无权最短路劲 地址：http://blog.csdn.net/midgard/article/details/4152336

<span style="font-family: Arial, Helvetica, sans-serif;">解决单源最短路径的一个常用算法叫做：Dijkstra算法，这是一个非常经典的贪心算法例子。</span>

<span style="font-family: Arial, Helvetica, sans-serif;">注意：这个算法只对权值非负情况有效。在每个阶段，Dijkstra算法选择一个顶点v，它在所有unknown顶点中具有最小的distance，同时算法将起点s到v的最短路径声明为known。这个算法的本质就是 给定起点，然后假设你有一个点集（known点集），对这个点集中的点，我们已经求出起点到其的最短距离。然后慢慢扩张这个集合。直到某一时刻它包括目标点。具体概念详细介绍见书吧，下面结合一个例子，阐述一下该算法遍历顶点的过程。    假设开始顶点s为v1。则，第一个选择的顶点是v1，路径长是0，该顶点标记为known，                1： known(v1)    unknown(v2,v3,v4,v5,v6,v7);    这时由known点集扩充，v4 为下一个最短路径顶点，路径长为1，标记v4为known                            2： known(v1,v4) unknown(v2,v3,v5,v6,v7);       这时由known点集扩充，v2 为下一个最短路径顶点，路径长为2，标记v2为known                3： known(v1,v4,v2) unknown(v3,v5,v6,v7);       这时由known点集扩充，v3，v5 为下一个最短路径顶点，路径长为3, 标记v3，v5为known                  4:  known(v1,v4,v2,v3,v5) unknown(v6,v7);       这时由known点集扩充，v7 为下一个最短路径顶点，路径长为5, 标记v7为known                5:  known(v1,v4,v2,v3,v5,v7) unknown(v6);       这时由known点集扩充，v6 为下一个最短路径顶点，路径长为6, 标记v6为known            // Map.cpp : 定义控制台应用程序的入口点。</span>

//#include "stdafx.h"#include <iostream>using namespace std;#define MAX_VERTEX_NUM    20#define INFINITY    2147483647 struct adjVertexNode {int adjVertexPosition;int weight;adjVertexNode* next; };struct VertexNode{char data[2];int distance;bool known;VertexNode* path;adjVertexNode* list;}; struct Graph{VertexNode VertexNode[MAX_VERTEX_NUM];int vertexNum;int edgeNum;};void CreateGraph (Graph& g){int i, j, edgeStart, edgeEnd, edgeWeight;adjVertexNode* adjNode;cout << "Please input vertex and edge num (vnum enum):" <<endl;cin >> g.vertexNum >> g.edgeNum;cout << "Please input vertex information (v1)/n note: every vertex info end with Enter" <<endl;for (i=0;i<g.vertexNum;i++) {cin >> g.VertexNode[i].data; // vertex data info.g.VertexNode[i].list=NULL; }cout << "input edge information(start end weight):" <<endl;for (j=0; j<g.edgeNum; j++) { cin >>edgeStart >>edgeEnd >> edgeWeight; adjNode = new adjVertexNode; adjNode->weight = edgeWeight;adjNode->adjVertexPosition = edgeEnd-1; // because array begin from 0, so it is j-1// 将邻接点信息插入到顶点Vi的边表头部,注意是头部！！！不是尾部。adjNode->next=g.VertexNode[edgeStart-1].list; g.VertexNode[edgeStart-1].list=adjNode; }}void PrintAdjList(const Graph& g){for (int i=0; i < g.vertexNum; i++){cout<< g.VertexNode[i].data << "->";adjVertexNode* head = g.VertexNode[i].list;if (head == NULL)cout << "NULL";while (head != NULL){cout << head->adjVertexPosition + 1 <<" ";head = head->next;}cout << endl;}}void DeleteGraph(Graph &g){for (int i=0; i<g.vertexNum; i++){adjVertexNode* tmp=NULL;while(g.VertexNode[i].list!=NULL){tmp = g.VertexNode[i].list;g.VertexNode[i].list = g.VertexNode[i].list->next;delete tmp;tmp = NULL;}}}VertexNode* FindSmallestVertex(Graph& g){int smallest = INFINITY;VertexNode* sp = NULL;for (int i=0; i<g.vertexNum; i++){if (!g.VertexNode[i].known && g.VertexNode[i].distance < smallest){smallest = g.VertexNode[i].distance;sp = &(g.VertexNode[i]);}}return sp;}void Dijkstra(Graph& g, VertexNode& s){int i;for (i=0; i<g.vertexNum; i++){g.VertexNode[i].known = false;g.VertexNode[i].distance = INFINITY;g.VertexNode[i].path = NULL;}s.distance = 0;for(i=0; i<g.vertexNum; i++){VertexNode* v = FindSmallestVertex(g);if(v==NULL)break;v->known = true;adjVertexNode* head = v->list;while (head != NULL){VertexNode* w = &g.VertexNode[head->adjVertexPosition];if( !(w->known) ){if(v->distance + head->weight < w->distance){w->distance = v->distance + head->weight;w->path = v;}}head = head->next;}}}void PrintPath(Graph& g, VertexNode* source, VertexNode* target){if (source!=target && target->path==NULL){cout << "There is no shortest path from " << source->data <<" to " << target->data <<endl;}else{if (target->path!=NULL){PrintPath(g, source, target->path);cout << " ";}cout << target->data ;}}int main(int argc, const char ** argv){Graph g;CreateGraph(g);PrintAdjList(g);VertexNode& start = g.VertexNode[0];VertexNode& end = g.VertexNode[6];Dijkstra(g, start);cout << "print the shortest path from v1 to v7" << endl;PrintPath(g, &start, &end);cout << endl;DeleteGraph(g);return 0;}