GATE | GATE-CS-2004 | Question 35

Consider the label sequences obtained by the following pairs of traversals on a labeled binary tree. Which of these pairs identify a tree uniquely ?

(i)     preorder and postorder
(ii)    inorder and postorder
(iii)   preorder and inorder
(iv)   level order and postorder

(A) (i) only
(B) (ii), (iii)
(C) (iii) only
(D) (iv) only


Answer: (B)

Explanation: Here, we consider each and every option to check whether it is true or false.

1) Preorder and postorder

anil_ds_35
For the above trees,

Preorder is AB



Postorder is BA

It shows that preorder and postorder can’t identify a tree uniquely.

2) Inorder and postorder define a tree uniquely

3) Preorder and Inorder also define a tree uniquely

4) Levelorder and postorder can’t define a tree uniquely. For the above example,

Level order is AB

Postorder is BA

See https://www.geeksforgeeks.org/if-you-are-given-two-traversal-sequences-can-you-construct-the-binary-tree/ for details

This solution is contributed by Anil Saikrishna Devarasetty

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