数据结构之图 Data Structure — graph
Adjacency Matrix用C实现如下：
#includenumVertexes;i++){
if(g->vexs[i]==ch)
break;
}
if(i>=g->numVertexes) //如果超过顶点数量了，返回-1
return -1;
return i; //return the index of the vertex you are looking
}
//建立一个无方向网图的邻接矩阵表示
void CreateGraph(Graph *g)
{
int i,j,k,w;
printf("Input the number of vertex and arc:\n");
scanf("%d %d", &(g->numVertexes), &(g->numEdges));
printf("#\n");
#ifdef DEBUG
printf("The number is %d and %d.\n",g->numVertexes,g->numEdges);
#endif
printf("The total amount of vertexes is %d. Assign to each.\n",g->numVertexes);
//assign a value to each vertex
for(i=0;inumVertexes;i++){
g->vexs[i]=getchar();
while(g->vexs[i] == '\n'){
g->vexs[i]=getchar();
}
}
#ifdef DEBUG
for(i=0;inumVertexes;i++){
printf("Vexs[i] is %c ",g->vexs[i]);
}
printf("\n");
#endif
//initialize each arc/edge as infinity
for(i=0;inumEdges;i++){
for(j=0;jnumEdges;j++){
g->arc[i][j]=INFINITY; //initialize
}
}
for (int i = 0; i < g->numEdges; ++i){
char p,q;
printf("input the i and j of (Vi,Vj), and the weight:\n"); //一条边的两个结点，和这条边的权重
p=getchar();
while(p=='\n'){
p=getchar();
}
q=getchar();
while(q=='\n'){
q=getchar();
}
scanf("%d",&w);
int m=-1;
int n=-1;
m=locates(g,p);
n=locates(g,q);
if(n==-1 || m==-1){
fprintf(stderr,"No such vertex\n");
return;
}
g->arc[m][n]=w;
g->arc[n][m]=g->arc[m][n];
}
}
void printGraph(Graph g){
int i,j;
for(i=0;ifor(j=0;jprintf("%d\t",g.arc[i][j] );
}
printf("\n\n\n");
}
}
int main(int argc, char const *argv[])
{
Graph g;
CreateGraph(&g);
printGraph(g);
return 0;
} Adjacency List的表示，用C实现
#includeif(ch==g->adjList[i].data){
break;
}
}
if(i>MAXVEX){
fprintf(stderr,"there is no such vertex.\n");
return -1;
}
return i;
}
void CreateGraph(GraphList *g)
{
int i,j,k;
EdgeNode *e;
EdgeNode *f;
printf("input the amount of matrixs and arcs:\n");
scanf("%d %d",&g->numVertexes,&g->numEdges);
#ifdef DEBUG
printf("numVertexes is %d. numEdges is %d.\n",g->numVertexes,g->numEdges);
#endif
for(i=0;inumVertexes;i++){
printf("输入顶点%d:\n",i);
g->adjList[i].data=getchar();
g->adjList[i].firstedge=NULL;
while(g->adjList[i].data=='\n'){
g->adjList[i].data=getchar();
}
}
//build 边表
for(k=0;knumEdges;k++){
printf("输入边(vi,vj)上的顶点序号:\n");
char p,q;
p=getchar();
while(p=='\n'){
p=getchar();
}
q=getchar();
while(q=='\n'){
q=getchar();
}
int m,n;
m=Locate(g,p);
n=Locate(g,q);
if(m==-1 || n==-1){
return;
}
#ifdef DEBUG
printf("p=%c\n",p);
printf("q=%c\n",q);
printf("m=%d\n",m);
printf("n=%d\n",n);
#endif
//申请内存空间生成边表结点
e=(EdgeNode *)malloc(sizeof(EdgeNode));
if(e==NULL){
fprintf(stderr,"malloc() error.\n");
return;
}
e->adjvex=n;
e->next=g->adjList[m].firstedge;
g->adjList[m].firstedge=e;
f=(EdgeNode *)malloc(sizeof(EdgeNode));
if(f==NULL){
fprintf(stderr,"malloc() error.\n");
return;
}
f->adjvex=m;
f->next=g->adjList[n].firstedge;
g->adjList[n].firstedge=f;
}
}
void printGraph(GraphList *g)
{
int i=0;
#ifdef DEBUG
