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I have the edges and i want to build a tree with it.

The problem is that i can construct my tree structure only when edges are in specific order. Example of orders:

(vertex, parent_vertex)

good:              bad:
(0,  ) <-top       (3, 2)
(1, 0)             (1, 0)
(2, 1)             (3, 2)
(3, 2)             (0,  ) <-top

I iterate throw the edges and for current vertex trying to find it's parent in created tree, then i construct the node and insert it.

result tree:

0 - 1 - 2 - 3

So there is always must exist a parent in the tree for the new added vertex. The question is how to sort the input edges. Voices tells me about the topological sort, but it's for vertexes. Is it possible to sort it right?

mirt
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    What is wrong with the topological sort? If you sort the vertices, your list will be correct. – Beta Jul 31 '12 at 14:02
  • If you have the edges, you have the tree. The only thing you seem to be missing is knowledge of which vertex is the root. Once you find the root (pick an arbitrary edge and start following the parent), I think what you are looking for is a pre-order traversal of the tree. – chepner Jul 31 '12 at 14:28

1 Answers1

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@mirt thanks for pointing out the optimizations on my approach, have you got any better? i will put the below algo for ref

initially construct a hash map to store elements that are there in tree : H, add the root (null in your case/ or anything that represent that root)

taking the pair (_child, _parent)

  1. loop through the whole list. in the list. (each pair is the element)
  2. for each pair, see if the _child and _parent is there in the hash map H, if you dont find, create the tree node for the missing ones and add them to H , and link them with the parent child relationship.
  3. you will be left with the tree at the end of iteration.

complexity is O(n).

Dhandeep Jain
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  • Briefly, i did it so: put all pairs in hash map H and iterate through it. So for each pair (C, P) i find C and P in H and bind them (set P as parent to C and add C as child to P). So it takes O(N). – mirt Aug 08 '12 at 12:29