GATE CS 2016 Set 2 — Question 46
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Programming & Data Structures → Trees → Expression Trees
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Question
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;
Correct answer
(C) - + 1 7 6 2 - 5 4 3
Solution
First, we construct the expression tree from the Reverse Polish (postfix) expression: Tree Construction:
1.Push 3, 4.
* Node * (left: 3, right: 4).2.Push 5.
- Node - (left: *, right: 5).3.Push 2.
^ Node ^ (left: -, right: 2).4.Push 6, 7.
* Node * (left: 6, right: 7).5.Push 1.
+ Node + (left: *, right: 1).6.
New-order Traversal (Root, Right, Left):- Root Node - (left: ^, right: +).1.Visit Root: -
2.Visit Right Subtree (
+):- Root: +
- Right: 1
- Left (
*): Root \*, Right 7, Left 6 \* 7 6 - Subtree result: + 1 * 7 6
^):- Root: ^
- Right: 2
- Left (
-): Root -, Right 5, Left (*): Root \*, Right 4, Left 3 \* 4 3 - Subtree result: ^ 2 - 5 * 4 3
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