printf("printGraph() starts.\n");
#endif
while(g->adjList[i].firstedge!=NULL && iprintf("顶点%c与这些点连接：",g->adjList[i].data);
EdgeNode *e=NULL;
e=g->adjList[i].firstedge;
while(e!=NULL){
printf("%d ",e->adjvex); //打印边表的节点
e=e->next;
}
i++;
printf("\n");
}
}
int main()
{
GraphList g;
CreateGraph(&g);
printGraph(&g);
return 0;
} Minimum Cost Spanning Tree
1.Prim Algorithm
用C++实现，代码如下：
/*
* prim.cpp
*
* Created on: May 3, 2017
* Author: yiyue
*/
#includecout<<"Enter Vertex1 ";
cin>>vertex1;
cout<<"Enter vertex2 ";
cin>>vertex2;
cout<<"Enter the cost of "<" and "<" ";
cin>>cost;
graph[vertex1][vertex2]=graph[vertex2][vertex1]=cost;
}
}
void prims::output()
{
for(int i=0;icout<for(int j=0;jcout.width(4);
cout<void prims::spanningtree(){
int min=9999,row,col,index=0;
for(int i=0;ifor(int j=i;jif(graph[i][j]0){
min=graph[i][j];
row=i; //set it to vertex1
col=j; //vertex2
}
}
}
visited[row]=visited[col]=1;
mindist[index++]=min;
for(int i=0;i2;i++){
min=9999;
for(int j=0;jif(visited[j]==1){
for(int k=i;kif(graph[j][k]0&&visited[k]==0){//visited[k]==0 makes sure it's not self-loop
min=graph[j][k];
row=j; //set it to vertex1
col=k; //vertex2
}
}
}
}
mindist[index++]=min;
visited[row]=visited[col]=1;
}
int total=0;
cout<cout<<"Minimum distance path is ";
for(int i=0;i1;i++){
cout<<" "<" ";
total=total+mindist[i];
}
cout<"Total path cost is "<int main()
{
prims obj;
obj.input();
obj.output();
obj.spanningtree();
return 0;
} 另一种实现： （参见数据结构（严蔚敏））
#include 的权值置为w
G.arcs[j][i] = G.arcs[i][j]; //置的对称边的权值为w
}//for
}//CreateUDN
int Min(AMGraph G){
//返回权值最小的点
int i;
int index = -1;
int min = MaxInt;
for(i = 0 ; i < G.vexnum ; ++i){
if(min > closedge[i].lowcost && closedge[i].lowcost != 0){
min = closedge[i].lowcost;
index = i;
}
}//for
return index;
}//Min
void MiniSpanTree_Prim(AMGraph G, VerTexType u){
//无向网G以邻接矩阵形式存储，从顶点u出发构造G的最小生成树T，输出T的各条边
int k , j , i;
VerTexType u0 , v0;
k =LocateVex(G, u); //k为顶点u的下标
for(j = 0; j < G.vexnum; ++j){ //对V-U的每一个顶点vi，初始化closedge[i]
if(j != k){
closedge[j].adjvex = u;
closedge[j].lowcost = G.arcs[k][j]; //{adjvex, lowcost}
}//if
}//for
closedge[k].lowcost = 0; //初始，U = {u}
for(i = 1; i < G.vexnum; ++i){ //选择其余n-1个顶点，生成n-1条边(n= G.vexnum)
k = Min(G);
//求出T的下一个结点：第k个顶点，closedge[k]中存有当前最小边
u0 = closedge[k].adjvex; //u0为最小边的一个顶点，u0∈U
v0 = G.vexs[k]; //v0为最小边的另一个顶点，v0∈V-U
cout << "边 " <"--->" << v0 << endl; //输出当前的最小边(u0, v0)
closedge[k].lowcost = 0; //第k个顶点并入U集
for(j = 0; j < G.vexnum; ++j)
if(G.arcs[k][j] < closedge[j].lowcost){ //新顶点并入U后重新选择最小边
closedge[j].adjvex = G.vexs[k];
closedge[j].lowcost = G.arcs[k][j];
}//if
}//for
}//MiniSpanTree_Prim
int main(){
cout << "************算法6.8 普里姆算法**************" << endl << endl;
AMGraph G;
CreateUDN(G);
cout << endl;
cout << "无向图G创建完成！" << endl;
cout <cout << "******利用普里姆算法构造最小生成树结果：******" << endl;
MiniSpanTree_Prim(G , 'a');
cout <return 0;
}//main