对加权(无负值边)的图进行最短路径搜索

摘要：本次对加权边的图进行单源最短路径搜索.

（1）与无权搜索有什么不一样？以前的算法在加权边上行不通了，这是因为从最短路径为k的点到相邻的点的路径不一定是最短路径，因为这条连接的边可能很长.

（2）基本思路：利用Dijkstra算法-

（3）注意细节：

struct TableEntry
{
List Header;
int distance;
int path;
bool known;
};
typedef TableEntry Table[Number];
void ReadGraph(Graph G,Table T)
{
for (int i =0;i<=Number -1;i++)
{
T[i].Header = G[i];
}
}
void InitTable(Table T,Graph G,int start,int mark)//mark = Infinity/0
{
ReadGraph(G,T);//将图的邻接情况读入表
for (int i = 0;i<=Number-1;i++)
{
T[i].known = false;
T[i].path = Notvertex;
T[i].distance = mark;
}
T[start].distance = Infinity - mark;
}
int FindMinunknown(Table T)
{
int min = Infinity,index;
for (int i = 0;i<=Number-1;i++)
{
if (T[i].known!=true&&T[i].distance < min)
{
min = T[i].distance;
index = i;
}
}
return index;
}

void Dijstra(Table T,int start)
{
//加权无负值
int v,w,cw,counter = 0;
while(counter <=Number-1)
{

//找到最小未知节点
v = FindMinunknown(T);
T[v].known = true;
T[v].Header = T[v].Header->Next;
counter++;//处理好的元素个数加1；
while(T[v].Header!=NULL)
{

w = T[v].Header->Element;
cw = T[v].Header->weight;
if(T[w].known != true&&cw+T[v].distance <T[w].distance)
{
//更新
T[w].distance = cw+T[v].distance;
T[w].path = v;
}
T[v].Header = T[v].Header->Next;
}
}
}