无向图的最短路径算法（队列实现 )

在程序的当前目录下，建立一个graph.txt，将以下内容保存其中，作为图的输入即可.

v1  v2 

v1  v3

v1  v4

v2  v4 

v2  v5

v3  v6

v4  v3

v4  v6

v4  v7

v5  v4

v5  v7

v7  v6

 

/* # Unweighted Graph Shortest Path Algorithm # Copyright (C) 2010-**** Long Cheng <fantasywindy@gmail.com> # @version 1.1.1-20100725 */ #include <iostream> #include <string> #include <queue> #include <fstream> #include <sstream> #include <limits.h> using std::cout; using std::cin; using std::endl; using std::string; using std::queue; using std::istringstream; using std::getline; using std::ifstream; #define MAX 100 //定义图的最大顶点数量为了100 #define INFINITY INT_MAX typedef struct Edge //定义图的边 { int weight; //边的权值,此程序中没有用上 int next; //边的结束顶点，如边v1->v2的话，那么next就是顶点v2的编号 struct Edge *nextEdge; //下一个邻边 } Edge; typedef struct Node { Edge *firstEdge; //从该顶点出发的第一条边 int no; //顶点的编号(程序中的内部编号) string val; //顶点的标签,如v1顶点显示为字符串"v1" int Dis; int path; bool known; }Node; typedef Node NodeList[MAX]; typedef struct Graph //定义图的数据结构 { int n; //图的顶点数 int e; //图的边数(此程序中没有用上) NodeList nodes; //图的顶点数组 }Graph; int SearchVertex(Graph *g, string str) //在图中寻找标记为"XXX"的顶点是否已经出现过 { for(int i=0; i<g->n; ++i) { if( str == g->nodes[i].val ) { return i; } } return -1; } void unweighted(Graph *g, string str) //无向图的最短路径算法 { queue<int> q; //初始化队列 int s=SearchVertex(g, str); //查找输入的点的真实编号 g->nodes[s].Dis=0; //将初始点的Dis设置为0，然后进入队列 q.push(s); while( q.empty() == false ) //当队列不空的时候循环 { int k = q.front(); //出队列，将出队列点的known域设置为已知，并且将邻接点中尚未知的点的Dis域设为自身的Dis域加1，然后推入队列 q.pop(); g->nodes[k].known = true; Edge *p = g->nodes[k].firstEdge; while( p != NULL ) { if( g->nodes[p->next].Dis == INFINITY ) { g->nodes[p->next].Dis = g->nodes[k].Dis + 1; g->nodes[p->next].path = k; q.push(p->next); } p = p->nextEdge; } } } void printPath(Graph *g, int i) //打印各点的路径 { if( g->nodes[i].path != -1 ) { printPath(g, g->nodes[i].path); } cout<<" "<<g->nodes[i].val; } void printAll(Graph *g) //打印总路径 { for(int i=0; i<g->n; ++i) { if( g->nodes[i].known == true ) { cout<<"Node: "<<g->nodes[i].val<<'/t'<<"Path: "; printPath(g, i); } else { cout<<"Node: "<<g->nodes[i].val<<" can not be touched"; } cout<<endl; } } int main() { Graph *g=new Graph; string v1; string v2; int nodecount=0; int edgecount=0; ifstream file("graph.txt"); string line; while(getline(file,line)) //输入所有的边 { istringstream istr(line); istr>>v1>>v2; int v1_no; int v2_no; if( ( v1_no=SearchVertex(g, v1) ) == -1 ) //判断边的两个顶点是否之前已经出现过，若未出现过，则初始化此顶点 { g->nodes[nodecount].val=v1; g->nodes[nodecount].no=nodecount; g->nodes[nodecount].firstEdge=NULL; g->nodes[nodecount].Dis=INFINITY; g->nodes[nodecount].known=false; g->nodes[nodecount].path=-1; v1_no=nodecount; ++nodecount; g->n=nodecount; } if( ( v2_no=SearchVertex(g, v2) ) == -1 ) { g->nodes[nodecount].val=v2; g->nodes[nodecount].no=nodecount; g->nodes[nodecount].firstEdge=NULL; g->nodes[nodecount].Dis=INFINITY; g->nodes[nodecount].known=false; g->nodes[nodecount].path=-1; v2_no=nodecount; ++nodecount; g->n=nodecount; } Edge *e=new Edge; //将边插入对应的顶点的边链表 e->next=v2_no; e->nextEdge=NULL; Edge *p=g->nodes[v1_no].firstEdge; Edge *q=NULL; while( p != NULL ) { q=p; p=p->nextEdge; } if( q == NULL ) { g->nodes[v1_no].firstEdge=e; } else { q->nextEdge=e; } } unweighted(g, "v1"); printAll(g); for(int i=0; i<g->n; ++i) //释放边new出来的堆空间 { Edge *pre, *cur; cur=g->nodes[i].firstEdge; pre=NULL; while( cur != NULL ) { pre=cur; cur=cur->nextEdge; delete pre; } } delete g; //释放图new 出来的空间 return 0; }