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Let LASTPOST, LASTIN and LASTPRE denote the last vertex visited in a postorder, inorder and preorder traversal. Respectively, of a complete binary tree. Which of the following is always true? (GATE CS 2000)
- a)LASTIN = LASTPOST
- b)LASTIN = LASTPRE
- c)LASTPRE = LASTPOST
- d)None of the above
Correct answer is option 'D'. Can you explain this answer?
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Let LASTPOST, LASTIN and LASTPRE denote the last vertex visited in a p...
It is given that the given tree is complete binary tree. For a complete binary tree, the last visited node will always be same for inorder and preorder traversal. None of the above is true even for a complete binary tree. The option (a) is incorrect because the last node visited in Inorder traversal is right child and last node visited in Postorder traversal is root. The option (c) is incorrect because the last node visited in Preorder traversal is right child and last node visited in Postorder traversal is root. For option (b), see the following counter example. Thanks to Hunaif Muhammed for providing the correct explanation.
Inorder traversal is 4 2 5 1 6 3 Preorder traversal is 1 2 4 5 3 6
Most Upvoted Answer
Let LASTPOST, LASTIN and LASTPRE denote the last vertex visited in a p...
Explanation:
In order to answer this question, let's first understand the concepts of pre-order, in-order, and post-order traversal in a binary tree.
Pre-order traversal: In pre-order traversal, the root node is visited first, followed by the left subtree, and then the right subtree.
In-order traversal: In in-order traversal, the left subtree is visited first, followed by the root node, and then the right subtree.
Post-order traversal: In post-order traversal, the left subtree is visited first, followed by the right subtree, and then the root node.
Now, let's analyze the given options:
a) LASTIN = LASTPOST
- This option states that the last vertex visited in in-order traversal is the same as the last vertex visited in post-order traversal.
- This is not always true. In a complete binary tree, the last vertex visited in in-order traversal will always be the rightmost leaf node. However, the last vertex visited in post-order traversal will be the root node of the tree.
b) LASTIN = LASTPRE
- This option states that the last vertex visited in in-order traversal is the same as the last vertex visited in pre-order traversal.
- This is not always true. In a complete binary tree, the last vertex visited in in-order traversal will always be the rightmost leaf node. However, the last vertex visited in pre-order traversal will be the root node of the tree.
c) LASTPRE = LASTPOST
- This option states that the last vertex visited in pre-order traversal is the same as the last vertex visited in post-order traversal.
- This is not always true. In a complete binary tree, the last vertex visited in pre-order traversal will be the root node of the tree. However, the last vertex visited in post-order traversal will be the root node of the tree.
d) None of the above
- This option is the correct answer because none of the given options are always true in a complete binary tree.
Therefore, the correct answer is option 'D' - None of the above.
In order to answer this question, let's first understand the concepts of pre-order, in-order, and post-order traversal in a binary tree.
Pre-order traversal: In pre-order traversal, the root node is visited first, followed by the left subtree, and then the right subtree.
In-order traversal: In in-order traversal, the left subtree is visited first, followed by the root node, and then the right subtree.
Post-order traversal: In post-order traversal, the left subtree is visited first, followed by the right subtree, and then the root node.
Now, let's analyze the given options:
a) LASTIN = LASTPOST
- This option states that the last vertex visited in in-order traversal is the same as the last vertex visited in post-order traversal.
- This is not always true. In a complete binary tree, the last vertex visited in in-order traversal will always be the rightmost leaf node. However, the last vertex visited in post-order traversal will be the root node of the tree.
b) LASTIN = LASTPRE
- This option states that the last vertex visited in in-order traversal is the same as the last vertex visited in pre-order traversal.
- This is not always true. In a complete binary tree, the last vertex visited in in-order traversal will always be the rightmost leaf node. However, the last vertex visited in pre-order traversal will be the root node of the tree.
c) LASTPRE = LASTPOST
- This option states that the last vertex visited in pre-order traversal is the same as the last vertex visited in post-order traversal.
- This is not always true. In a complete binary tree, the last vertex visited in pre-order traversal will be the root node of the tree. However, the last vertex visited in post-order traversal will be the root node of the tree.
d) None of the above
- This option is the correct answer because none of the given options are always true in a complete binary tree.
Therefore, the correct answer is option 'D' - None of the above.
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Let LASTPOST, LASTIN and LASTPRE denote the last vertex visited in a postorder, inorder and preorder traversal. Respectively, of a complete binary tree. Which of the following is always true? (GATE CS 2000)a)LASTIN = LASTPOSTb)LASTIN = LASTPREc)LASTPRE = LASTPOSTd)None of the aboveCorrect answer is option 'D'. Can you explain this answer?
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