图的邻接矩阵表示方式——无权图的最短路径

Posted 2020-10-13 accomplishment

  1 #include<stdio.h>
  2 #include<stdlib.h>
  3 
  4 #define OK 1
  5 #define NO 0
  6 #define TRUE 1
  7 #define FALSE 0
  8 #define ERROR -1 
  9 
 10 #define MaxVerTexNum 100
 11 #define INFINITY 65535
 12 typedef int ElementType;
 13 typedef int Status;
 14 typedef int WeightType;
 15 typedef int Vertex;
 16 typedef char DataType;
 17 
 18 typedef int Position;
 19 typedef struct QNode{
 20     ElementType *Data;
 21     Position Front, Rear;
 22     int MaxSize;  
 23 }QNode,*Queue;
 24 
 25 typedef  struct  ENode{
 26     Vertex V1,V2;     //有向边<v1,V2>
 27     WeightType Weight;//权重
 28 }ENode,*PtrToENode ;
 29 
 30 typedef PtrToENode Edge;
 31 
 32 Status IsFull( Queue Q );
 33 
 34 typedef struct GNode{
 35     int Nv;//顶点数
 36     int Ne;//边数
 37     WeightType G[MaxVerTexNum][MaxVerTexNum];//邻接矩阵
 38     DataType Data[MaxVerTexNum];//save data of the Vertex;
 39 }GNode,*PtrToGNode;
 40 
 41 typedef PtrToGNode MGraph;
 42 
 43 ElementType DeleteQ( Queue Q );
 44 
 45 Queue CreateQueue( int MaxSize );
 46 
 47 Status IsEmpty( Queue Q );
 48 
 49 Status AddQ( Queue Q, ElementType X );
 50 
 51 MGraph CreateGraph(int VertexNum);//Create a Graph with VertexNum Vertex but without an ege;
 52 
 53 void InsertEdge(MGraph Graph,Edge E);
 54 
 55 MGraph BuildGraph();
 56 
 57 Status IsEdge(MGraph Graph,Vertex V,Vertex W);//检查<V,W>是不是图中的一条边，即W是不是V的邻接点
 58 
 59 void BFS(MGraph Graph,Vertex S);
 60 
 61 void Unweighted(MGraph Graph,int dist[],int path[],Vertex);
 62 
 63 int main(int argc,char** argv)
 64 {
 65     MGraph Graph;
 66     Graph=BuildGraph();
 67 
 68     int i,j;
 69     int dist[100];
 70     int path[100];
 71 
 72     Vertex S=1;
 73     int sum;
 74     for(i=0;i<=99;i++)
 75     {
 76         dist[i]=path[i]=-1;
 77     }
 78 
 79     printf("无向图最短路径\\n");
 80     Unweighted(Graph,dist,path,S);
 81 
 82     for(j=0;j<Graph->Nv;j++){     //出现死循环要多调试
 83         i=j;
 84         sum=0;
 85     while(i!=-1){
 86         
 87         printf("%d",i);
 88         i=path[i];
 89         if(i!=-1){
 90             printf("<--");
 91             sum++;
 92         }
 93         
 94     }
 95     printf("\\n");
 96     printf("从%d到%d的无权图最短路径为%d\\n",S,j,sum);
 97     printf("\\n");
 98     }
 99 
100     //DFS(Graph, 1);
101     return 0;
102 }
103 
104 MGraph CreateGraph(int VertexNum){
105     Vertex V,W;
106     MGraph Graph;
107     Graph=(MGraph)malloc(sizeof(GNode));//form a Graph
108     Graph->Nv=VertexNum;
109     Graph->Ne=0;//
110     for(V=0;V<Graph->Nv;V++)
111         for(W=0;W<Graph->Nv;W++)
112             Graph->G[V][W]=INFINITY;
113         return Graph;
114 }
115 
116 void InsertEdge(MGraph Graph,Edge E){
117     Graph->G[E->V1][E->V2]=E->Weight;
118     //若是无向图还要插入
119     Graph->G[E->V2][E->V1]=E->Weight;
120 }
121 
122 MGraph BuildGraph(){
123     MGraph Graph;
124     Edge E;
125     Vertex V;
126     int Nv,i;
127     printf("输入结点的个数\\n");
128     scanf("%d",&Nv);//the number of vertex
129     Graph=CreateGraph(Nv);//initate graph with Nv vertexs  !!return 回去要赋值给Graph；
130     //getchar();
131     printf("输入弧的个数\\n");
132     scanf("%d",&(Graph->Ne));//read the number of ege
133     if(Graph->Ne!=0)
134     {
135         E=(Edge)malloc(sizeof(ENode));
136         for(i=0;i<Graph->Ne;i++){
137             // getchar();
138             printf("输入弧的信息V1 V2 Weight\\n");
139             scanf("%d %d %d",&(E->V1),&(E->V2),&(E->Weight));
140             InsertEdge(Graph,E);
141         }
142     }
143     // for(V=0;V<Graph->Nv;V++)
144     //     scanf("%c",&(Graph->Data[V]));
145     return Graph;
146 
147 }
148 
149 void Visit(Vertex V){
150     printf("正在访问顶点%d\\n",V);
151 }
152 
153 Status IsEdge(MGraph Graph,Vertex V,Vertex W){
154     return Graph->G[V][W]<INFINITY?TRUE:FALSE;
155 }
156 
157 Queue CreateQueue( int MaxSize )
158 {
159     Queue Q = (Queue)malloc(sizeof(struct QNode));
160     Q->Data = (ElementType *)malloc(MaxSize * sizeof(ElementType));
161     Q->Front = Q->Rear = 0;
162     Q->MaxSize = MaxSize;
163     return Q;
164 }
165  
166 Status AddQ( Queue Q, ElementType X )
167 {
168     if ( IsFull(Q) ) {
169         printf("队列满");
170         return FALSE;
171     }
172     else {
173         Q->Rear = (Q->Rear+1)%Q->MaxSize;
174         Q->Data[Q->Rear] = X;
175         return FALSE;
176     }
177 }
178 ElementType DeleteQ( Queue Q )
179 {
180     if ( IsEmpty(Q) ) { 
181         printf("队列空");
182         return ERROR;
183     }
184     else  {
185         Q->Front =(Q->Front+1)%Q->MaxSize;
186         return  Q->Data[Q->Front];
187     }
188 }
189 
190 Status IsEmpty( Queue Q )
191 {
192     return (Q->Front == Q->Rear);
193 }
194 Status IsFull( Queue Q )
195 {
196     return ((Q->Rear+1)%Q->MaxSize == Q->Front);
197 }
198 
199 void Unweighted(MGraph Graph,int dist[],int path[],Vertex S){
200     Queue Q;
201     Vertex V,W;
202     int MaxSize=100;
203     Q=CreateQueue(MaxSize);
204     dist[S]=0;
205     AddQ(Q,S);
206     while(!IsEmpty(Q))
207     {
208         V=DeleteQ(Q);
209         for(W=0;W<Graph->Nv;W++)
210             if(Graph->G[V][W]!=0&&Graph->G[V][W]!=INFINITY){
211                 if(dist[W]==-1){
212                     dist[W]=dist[V]+1;
213                     path[W]=V;
214                 AddQ(Q,W);
215             }
216             }
217     }
218 }

输入输出示例：