数据结构——图-最短路径长度中最大的一个

在这里插入图片描述

#include<stdio.h>
#include<string.h>
#define INF 32767
#define MAXVEX 30
int dist[MAXVEX];		 //建立dist数组int path[MAXVEX];		 //建立path数组int S[MAXVEX];		 //建立S数组typedef char VertexType;typedef struct graph
{int n,e;VertexType vexs[MAXVEX];int edges[MAXVEX][MAXVEX];
}MGraph;void CreateMGraph(MGraph &G)
{int n,e;int value;char temp_i;char temp_j;printf("请输入图的顶点数和边数（以空格分隔）：");scanf("%d%d",&n,&e);G.n=n;G.e=e;for(int i=0;i<n;i++){for(int j=0;j<n;j++){if(i==j)G.edges[i][j]=0;elseG.edges[i][j]=32767;}}printf("输入顶点信息：");for(int j=0;j<G.n;j++){getchar();scanf("%c",&G.vexs[j]);}int temp_number_i;int temp_number_j;printf("请输入每条边的权值：\n");for(int j=0;j<e;j++){getchar();scanf("%c %c %d",&temp_i,&temp_j,&value);for(int i=0;i<n;i++){if(G.vexs[i]==temp_i)temp_number_i=i;if(G.vexs[i]==temp_j)temp_number_j=i;}G.edges[temp_number_i][temp_number_j]=value;}}void DispMGraph(MGraph &G)
{printf("输出顶点信息：\n");for(int i=0;i<G.n;i++){printf("%c",G.vexs[i]);} printf("\n输出邻接矩阵：\n");printf("\t");for(int i=0;i<G.n;i++)printf("%8c",G.vexs[i]); for(int i=0;i<G.n;i++){printf("\n%8c",G.vexs[i]);for(int j=0;j<G.n;j++){if(G.edges[i][j]==32767) //两点之间无连接时权值为默认的32767，// 在无向图中一般用"0"表示，在有向图中一般用"∞",// 这里为了方便统一输出 "∞"printf("%8s", "∞");elseprintf("%8d",G.edges[i][j]);}printf("\n");}
}void Dijkstra(MGraph g, int v)
{  //求从v到其他顶点的最短路径int mindis,i,j,u=0;for (i=0;i<g.n;i++){	dist[i]=g.edges[v][i]; //距离初始化S[i]=0;			 //S[]置空if (g.edges[v][i]<INF) //路径初始化path[i]=v;		 //v→i有边时，置i前一顶点为velse			 //v→i没边时，置i前一顶点为-1path[i]=-1;}S[v]=1;			//源点编号v放入S中for (i=0;i<g.n-1;i++)	//循环向S中添加n-1个顶点{  mindis=INF;		//mindis置最小长度初值for (j=0;j<g.n;j++)	//选取不在S中且有最小距离顶点uif (S[j]==0 && dist[j]<mindis) {  u=j;mindis=dist[j];}S[u]=1;			//顶点u加入S中for (j=0;j<g.n;j++)	//修改不在s中的顶点的距离if (S[j]==0)if (g.edges[u][j]<INF&& dist[u]+g.edges[u][j]<dist[j]){  dist[j]=dist[u]+g.edges[u][j];path[j]=u;}}
}void Print(MGraph G,int v)
{printf("\n");for(int i=0;i<G.n;i++){if(i!=v && dist[i]!=INF){printf("%c到%c的最短距离为：%d\n",G.vexs[v],G.vexs[i],dist[i]);}else if(dist[i]==INF){printf("%c与%c之间无路径！\n",G.vexs[v],G.vexs[i]); } }printf("\n"); 
}/*------------------输出从顶点v出发的所有最短路径-------------------*/
static void Dispath(MGraph g, int v)
{int i, j, k;int apath[MAXVEX], d;                         //存放一条最短路径(逆向)及其顶点个数//循环输出从顶点v到i的路径for(i = 0; i < g.n; i++){if(S[i] == 1 && i != v){printf("从顶点%c到顶点%c的路径长度为:%d\t路径为:", g.vexs[v], g.vexs[i], dist[i]);d = 0; apath[d] = i;                //添加路径上的终点k = path[i];if(k == -1)                         //没有路径的情况printf("无路径\n");else                                //存在路径时输出该路径{while(k != v){d++;apath[d] = k;k = path[k];}d++; apath[d] = v;              //添加路径上的起点printf("%c ",  g.vexs[apath[d]]);         //先输出起点for(j = d - 1; j >= 0; j--)     //再输出其余顶点printf("  %c ", g.vexs[apath[j]]);printf("\n");}}}
}
static void Dispath2(MGraph g, int v,int w)
{int i, j, k;int apath[MAXVEX], d;                         //存放一条最短路径(逆向)及其顶点个数//循环输出从顶点v到i的路径for(i = 0; i < g.n; i++){if(S[i] == 1 && i != v&&i==w){printf("%d\n",dist[i]);d = 0; apath[d] = i;                //添加路径上的终点k = path[i];if(k == -1)                         //没有路径的情况printf("无路径\n");else                                //存在路径时输出该路径{while(k != v){d++;apath[d] = k;k = path[k];}d++; apath[d] = v;	              //添加路径上的起点printf("%c ",  g.vexs[apath[d]]);         //先输出起点for(j = d - 1; j >= 0; j--)     //再输出其余顶点printf("  %c ", g.vexs[apath[j]]);printf("\n");}}}
}void min_shortest_path(MGraph G,int v)
{int mindist=dist[0];int temp;for(int i=1;i<G.n;i++){if(mindist<dist[i]){mindist=dist[i];temp=i;}}printf("图中距离顶点%c最短路径长度中最大的为:",G.vexs[v]);Dispath2(G, v,temp);} 
int main()
{MGraph G;CreateMGraph(G);DispMGraph(G);Dijkstra(G,0);Print(G,0);Dispath(G,0);min_shortest_path(G,0);
}