bool Shortest_Path_Faster_Algorithm(int source,int destination)//if by Adjacency Matrix is in O(N^3)
{
// Step 1: initialize graph
AStack stk;
LQueue<int> Q;
int minDistanceMatrix[numVertex];
int prevNode[numVertex];
for (int i=0;i<numVertex;++i) prevNode[i]=UNDEFINED;
for (int i=0;i<numVertex;++i) minDistanceMatrix[i]=INFINITY;
minDistanceMatrix[source]=0;
Q.enqueue(source);
while (Q.length>0){
int v=Q.dequeue();
for (int w=first(v);w<numVertex;w=next(v,w)){
if (getWeight(v,w)+minDistanceMatrix[v]<minDistanceMatrix[w]){
minDistanceMatrix[w]=minDistanceMatrix[v]+getWeight(v,w);
prevNode[w]=v;
Q.enqueue(w);
}
}
}
cout<<minDistanceMatrix[destination]<<endl;
cout<<source+1<<" ";
while (prevNode[destination]!=UNDEFINED){
stk.push(destination+1);
destination=prevNode[destination];
}
while (stk.length()>0) cout<<stk.pop()<<" ";
cout<<endl;
}
void Dijkstra_Algorithm(int source,int destination)
{
AStack stk;
int minDistanceMatrix[numVertex];
int prevNode[numVertex];
for (int i=0;i<numVertex;++i) minDistanceMatrix[i]=INFINITY;
for (int i=0;i<numVertex;++i) prevNode[i]=UNDEFINED;
minDistanceMatrix[source]=0;
for (int i=0;i<numVertex;++i) mark[i]=UNVISTED;
for (int i=0;i<numVertex;++i){
int v=findMin(minDistanceMatrix);
mark[v]=VISTED;
for (int w=first(v);w<numVertex;w=next(v,w)){
if (minDistanceMatrix[v]+getWeight(v,w)<minDistanceMatrix[w]) {
minDistanceMatrix[w]=minDistanceMatrix[v]+getWeight(v,w);
prevNode[w]=v;
}
}
}
cout<<minDistanceMatrix[destination]<<endl;
cout<<source+1<<" ";
while (prevNode[destination]!=UNDEFINED){
stk.push(destination+1);
destination=prevNode[destination];
}
while (stk.length()>0) cout<<stk.pop()<<" ";
cout<<endl;
}