How to recognize some binary search tree traversal belongs to post-order or in-order?

Question

If the pre-order of a binary search tree is [P, A, R, S], How to recognize [R, S, A, P] belongs to in-order or post-order? If is post-order how to find out is (Left, Right, Root) or (Right, Left, Root)?

Programatically? What about just construct that tree from the input data and then traverse it with `in-`/ `post-` order and get the results? Its `O(n)` — libik, Jul 31 '18 at 08:20
Can you come up with a code? We can help you with this. `How to recognize [R, S, A, P] belongs to in-order or post-order?`- Build the tree using preorder traversal and Binary search tree property.Then do a inorder and postorder of it and which ever matches with `[R, S, A, P] `, it is that order. — nice_dev, Jul 31 '18 at 09:46

score 2 · Answer 1 · answered Jul 31 '18 at 08:14

2

In order of a binary search tree will always be in sorted order. As [R, S, A, P] is not in sorted order, it should be post order.

answered Jul 31 '18 at 08:14

learner

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Now how to find out is (Left, Right, Root) or (Right, Left, Root)? – SajjadSM Jul 31 '18 at 08:31
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@S.Safari that's now a standard problem you can search. – Shashwat Kumar Jul 31 '18 at 08:32

score 2 · Accepted Answer · answered Jul 31 '18 at 15:03

If the pre-order traversal is [P, A, R, S], then P must be the root. And since it's a binary search tree, then A must be the left child and R and S must be in the right subtree. That gives you two possible trees:

      P                 P
    A   R            A     S
          S              R

A reverse post-order traversal of the second tree will provide the sequence [R, S, A, P].

How to recognize some binary search tree traversal belongs to post-order or in-order?

2 Answers2