Dijkstra算法实现类—邻接矩阵，一般实现

（在后面更新了Dijkstra算法的实现，用邻接表+优先队列实现。链接如下：http://blog.csdn.net/betabin/article/details/7390403）

有向权图关于单源最短路径算法，Dijkstra算法。

算法可以形象理解为小城镇（最开始就是起点）的扩张，最后把世界吃掉。每次挑选一个离小城镇最近的地点，然后吃掉，更新各个未吃掉的地点到小城镇的距离。刷新距离主要是比较到刚刚吃掉的地点的距离和之前的最短距离。详细的也不多讲，贴出代码。简单易懂，图就用简单的矩阵表示，时间复杂度O(V²)。（V表示点数。）

#include <iostream>#include <set>using namespace std;#define GRAPHSIZE 100#define NOSET_INT -1#define ERROR_POSITIVE_NUM -1#define INFINITE 2147483647class Graph{public:int weight[GRAPHSIZE][GRAPHSIZE];int source;int destination;Graph();//Initialize all variables.int getShortByDijkstra();//Get the shortest weight by Dijkstra.private:set<int> sourceSet;set<int> destinationSet;int getNextShortPoint(int shortvalue[]);//Find next shortest point in destination set.void refreshShortest(int nextshortpoint, int shortvalue[]);//Refresh the array of shortvalue.};Graph::Graph(){source = NOSET_INT;destination = NOSET_INT;for (int i = 0; i < GRAPHSIZE; i++){for (int j = 0; j < GRAPHSIZE; j++){weight[i][j] = INFINITE;}destinationSet.insert(i);}}int Graph::getShortByDijkstra(){if ( NOSET_INT == source || NOSET_INT == destination){return ERROR_POSITIVE_NUM;}else if (source == destination){return 0;}sourceSet.insert(source);destinationSet.erase(source);int shortest[GRAPHSIZE];for (int i = 0; i < GRAPHSIZE; i++){shortest[i] = weight[source][i];}shortest[source] = 0;int shortestPoint;for (int j = 1; j < GRAPHSIZE; j++){shortestPoint = getNextShortPoint(shortest);if (INFINITE == shortest[shortestPoint]){return INFINITE;}else if (shortestPoint == destination){return shortest[shortestPoint];}sourceSet.insert(shortestPoint);destinationSet.erase(shortestPoint);refreshShortest(shortestPoint, shortest);}return ERROR_POSITIVE_NUM;}int Graph::getNextShortPoint(int shortvalue[]){set<int>::iterator scanner = destinationSet.begin();int shortestpoint = *scanner;while (scanner != destinationSet.end()){if (shortvalue[shortestpoint] > shortvalue[*scanner]){shortestpoint = *scanner;}scanner++;}return shortestpoint;}void Graph::refreshShortest(int nextshortpoint, int shortvalue[]){set<int>::iterator scanner = destinationSet.begin();while (scanner != destinationSet.end()){unsigned int a = shortvalue[*scanner];unsigned int b = (unsigned int)shortvalue[nextshortpoint] + (unsigned int)weight[nextshortpoint][*scanner];if (a > b){shortvalue[*scanner] = shortvalue[nextshortpoint] + weight[nextshortpoint][*scanner];}scanner++;}}int main(){Graph school;int n;int s, d, w;cin >> n;for (int i = 0; i < n; i++){cin >> s >> d >> w;school.weight[s][d] = w;}cin >> school.source >> school.destination;cout << school.getShortByDijkstra() << endl;return 0;}