Question

We are given a binary search tree; we need to find out its border.

So, if the binary tree is

           10
       /         \
     50           150
    /  \         /   \
  25    75     200    20
 / \           /      / \
15 35        120    155 250 

It should print out 50 25 15 35 120 155 250 20 150 10.

If the binary tree is

               10
           /         \
         50           150
        /  \         /   
      25    75     200   
     / \   / \    
    15 35 65 30  

It should be like 50 25 15 35 65 30 200 150 10.

How can this be done? Does generalising this for a binary tree make the problem any harder?

Any help through links will also be appreciated.

P.S.: please see that the pattern does not start from root but from the left (in this case). It might also start with right, but it always ends with the root.

Answer 1

What you are asking for is a modified depth-first traversal where the node’s values are only printed/returned if either 1) the node is a leaf node or 2) the node is along the “outer path” of the tree, where “outer path” is defined as

A node is a part of the “outer path” if you arrived at the node by following all of the left (or right) paths from the root, or if the node is the right (or left) child of a parent node that was itself a part of the “outer path” but had no left (or right) children.

If you know how to code DFS, then the modification here could be implemented by checking a few extra conditions during the traversal.