Dijkstra's algorithm (updating the heap)

Question

I am implementing Dijkstra's algorithm using a heap data structure. I also use an array that keeps track of the "probable minimum distances" of the nodes. The problem is when I am updating the array, how to update the corresponding values in the heap?

ok here's the code

typedef struct temp                       
{
    int nodeTag;    
    int weight; 
    struct temp *next;
}myStruct;  //this structure corresponds to the elements of the linked list 

typedef struct temp *link;

typedef struct
{ 
    int nodeTag;   //each node has an integer nodeTag associated with it
    link l;
}head;    //the head of the elements of the adjacency list

typedef struct {
    head *adjList;
    int numNodes;
    int numEdges;
} Graph;

typedef struct {
    int possibleMinWeight;
    int minFound;    //minFound==1 if true min is found
} dummy;

dummy *dijkstraSSSP(Graph G, int nodeTag)
{
    minHeap H=createEmptyHeap(G.numNodes);  
    while(i=0;i<G.numNodes;i++)
    {
        if(i!=nodeTag)      
            H.A[i].priority=INFINITY;
        else 
            H.A[i].priority=0;
        H.A[i].nodeTag=i;
    }

    convertIntoHeap(H);

    int min;    

    dummy *A=(dummy *)malloc(sizeof(int)*G.numNodes);

    A[nodeTag-1].possibleMinWeight=0;
    A[nodeTag-1].minFound=1; 

    while(!isEmpty(H))
    {
        element e=findMin(H);   H=deleteMin(H);

        A[e.nodeTag-1].minFound=1;      

        link l=G.adjList[e.nodeTag-1].l;        
        while(l!=NULL)
        {
            if(A[l->nodeTag-1].minFound==0);    //its true minimum distance is yet to be found 
            {               
                if(A[l->nodeTag-1].possibleMinWeight>A[x-1].possibleMinWeight+(l->weight))
                    A[l->nodeTag-1].possibleMinWeight=A[x-1]+(l->weight);
            }                   
            l=l->next;
        }
    }   
    return A;
}

Answer 1

To write DecreaseKey, you need the priority-queue implementation to maintain a map from nodeTags to locations in the queue. That means updating this map whenever the binary-heap data structure calls for a swap or perhaps choosing a pointer-based implementation like pairing heaps that never moves nodes in memory.

Unless you have a large, somewhat dense graph, DecreaseKey isn't worth it; just insert a node multiple times and ignore duplicate results from ExtractMin. (To detect duplicates: every time I've implemented Dijkstra, I've needed either the distances or the tree. In my programming languages of choice, it's easy enough to shake loose a bit from either array to remember whether each node has been visited.)