~ListUDG(){

};
char ListUDG::rChar(){
    return readChar();
};
int ListUDG::getPost(char ch){
    return getPosition(ch);
};
int ListUDG::getmVexNum(){
    return mVexNum;
};
int ListUDG::getmEdgNum(){
    return mEdgNum;
};
int ListUDG::getWeight(int v,int u){
    Enode *enode;
    if(v==u)
        return 0;
    else{
        enode = mVexs[v].firstEdge;
        while(enode){
            if(enode->ivex==u)
                return enode->weight;
            else
                enode = enode->nextEdge;
        }
        return INF;
    }
};
void ListUDG::print(){
    cout<<"ListUDG"<<endl;
    for(int i=0;i<mVexNum;i++){
        cout<<i<<" ("<<mVexs[i].data<<"): ";
        Enode *p = mVexs[i].firstEdge;
        while(p){
            cout<<p->ivex<<"("<<mVexs[p->ivex].data<<")["<<p->weight<<"] ";
            p = p->nextEdge;
        }
        cout<<endl;
    }
    return ;
};
char ListUDG::readChar(){
    char cha;
    cin>>cha;
    while(!((cha>=‘a‘&&cha<=‘z‘)||(cha>=‘A‘&&cha<=‘Z‘))){
        cin>>cha;
    }
    return cha;
};
int ListUDG::getPosition(char ch){
    for(int i = 0;i<mVexNum;i++){
        if(mVexs[i].data==ch)
            return i;
    }
    return -1;
}
void ListUDG::LinkLast(Enode*list,Enode *node){
    Enode *p = list;
    while(p->nextEdge)
        p = p->nextEdge;
    p->nextEdge = node;
    return;
};
/*
 * Dijkstra 算法----最短路径
 */
void ListUDG::Dijkstra(ListUDG *listudg,int v,int pre[],int dist[]){
    bool s[MAXSIZE];

    /*
     * 第一步:初始化S集合以及距离dist
     */
    for(int i=0;i<listudg->getmVexNum();i++){
        s[i] = false;
        dist[i] = listudg->getWeight(v,i);
        if(dist[i]==INF)
            pre[i] = -1;
        else
            pre[i] = v;
    }
    s[v] = true;
    dist[v] = 0;
    /*
     * 第二步:寻找dist中的最小值加入到S集合中
     */
    for(int i=1;i<listudg->getmVexNum();i++){
        int min = INF;
        int u = v;
        for(int j=0;j<listudg->getmVexNum();j++){
            if(s[j]==false&&dist[j]<min){
                min = dist[j];
                u = j;
            }
        }
        s[u] = true;//将顶点u加入到集合S中
        /*
         * 第三步:更新dist
         */
        for(int j=0;j<listudg->mVexNum;j++){
            if(s[j]==false&&listudg->getWeight(u,j)<INF){
                int newdist = dist[u] + listudg->getWeight(u,j);
                if(newdist<dist[j]){
                    dist[j] = newdist;
                    pre[j] = u;
                }
            }
        }
    }
};
void ListUDG::trace(ListUDG *listudg,int v,int u,int pre[]){
    int start = v;
    int end = u;
    while(start!=end){
        cout<<listudg->mVexs[end].data<<"<---";
        end = pre[end];
    }
    cout<<listudg->mVexs[start].data<<endl;
};
/*
 * 广度优先搜索邻接表
 */
void ListUDG::BFS(){
    for(int i=0;i<MAXSIZE;i++)
        visited[i] = false;
    queue<int>que;
    que.push(0);
    visited[0] = true;
    int out;
    Enode *outNext;
    while(!que.empty()){
        out = que.front();
        outNext = mVexs[out].firstEdge;
        que.pop();
        cout<<mVexs[out].data<<" ";

        /****************-----ERROR-----*****************
         * 此处刚开始将判断条件visited[outNext->ivex]==false
         * 写入while循环的判断语句中,导致某一个顶点的边链表没有
         * 访问完就结束了循环(可能某边之前已经访问过),丢掉了后面
         * 的节点
         ************************************************/
        while(outNext!=NULL){
            if(visited[outNext->ivex]==false){
                que.push(outNext->ivex);
                visited[outNext->ivex] = true;
                outNext = outNext->nextEdge;
            }else
                outNext = outNext->nextEdge;
        }
    }
    cout<<endl;
};
void ListUDG::DFS(){
    for(int i=0;i<MAXSIZE;i++)
        visited[i] = false;
    for(int i=0;i<mVexNum;i++)
        if(visited[i]==false)
            DFSK(i);
    cout<<endl;
};
void ListUDG::DFSK(int k){
    visited[k]=true;
    cout<<mVexs[k].data<<" ";
    Enode *enode = mVexs[k].firstEdge;
    while(enode){
        if(visited[enode->ivex]==false){
            DFSK(enode->ivex);
            enode = enode->nextEdge;
        }
        else

            /************-----ERROR-----*************
             *开始时候忘掉了写此句,导致顶点的边链表没有访问完
             *而到时enode没有向后移动,从而导致循环无法结束,因此
             *程序死循环
             ****************************************/
            enode = enode->nextEdge;

    }
    return ;
}
int main(){
    char vexs[]={‘a‘,‘b‘,‘c‘,‘d‘,‘e‘,‘f‘,‘g‘};
    char edges[][2]={
        {‘a‘,‘b‘},
        {‘a‘,‘d‘},
        {‘a‘,‘g‘},
        {‘b‘,‘f‘},
        {‘c‘,‘d‘},
        {‘c‘,‘g‘},
        {‘d‘,‘f‘},
        {‘e‘,‘g‘},
        {‘f‘,‘g‘}
    };
    int pre[MAXSIZE];
    int dist[MAXSIZE];
    int weight[]={1,3,2,2,6,4,3,7,1};
    int vlen = sizeof(vexs)/sizeof(vexs[0]);
    int elen = sizeof(edges)/sizeof(edges[0]);
    ListUDG *listudg1 = new ListUDG(vexs,vlen,edges,elen,weight);
    listudg1->print();
    listudg1->BFS();
    listudg1->DFS();
    listudg1->Dijkstra(listudg1,0,pre,dist);
    listudg1->trace(listudg1,0,2,pre);
    return 0;
}

 

运行结果如下

ListUDG
0 (a): 1(b)[1] 3(d)[3] 6(g)[2]
1 (b): 0(a)[1] 5(f)[2]
2 (c): 3(d)[6] 6(g)[4]
3 (d): 0(a)[3] 2(c)[6] 5(f)[3]
4 (e): 6(g)[7]
5 (f): 1(b)[2] 3(d)[3] 6(g)[1]
6 (g): 0(a)[2] 2(c)[4] 4(e)[7] 5(f)[1]
a b d g f c e
a b f d c g e
c<---g<---a