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Q: My cycles are not same as the samples provided.

A: That is very possible because of your different ordering of vertices in adjacency lists. Your
   cycles may fail to match the cycles given in samples even after cyclic permutations and writing
   the cycles in the opposite directions.

   My hunch suggests that you should get exactly the same number of cycles as in the samples.

   Look at this graph:

   a --- b
   |     |
   c --- d
   |     |
   e --- f

   This graph has three cycles. But any DFS will reveal only two. You work with different visiting
   orders, and see yourself. It is possible that only the smaller (length-four) cycles are revealed.
   It is also possible that the large cycle (length six) and a small cycle is revealed by DFS.
   Given any two cycles, the third one can be derived (it uses two backward/forward edges, so your
   DFS missed it).
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Q: Do I need to keep the adjacency lists sorted?

A: No.
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Q: Can we use vectors or lists from STL?

A: Yes.
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Q: Can the graphs be assumed to be connected?

A: Neither G nor GR nor GB nor GRB is needed to be connected. That is why you use multi-DFS, and
   talk about DFS forests (not trees).
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Q: What is vertex number?

A: These are the numbers like 2,4,5,6,11,13,15 (see the red graph) which are not the same as the
   indices 0,1,2,3,4,5,6.
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Q: Why is it necessary to keep track of levels in DFS?

A: You need to distinguish parent from other ancestors. That's why people use levels in DFS. Here,
   you maintain parent information, so maintaining levels is apparently not necessary. A visited
   neighbor which is not the parent of the current node seems to give a back edge. But note that a
   visited neighbor which is not the parent may very well imply a FORWARD edge. So maintain levels.

   More explanation requested: Look at the blue subgraph in the assignment. You start DFS at 7 and
   visit 10, 9, 12, 3, 0. Then you backtrack. The edge (3,10) is a back edge when you come to 3,
   and a forward edge when you come to 10.

   When the DFS traversal first reaches 10, the vertex 3 is unvisited, but the traversal chooses
   vertex 9 to move forward. Eventually, it reaches 3 and sees 10 visited (before or after exploring
   0). So the edge (3,10) is a backward edge to vertex 3. After you track back and come again to 10
   in order to explore further, you discover 3 as a visited neighbor. So to the vertex 10, the same
   edge (10,3) is a forward edge.
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Q: What is multi-DFS?

A: You start DFS from a node, and visit all vertices that can be visited. If there are still some
   vertices unvisited, pick any such vertex, and run a second DFS from that vertex. When that ends,
   check if there are any more unvisited vertices. If so, start a third DFS. Repeat until all
   vertices are marked visited. This is multi-DFS.
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Q: How to print a cycle?

A: Let (u,v) be a backward edge. You know parent(u), parent(parent(u)), and so on. Keep on printing
   u, its parent, its grandparent, ... until you reach v.

   If (u,v) is a forward edge, you cannot reach v from u by following parent information. This is
   the reason why it is necessary to maintain levels to distinguish between forward and backward
   edges.
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