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Consider the following nested representation of binary trees: (X Y Z) indicates Y and Z are the left and right sub stress, respectively, of node X. Note that Y and Z may be NULL, or further nested. Which of the following represents a valid binary tree?
  • a)
     (1 2 (4 5 6 7))
  • b)
     (1 (2 3 4) 5 6) 7)
  • c)
     (1 (2 3 4)(5 6 7))
  • d)
     (1 (2 3 NULL) (4 5))
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
Consider the following nested representation of binary trees: (X Y Z) ...
The correct representation of a valid binary tree among the given options is option C: (1 (2 3 4)(5 6 7)). Let's break down the answer in detail:

Explanation:
A binary tree is a hierarchical data structure in which each node has at most two children, referred to as the left child and the right child. The given nested representation of binary trees follows the format (X Y Z), where X is the root node, Y is the left subtree, and Z is the right subtree.

Now, let's analyze each option to determine which one represents a valid binary tree:

a) (1 2 (4 5 6 7)):
This representation is not valid because the node with value 1 has two right children, 6 and 7, which violates the definition of a binary tree.

b) (1 (2 3 4) 5 6) 7):
This representation is also not valid because the node with value 1 has four children, 2, 3, 4, and 5, which exceeds the limit of two children per node in a binary tree.

c) (1 (2 3 4)(5 6 7)):
This representation is valid because it follows the binary tree structure. The node with value 1 is the root, and its left subtree is represented by (2 3 4), where 2 is the root of its left subtree and 3 and 4 are its left and right children, respectively. Similarly, the right subtree of node 1 is represented by (5 6 7), where 5 is the root of its left subtree and 6 and 7 are its left and right children, respectively.

d) (1 (2 3 NULL) (4 5)):
This representation is not valid because it includes the term "NULL," which is not a valid representation in the given format. The format only allows for nested representations of binary trees within parentheses.

Therefore, the correct representation of a valid binary tree among the given options is option C: (1 (2 3 4)(5 6 7)).
Free Test
Community Answer
Consider the following nested representation of binary trees: (X Y Z) ...
(1 (2 3 4)(5 6 7)) represents following binary tree 
A) (1 2 (4 5 6 7)) is not fine as there are 4 elements in one bracket.
B) (1 (2 3 4) 5 6) 7) is not fine as there are 2 opening brackets and 3 closing.
D) (1 (2 3 NULL) (4 5)) is not fine one bracket has only two entries (4 5)
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Consider the following nested representation of binary trees: (X Y Z) indicates Y and Z are the left and right sub stress, respectively, of node X. Note that Y and Z may be NULL, or further nested. Which of the following represents a valid binary tree?a)(1 2 (4 5 6 7))b)(1 (2 3 4) 5 6) 7)c)(1 (2 3 4)(5 6 7))d)(1 (2 3 NULL) (4 5))Correct answer is option 'C'. Can you explain this answer?
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