let A,B,C be nodes of directed graph with edges A->B,B->A,A->C,C->A,B->C,C->B then no of paths will be 5 that is A,A->B,A->C,A->B->C,A->C->B
If i apply dfs and increase counter for every node i visit, it wont find all paths for example if it finds A,A->B,A->B->C then after backtrack it wont traverse A->C and further A->C->B because C and B are marked as visited.
So i modified the dfs where i unmarked the visited node when algorithm backtracks to its parent.
Procedure dfs(arr,s,vis): #s is source node vis[s]=True #mark as visited count+=1 #no of paths for all i adjacent to s: if not vis[i]: dfs(arr,i,vis) vis[s]=False #mark visited as false again(modification)
After modification, algorithm gives correct result but the time complexity goes exponential.
Is there any optimized way to do it? Note that i am developing a game and in my specific scenario
- In-degree/Out-degree of any node is at most 4
- In-degree/Out-degree of source node is at most 2