1． 交通咨询系统
任务：设计一个简易交通咨询系统，能让旅客咨询从人一个城市到另一个城市之间的最短路径。
功能要求：
（1） 建立交通网络图的存储结构，并输出
（2） 求单源最短路径（Dijkstra算法），并输出；
（3） 求任一对城市之间的最短路径，并输出。
#include <stdio.h>
#include<malloc.h>
#include <stdlib.h>
#define MaxVerNum 30//定义存储的最大个数
#define NIF 32767 //定义无穷大
#define false 0
#define true 1
typedef char VertexType;//定义顶点表类型是字符型
typedef int Edgetype;
/**建立结构体**/
typedef struct{
VertexType vexs[MaxVerNum];/*顶点表*/
Edgetype edges[MaxVerNum][MaxVerNum];//边表
int n,e; //顶点数和边数
}MGraph;
/**初始化有向图的邻接矩阵存储**/
void CreatGraph(MGraph *G)
{ /**接口参数：图的结构体指针**/
int i,j,k;
printf("How many City and Path?\t(example:4,5):\t");
scanf("%d,%d",&(G->n),&(G->e));//顶点数及边数
printf("\nInput each City's information .\n");
for(i=0;i<G->n;i++)
{
scanf("%s",&(G->vexs[i]));/**输入顶点信息**/
}
for(i=0;i<G->n;i++)
for(j=0;j<G->n;j++)
{
if(i==j) G->edges[i][j]=0;
else G->edges[i][j]=NIF; /**对角线为0,其他为无穷大**/
}
for(k=0;k<G->e;k++)
{
printf("\nInput two Cities include this path(eg:2,3):\t");
scanf("%d,%d",&i,&j);/**输入边的信息**/
printf("\nThen input its weigth:");
scanf("%d",&(G->edges[i][j]));/***权值***/
}
/*****************输出建立好的矩阵********************/
printf("\n==>HAHA!We can easily get this matrix from your input<==\n\n");
for(i=0;i<G->n;i++)
{
printf("%5c",G->vexs[i]);
printf("\t ");
}
printf("\n _________________________________________________\n");
for(i=0;i<G->n;i++)
{
printf("%c|",G->vexs[i]);
for(j=0;j<G->n;j++)
{
printf("%5d ",G->edges[i][j]);
if(j==G->n-1)
printf(" |\n");
}
}
printf(" -------------------------------------------------\n");
}
/***Dijkstra：求得最短路径***/
int Dijkstra(MGraph *G,int v0)
{
int D[MaxVerNum];/**存储v0分别到每个顶点的最短路径**/
int final[MaxVerNum];/**记录是否在D中**/
int i,v,w,min;
for(v=0;v<G->n;++v)
{
final[v]=false;
D[v]=G->edges[v0][v];
}
D[v0]=0;
final[v0]=true;/**v0属于S集**/
for(i=1;i<G->n;++i)
{
min=NIF;
for(w=0;w<G->n;++w)
if(!final[w]&&D[w]<min)
{
v=w;
min=D[w];
}
final[v]=true;
for(w=0;w<G->n;++w)
{
if(!final[w]&&(min+G->edges[v][w]<D[w]))
{
D[w]=min+G->edges[v][w];
}
}
}
printf("\nThe shortest path from $$$> %c <$$$ to each destination is:\n\n",G->vexs[v0]);
for(i=0;i<G->n;i++)
{
printf("%5c",G->vexs[i]);
printf("\t "); /**此部分实现可视化**/
}
printf("\n _______________________________________________\n");
printf("%c|",G->vexs[v0]);
for(w=0;w<G->n;w++)
printf("%5d |",D[w]);
printf("\n -----------------------------------------------\n");
return 1;
}//:~
/**Floyd求得各顶点间最短路径**/
int Floyd(MGraph *G,int n)
{
int P[MaxVerNum][MaxVerNum][MaxVerNum];
int D[MaxVerNum][MaxVerNum];
int u,v,w,i;
for(v=0;v<G->n;++v)
for(w=0;w<G->n;++w)
{
D[v][w]=G->edges[v][w];
for(u=0;u<G->n;++u)
P[v][w][u]=0;
if(D[v][w]<NIF)
{
P[v][w][v]=1;
P[v][w][w]=1;
}//if
}//for
for(u=0;u<G->n;++u)
for(v=0;v<G->n;++v)
for(w=0;w<G->n;++w)
if(D[v][u]+D[u][w]<D[v][w])
{
D[v][w]=D[v][u]+D[u][w];
for(i=0;i<G->n;++i)
P[v][w][i]=P[v][u][i]||P[u][w][i];
}
/*********输出最后结果***********/
for(i=0;i<G->n;i++)
{
printf("%5c",G->vexs[i]);
printf("\t ");
}
printf("\n\nAfter search,we can get this minumum matrix.\n\n");
for(i=0;i<G->n;i++)
{
printf("%5c",G->vexs[i]);
printf("\t ");
}
printf("\n _______________________________________________\n");
for(i=0;i<G->n;i++)
{
printf("%c|",G->vexs[i]);
for(v=0;v<G->n;v++)
{
if(!D[i][v]||D[i][v]==NIF) printf("-----\t");
else printf("%5d \t",D[i][v]);
if(v==G->n-1)
printf(" |\n");
}
}
printf(" -----------------------------------------------\n");
/********************输出最短路径*******************************/
printf("\nThis matrix can tell us the path to each destintion\n");
for(i=0;i<G->n;i++)
{
printf("%5c",G->vexs[i]);
printf("\t ");
}
printf("\n _________________________________________________\n");
for(i=0;i<G->n;i++)
{
printf("%c|",G->vexs[i]);
for(u=0;u<G->n;u++)
{
printf("%5d ",P[i][u][i]);
if(u==G->n-1)
printf(" |\n");
}
}
printf(" -------------------------------------------------\n");
/***************************************************************/
return 1;
}
/**************主函数部分***************/
int main()
{
int m;
int ch;
MGraph *S;
S=(MGraph*)malloc(sizeof(MGraph));
printf("\t***************************************************\n");
printf("\t*\t WELCOME TO USE OUR SMART SYSTEM \t *\n");
printf("\t*\tWe would try our best to serve for you! *\n");
printf("\t***************************************************\n");
poin1:/**跳转作用**/
printf("\n\t What can I do for you sir?\n");
printf("---------------------------------------------------\n");
printf("|1.Creat a graph\n|2.Search the shortest path\n");
printf("|3.Find the shortest path between each two solutin\n");
printf("|4.exit system!\n");
printf("---------------------------------------------------\n");
printf("Input here please:\t");
scanf("%d",&ch);
switch(ch)
{
/**********调用创建邻接矩阵函数***********/
case 1: CreatGraph(S);goto poin1;
/************调用Djkstra函数************/
case 2:
printf("\nWhere are you now?[tips==>(0~5) stand for (a~f)]:");
scanf("%d",&m);
Dijkstra(S,m);goto poin1;
/*************调用Floyd函数*************/
case 3:
Floyd(S,S->n);goto poin1;
case 4:
return 0;break;//直接推出系统
default:
printf("\n\tWarning!!!==>Input errer!Try again please!\n");
goto poin1;
}
return 0;
}