图的相关算法

图的广度优先搜索和深度优先搜索：

#include <iostream>#include <queue>#include <stdio.h>#include <queue>#include <stdlib.h>#include <list>using namespace std;#define VERTEXNUM 100//最大顶点数#define INF  65535enum nodecolor {white,gray,black};typedef struct node//参见算法导论322{    int adjvex;//顶点位置    struct node *next;//指向下一条边的指针}EdgeNode;typedef struct vnode{    char vertex;//顶点信息    EdgeNode *firstedge;//指向第一条依附该顶点的边的指针    nodecolor color;    int d;//广度优先中到第一个点的距离,深度优先中被发现的时间    int f;//深度优先中结束检查此结点的邻接表的时间    vnode* pi;//父结点}AdjList[VERTEXNUM];typedef struct{    AdjList vertexs;//邻接表    int vernum,edgenum;//图中当前的顶点和边数}Graph;//建立邻接表void MakeGraph(Graph *G){    int v1,v2;    int i,j,k;    cout<<"请输入图的顶点数和边数"<<endl;    cin>>G->vernum>>G->edgenum;    cout<<"请输入顶点信息(顶点号<CR>)每个顶点以回车作为结束:"<<endl;    for(i=0;i<G->vernum;++i)    {        //getchar();        cin>>G->vertexs[i].vertex;        G->vertexs[i].firstedge=NULL;//初始第一条边为空    }    cout<<"请输入每条边对应的两个顶点的序号(格式为i,j):"<<endl;    EdgeNode *p;    for(k=0;k<G->edgenum;k++)    {        cin>>i>>j;//读入边<vi,vj>的序号        p=(node*)malloc(sizeof(node));//生成新的结点        p->adjvex=j-1;        p->next=G->vertexs[i-1].firstedge;        G->vertexs[i-1].firstedge=p;//这3行是插入链表的操作    }}//广度优先遍历void BFS(Graph *G,vnode *s){    int i;    queue<vnode *> Q;    EdgeNode *p;    vnode *u;    for(i=0;i<G->vernum;i++)    {        G->vertexs[i].d=INF;        G->vertexs[i].pi=NULL;        G->vertexs[i].color=white;    }    s->color=gray;    s->d=0;    s->pi=NULL;    Q.push(s);    while(!Q.empty())    {        u=Q.front();        Q.pop();//出队        p=u->firstedge;        while(p)        {            if(G->vertexs[p->adjvex].color==white)            {                G->vertexs[p->adjvex].color=gray;                G->vertexs[p->adjvex].d=u->d+1;                G->vertexs[p->adjvex].pi=u;                Q.push(&G->vertexs[p->adjvex]);            }            p=p->next;        }        u->color=black;    }    for(i=0;i<G->vernum;i++)     {        u=&G->vertexs[i];        cout<<"结点:"<<u->vertex<<"距离:"<<u->d<<"颜色:"<<u->color<<endl;    }        }//深度优先遍历void DFS_visit(Graph *G,vnode *u);int t=0;//时间list<vnode*> L;//用于拓扑排序void DFS(Graph *G){    int i;    for(i=0;i<G->vernum;i++)    {        G->vertexs[i].d=INF;        G->vertexs[i].pi=NULL;        G->vertexs[i].color=white;    }    for(i=0;i<G->vernum;i++)    {        if(G->vertexs[i].color==white)            DFS_visit(G,&G->vertexs[i]);     }    for(i=0;i<G->vernum;i++)     {        vnode *u=&G->vertexs[i];        cout<<"结点:"<<u->vertex<<"开始:"<<u->d<<"结束:"<<u->f<<endl;    }        }void DFS_visit(Graph *G,vnode *u){    EdgeNode *p;    u->color=gray;    u->d=++t;    p=u->firstedge;    while(p)    {       if(G->vertexs[p->adjvex].color==white)       {           G->vertexs[p->adjvex].pi=u;           DFS_visit(G,&G->vertexs[p->adjvex]);       }        p=p->next;    }    u->color=black;    u->f=++t;    L.insert(L.begin(),u);//用于拓扑排序}    //拓扑排序list<vnode*>& topological_sort(Graph* G){    DFS(G);    return L;}int main(){    int j;    Graph *G=(Graph *)malloc(sizeof(Graph));    MakeGraph(G);    cout<<"请输入广度优先开始遍历的结点的序号:"<<endl;    cin>>j;    cout<<"广度优先遍历:"<<endl;    BFS(G,&G->vertexs[j-1]);    cout<<"深度优先遍历:"<<endl;    DFS(G);    return 0;}

最小生成树：

//Kruskalconst int maxint = 999999;typedef struct Road{    int c1,c2;//a到b    int value;//权值}Road;int no;int line;Road road[100];int node[101];bool myCmp(const Road &a,const Road &b){    return (a.value<b.value);}int Find_Set(int n){    if(node[n]==-1)        return n;    else        return Find_Set(node[n]);//其实就是沿着树找到根}bool Merge(int s1,int s2){    int r1=Find_Set(s1);    int r2=Find_Set(s2);    if(r1==r2)//根相同就是属于同一棵树        return 0;    if(r1<r2)        node[r2]=r1;    else        node[r1]=r2;    return 1;}int main(){    freopen("input.txt","r",stdin);    memset(node,-1,sizeof(node));    cout<<"Input the number of the node:";    cin>>no;    cout<<"Input the number of the line:";    cin>>line;    cout<<"Input the edge:";    for(int i=0;i<line;++i)    {        cin>>road[i].c1>>road[i].c2>>road[i].value;    }    sort(road,road+line,myCmp);    int sum=0,count=0;    for(int i=0;i<line;++i)    {        if(Merge(road[i].c1,road[i].c2))        {            count++;            sum+=road[i].value;        }        if(count==no-1)            break;    }    cout<<sum<<endl;}//Primconst int INF=1001;int no,line;int arcs[101][101];int dis[101],vis[101];int _min;int main(){    freopen("input.txt","r",stdin);    cout<<"Input the number of the node:";    cin>>no;    cout<<"Input the number of the line:";    cin>>line;    for(int i=0;i<no;++i)        for(int j=0;j<no;++j)            arcs[i][j]=INF;    cout<<"Input the edge:";    int p,q,len;//输入p,q两点及路径长度    for(int i=0;i<line;++i)    {        cin>>p>>q>>len;        if(len<arcs[p-1][q-1])//有重边        {            arcs[p-1][q-1]=len;            arcs[p-1][q-1]=len;//表示无向图        }    }    memset(vis,0,sizeof(vis));    for(int i=1;i<no;++i)        dis[i]=arcs[0][i];    vis[0]=1;    int sum=0,rec=0;    dis[0]=0;    for(int i=1;i<no;++i)    {        _min=INF;        for(int j=0;j<no;++j)            if(!vis[j]&&dis[j]<_min)            {                rec=j;                _min=dis[j];            }        cout<<"min:"<<_min<<endl;        sum+=_min;        vis[rec]=1;        for(int j=0;j<no;++j)            if(!vis[j]&&arcs[rec][j]<dis[j])                dis[j]=arcs[rec][j];    }    printf("%d\n",sum);    return 0;}