图的邻接矩阵表示方式——有权图的最短路径Floyd算法

最新推荐文章于 2022-05-20 18:59:02 发布

转载最新推荐文章于 2022-05-20 18:59:02 发布 · 141 阅读

0 ·

CC 4.0 BY-SA版权

原文链接：http://www.cnblogs.com/lovecodepql/p/7781046.html

本文介绍了一种使用C语言实现图论中Floyd算法的方法。通过定义顶点和边的数据结构，初始化邻接矩阵，并实现Floyd算法来求解任意两点间的最短路径。此外，还提供了完整的代码示例。

  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 
 13 typedef int ElementType;
 14 typedef int Status;
 15 typedef int WeightType;
 16 typedef int Vertex;
 17 typedef char DataType;
 18 
 19 typedef  struct  ENode{
 20     Vertex V1,V2;     //有向边<v1,V2>
 21     WeightType Weight;//权重
 22 }ENode,*PtrToENode ;
 23 
 24 typedef PtrToENode Edge;
 25 
 26 typedef struct GNode{
 27     int Nv;//顶点数
 28     int Ne;//边数
 29     WeightType G[MaxVerTexNum][MaxVerTexNum];//邻接矩阵
 30     DataType Data[MaxVerTexNum];//save data of the Vertex;
 31 }GNode,*PtrToGNode;
 32 
 33 typedef PtrToGNode MGraph;
 34 
 35 MGraph CreateGraph(int VertexNum);//Create a Graph with VertexNum Vertex but without an ege;
 36 
 37 void InsertEdge(MGraph Graph,Edge E);
 38 
 39 MGraph BuildGraph();
 40 
 41 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
 42 
 43 Status Floyd( MGraph Graph, WeightType D[][MaxVerTexNum], Vertex path[][MaxVerTexNum] );
 44 
 45 int main(int argc,char** argv)
 46 {
 47     MGraph Graph;
 48     Graph=BuildGraph();
 49     int D[MaxVerTexNum][MaxVerTexNum];
 50     int path[MaxVerTexNum][MaxVerTexNum];
 51     int i,j;
 52     int count=0;
 53     Floyd(Graph,D,path);
 54 
 55     for(i=0;i<Graph->Nv;i++)
 56         for(j=0;j<Graph->Nv;j++)
 57         {    
 58             count++;
 59             printf("%d ",D[i][j]);
 60             if(count%Graph->Nv==0)
 61                 printf("\n");
 62         }
 63         count=0;
 64     for(i=0;i<Graph->Nv;i++)
 65         for(j=0;j<Graph->Nv;j++)
 66         {    
 67             count++;
 68             if(path[i][j]==-1)
 69             printf("%d ",path[i][j]);
 70             else
 71                 printf(" %d ",path[i][j]);
 72 
 73             if(count%Graph->Nv==0)
 74                 printf("\n");
 75         }
 76     return 0;
 77 }
 78 
 79 MGraph CreateGraph(int VertexNum){
 80     Vertex V,W;
 81     MGraph Graph;
 82     Graph=(MGraph)malloc(sizeof(GNode));
 83     Graph->Nv=VertexNum;
 84     Graph->Ne=0;//
 85     for(V=0;V<Graph->Nv;V++)
 86         for(W=0;W<Graph->Nv;W++)
 87             Graph->G[V][W]=INFINITY;
 88         return Graph;
 89 }
 90 
 91 void InsertEdge(MGraph Graph,Edge E){
 92     Graph->G[E->V1][E->V2]=E->Weight;
 93     //若是无向图还要插入
 94     Graph->G[E->V2][E->V1]=E->Weight;
 95 }
 96 
 97 MGraph BuildGraph(){
 98     MGraph Graph;
 99     Edge E;
100     Vertex V;
101     int Nv,i;
102     printf("输入结点的个数\n");
103     scanf("%d",&Nv);//the number of vertex
104     Graph=CreateGraph(Nv);//initate graph with Nv vertexs  !!return 回去要赋值给Graph；
105     //getchar();
106     printf("输入弧的个数\n");
107     scanf("%d",&(Graph->Ne));//read the number of ege
108     if(Graph->Ne!=0)
109     {
110         E=(Edge)malloc(sizeof(ENode));
111         for(i=0;i<Graph->Ne;i++){
112             // getchar();
113             printf("输入弧的信息V1 V2 Weight\n");
114             scanf("%d %d %d",&(E->V1),&(E->V2),&(E->Weight));
115             InsertEdge(Graph,E);
116         }
117     }
118     // for(V=0;V<Graph->Nv;V++)
119     //     scanf("%c",&(Graph->Data[V]));
120     return Graph;
121 
122 }
123 Status IsEdge(MGraph Graph,Vertex V,Vertex W){
124     return Graph->G[V][W]<INFINITY?TRUE:FALSE;
125 }
126 
127 
128 Status Floyd( MGraph Graph, WeightType D[][MaxVerTexNum], Vertex path[][MaxVerTexNum] ){
129     Vertex i, j, k;
130     //上面默认没有赋值的便都是INFINITY,因此要重新置零
131         for(i=0;i<Graph->Nv;i++)
132             for(j=0;j<Graph->Nv;j++)
133                 if(i==j)
134                     Graph->G[i][j]=0;
135 
136     
137     
138     for ( i=0; i<Graph->Nv; i++ )
139         for( j=0; j<Graph->Nv; j++ ) {
140             D[i][j] = Graph->G[i][j];
141             path[i][j] = -1;
142         }
143 
144     for( k=0; k<Graph->Nv; k++ )
145         for( i=0; i<Graph->Nv; i++ )
146             for( j=0; j<Graph->Nv; j++ )
147                 if( D[i][k] + D[k][j] < D[i][j] ) {
148                     D[i][j] = D[i][k] + D[k][j];
149                     if ( i==j && D[i][j]<0 ) /* 若发现负值圈 */
150                         return FALSE; /* 不能正确解决，返回错误标记 */
151                     path[i][j] = k;
152                 }
153     return OK;
154 
155 
156 
157 }

转载于:https://www.cnblogs.com/lovecodepql/p/7781046.html