This set of Data Structures & Algorithms Multiple Choice Questions & Answers (MCQs) focuses on “Postorder Traversal”.
1. In postorder traversal of binary tree right subtree is traversed before visiting root.
Explanation: Post-order method of traversing involves – i) Traverse left subtree in post-order, ii) Traverse right subtree in post-order, iii) visit the root.
2. What is the possible number of binary trees that can be created with 3 nodes, giving the sequence N, M, L when traversed in post-order.
3. The post-order traversal of a binary tree is O P Q R S T. Then possible pre-order traversal will be ________
a) T Q R S O P
b) T O Q R P S
c) T Q O P S R
d) T Q O S P R
Explanation: The last, second last nodes visited in post-order traversal are root and it’s right child respectively. Option T Q R S O P can’t be a pre-order traversal, because nodes O, P are visited after the nodes Q, R, S. Option T O Q R P S, can’t be valid, because the pre-order sequence given in option T O Q R P S and given post-order traversal creates a tree with node T as root and node O as left subtree. Option T Q O P S R is valid. Option T Q O S P R is not valid as node P is visited after visiting node S.
4. A binary search tree contains values 7, 8, 13, 26, 35, 40, 70, 75. Which one of the following is a valid post-order sequence of the tree provided the pre-order sequence as 35, 13, 7, 8, 26, 70, 40 and 75?
a) 7, 8, 26, 13, 75, 40, 70, 35
b) 26, 13, 7, 8, 70, 75, 40, 35
c) 7, 8, 13, 26, 35, 40, 70, 75
d) 8, 7, 26, 13, 40, 75, 70, 35
Explanation: The binary tree contains values 7, 8, 13, 26, 35, 40, 70, 75. The given pre-order sequence is 35, 13, 7, 8, 26, 70, 40 and 75. So, the binary search tree formed is
Thus post-order sequence for the tree is 8, 7, 26, 13, 40, 75, 70 and 35.
5. Which of the following pair’s traversals on a binary tree can build the tree uniquely?
a) post-order and pre-order
b) post-order and in-order
c) post-order and level order
d) level order and preorder
Explanation: A binary tree can uniquely be created by post-order and in-order traversals.
6. A full binary tree can be generated using ______
a) post-order and pre-order traversal
b) pre-order traversal
c) post-order traversal
d) in-order traversal
Explanation: Every node in a full binary tree has either 0 or 2 children. A binary tree can be generated by two traversals if one of them is in-order. But, we can generate a full binary tree using post-order and pre-order traversals.
7. The maximum number of nodes in a tree for which post-order and pre-order traversals may be equal is ______
d) any number
Explanation: The tree with only one node has post-order and pre-order traversals equal.
8. The steps for finding post-order traversal are traverse the right subtree, traverse the left subtree or visit the current node.
Explanation: Left subtree is traversed first in post-order traversal, then the right subtree is traversed and then the output current node.
9. The pre-order and in-order are traversals of a binary tree are T M L N P O Q and L M N T O P Q. Which of following is post-order traversal of the tree?
a) L N M O Q P T
b) N M O P O L T
c) L M N O P Q T
d) O P L M N Q T
Explanation: The tree generated by using given pre-order and in-order traversal is
Thus, L N M O Q P T will be the post-order traversal.
10. For a binary tree the first node visited in in-order and post-order traversal is same.
Explanation: Consider a binary tree,
Its in-order traversal – 13 14 16 19
Its post-order traversal- 14 13 19 16. Here the first node visited is not same.
Explanation: In postorder traversal the left subtree is traversed first and then the right subtree and then the current node. So, the posturer traversal of the tree is, S W T Q X U V R P.
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