Bellman-Ford算法实现类

貌似Bellman-Ford算法和Dijkstra算法类似，只是多了个处理负权值的考虑。不过Bellman-Ford算法比较简单易懂，虽然复杂度较高，有O(VE)。

算法类如下，至于介绍吧，维基（http://en.wikipedia.org/wiki/Bellman%E2%80%93Ford_algorithm）上面蛮详细的。

三个步骤：

1、数组Distant[i]记录从源点s到顶点i的路径长度，初始化数组Distant[n]为无穷大, Distant[s]为0；
2、以下操作循环执行至多n-1次，n为顶点数：
对于每一条边e(u, v)，如果Distant[u] + w(u, v) < Distant[v]，则另Distant[v] = Distant[u]+w(u, v)。w(u, v)为边e(u,v)的权值；
若上述操作没有对Distant进行更新，说明最短路径已经查找完毕，或者部分点不可达，跳出循环。否则执行下次循环；
3、为了检测图中是否存在负环路，即权值之和小于0的环路。对于每一条边e(u, v)，如果存在Distant[u] + w(u, v) < Distant[v]的边，则图中存在负环路，即是说改图无法求出单源最短路径。否则数组Distant[n]中记录的就是源点s到各顶点的最短路径长度。

#include <iostream>#define POINTNUM 10#define NOSET_POSITIVE_INT -1#define INIFINITE 2147483647using namespace std;struct Edge {int source;int destination;int weight;};class Graph{public:Edge graphEdge[POINTNUM * POINTNUM];int edgeNum;int pointNum;int source;int destination;int distance[POINTNUM];Graph();bool BellmanFord();private:void initialize();//Initialize the variables.void relaxEdges();//Relax the edges.bool checkNegativeCycle();//Check negative weight cycles.};Graph::Graph(){edgeNum = 0;pointNum = 0;source = NOSET_POSITIVE_INT;destination = NOSET_POSITIVE_INT;}void Graph::initialize(){for (int i = 0; i < pointNum; i++){distance[i] = INIFINITE;}distance[source] = 0;}void Graph::relaxEdges(){unsigned int a;unsigned int b;for (int i = 1; i < pointNum; i++){for (int j = 0; j < edgeNum; j++){a = (unsigned int)distance[graphEdge[j].source] + (unsigned int)graphEdge[j].weight;b = (unsigned int)distance[graphEdge[j].destination];if (a < b){distance[graphEdge[j].destination] = a;}}}}bool Graph::checkNegativeCycle(){unsigned int a;unsigned int b;for (int i = 0; i < edgeNum; i++){a = (unsigned int)distance[graphEdge[i].source] + (unsigned int)graphEdge[i].weight;b = (unsigned int)distance[graphEdge[i].destination];if (a < b){return false;}}return true;}bool Graph::BellmanFord(){initialize();relaxEdges();return checkNegativeCycle();}int main(){Graph a;cin >> a.edgeNum;cin >> a.pointNum;for (int i = 0; i < a.edgeNum; i++){cin >> a.graphEdge[i].source >> a.graphEdge[i].destination >> a.graphEdge[i].weight;}cin >> a.source;if( a.BellmanFord() ){for (int i = 0; i < a.pointNum; i++){cout << "Distance: " << a.distance[i] << endl;}}return 0;}