## Friday, July 19, 2013

### Printing Outside Nodes (Boundary) Of A Binary Tree

Contrary to many solutions I found online for this problem - I'm going to say a breadth first search (while printing the first and the last element) is not appropriate here and it won't help in cases where the tree has leafs at levels closer to the root, and those algorithms would miss that. The solution here is a depth first pre-order algorithm, but let me explain the problem statement first. So having the tree below (it is a binary search tree), print the boundary nodes of the tree anticlockwise. Printing the boundary nodes for our tree should result in the following sequence: [60, 41, 16, 25, 42, 55, 62, 64, 70, 65, 74].

 Fig. 1 - Simple Binary Search Tree

A pre-order traversal is more appropriate here because it traverses branches in the way we need; for example, it will traverse [60, 41, 16, 25] first which is what we need and we print them. The next sequences are of no interest to us, so we could add a flag that determines whether nodes should be printed out or not (ex: print only leaf nodes). So out of [53, 46, 42, 55, 74, 65, 63, 62, 64, 70] we would print only leaf nodes [42, 55, 62, 64, 70]. We're left with right branch only, where we have to print all the non-leaf nodes. For this we could have a separate stack where, while traversing we add the non-leaf nodes. In code this may look like this:

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