Which of the following statements is false?a)A tree with n nodes has (n - 1) edges.b)A labeled rooted binary tree can be uniquely constructed given its postorder and preorder traversal results.c)A complete binary tree with n internal nodes has (n + 1) leaves.d)The maximum number of nodes in a binary tree of height h is (2h+1 - 1).Correct answer is option 'B'. Can you explain this answer?

Question

Answer

False Statement: A labeled rooted binary tree can be uniquely constructed given its postorder and preorder traversal results.

Explanation:
To understand why this statement is false, let's first understand the concepts of preorder and postorder traversal of a binary tree.

Preorder Traversal: In this traversal, the root node is visited first, followed by recursively visiting the left subtree and then the right subtree.

Postorder Traversal: In this traversal, the left subtree is visited first, followed by the right subtree, and finally the root node.

Now, let's consider an example to demonstrate why the given statement is false.

Example:
Consider the following binary tree:

A
/ \
B C
/ \ / \
D E F G

Preorder Traversal: A, B, D, E, C, F, G
Postorder Traversal: D, E, B, F, G, C, A

Now, let's try to construct the binary tree using only the preorder and postorder traversals.

Using the preorder traversal, we know that A is the root node. And using the postorder traversal, we know that D, E, B, F, G, C are the nodes in the subtree rooted at A.

However, we cannot determine the exact structure of the left and right subtrees of A. We don't know whether B is the left child and C is the right child, or vice versa.

Therefore, given only the preorder and postorder traversals, we cannot uniquely construct the binary tree. The statement that a labeled rooted binary tree can be uniquely constructed given its postorder and preorder traversal results is false.

Conclusion:
The false statement is option 'B'. A labeled rooted binary tree cannot be uniquely constructed given its postorder and preorder traversal results.

Answer

Why isn't the answer 'C'?

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