GATE | GATE-CS-2016 (Set 2) | Question 46

Consider the following New-order strategy for traversing a binary tree:

Visit the root;
Visit the right subtree using New-order
Visit the left subtree using New-order

The New-order traversal of the expression tree corresponding to the reverse polish expression 3 4 * 5 – 2 ˆ 6 7 * 1 + – is given by:
(A) + – 1 6 7 * 2 ˆ 5 – 3 4 *
(B) – + 1 * 6 7 ˆ 2 – 5 * 3 4
(C) – + 1 * 7 6 ˆ 2 – 5 * 4 3
(D) 1 7 6 * + 2 5 4 3 * – ˆ –


Answer: (C)

Explanation:  

Reverse Polish expression is derived through Post-Order i.e.
1)  Visit Left Node
  2)  Visit Right Node                                    (L R N)
  3)  Visit Root Node

— Acc. to Ques. New Order algorithm is :
   1)  Visit Root Node
   2)  Visit Right Node                                     (N R L)
   3)  Visit Left Node
ie. New Order Expression will be a total reverse of the Post-Order algorithm
Post-Order Expression               :  3 4 * 5 – 2 ˆ 6 7 * 1 + –
Hence , New Order Expression :  – + 1 * 7 6 ^ 2 – 5 * 4 3 

This solution is contributed by Mohit Gupta.


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