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The numbers 1 , 2 .... n are inserted in a binary search tree in some order, In the resulting tree, the right subtree of the root contains p nodes. The first number to be inserted in the tree must be
- a)p
- b)p + 1
- c)n - p
- d)n - p + 1
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
The numbers 1 , 2 .... n are inserted in a binary search tree in some ...
Number 1 ,2 , 3, ....... n are inserted into BST in some order.
Since we know total nodes = n
So, Left (root) + 1 + p = n
Left (root) = n - p - 1
Left (root) = n - (p + 1)
So, root element will be = left element + 1
= n - (p + 1) + 1
= n - p - 1 + 1
= n - p
Since we know total nodes = n
So, Left (root) + 1 + p = n
Left (root) = n - p - 1
Left (root) = n - (p + 1)
So, root element will be = left element + 1
= n - (p + 1) + 1
= n - p - 1 + 1
= n - p
Most Upvoted Answer
The numbers 1 , 2 .... n are inserted in a binary search tree in some ...
Solution:
To understand why the correct answer is option 'C', let's analyze the scenario step by step.
The given problem states that the numbers 1, 2, ..., n are inserted into a binary search tree in some order. In the resulting tree, the right subtree of the root contains p nodes.
Key Points:
1. Binary Search Tree (BST): A binary search tree is a binary tree where each node has a key greater than all the keys in its left subtree and smaller than all the keys in its right subtree.
2. Right Subtree of Root: The right subtree of the root node contains all the elements greater than the root node.
Now, let's consider the possible cases and analyze them one by one.
Case 1: p = 0
If the right subtree of the root contains 0 nodes (p = 0), it means that all the elements from 1 to n must be in the left subtree of the root. In this case, the first number to be inserted in the tree will be n. Therefore, the answer is n - p - 1 = n - 0 - 1 = n - 1.
Case 2: p = n - 1
If the right subtree of the root contains n - 1 nodes (p = n - 1), it means that all the elements from 1 to n must be in the right subtree of the root. In this case, the first number to be inserted in the tree will be 1. Therefore, the answer is n - p - 1 = n - (n - 1) - 1 = 1.
Case 3: 0 < p="" />< n="" -="" />
If the right subtree of the root contains p nodes (0 < p="" />< n="" -="" 1),="" it="" means="" that="" there="" are="" some="" elements="" greater="" than="" the="" root="" and="" some="" elements="" smaller="" than="" the="" root.="" in="" this="" case,="" the="" first="" number="" to="" be="" inserted="" in="" the="" tree="" will="" be="" the="" (p="" +="" 1)th="" element,="" as="" it="" will="" be="" the="" first="" element="" to="" be="" inserted="" in="" the="" right="" subtree.="" therefore,="" the="" answer="" is="" p="" +="" />
Conclusion:
From the above analysis, we can conclude that the correct answer is option 'C', which states that the first number to be inserted in the tree is n - p - 1 when p = 0, 1 when p = n - 1, and p + 1 when 0 < p="" />< n="" -="" 1.="" n="" -="" />
To understand why the correct answer is option 'C', let's analyze the scenario step by step.
The given problem states that the numbers 1, 2, ..., n are inserted into a binary search tree in some order. In the resulting tree, the right subtree of the root contains p nodes.
Key Points:
1. Binary Search Tree (BST): A binary search tree is a binary tree where each node has a key greater than all the keys in its left subtree and smaller than all the keys in its right subtree.
2. Right Subtree of Root: The right subtree of the root node contains all the elements greater than the root node.
Now, let's consider the possible cases and analyze them one by one.
Case 1: p = 0
If the right subtree of the root contains 0 nodes (p = 0), it means that all the elements from 1 to n must be in the left subtree of the root. In this case, the first number to be inserted in the tree will be n. Therefore, the answer is n - p - 1 = n - 0 - 1 = n - 1.
Case 2: p = n - 1
If the right subtree of the root contains n - 1 nodes (p = n - 1), it means that all the elements from 1 to n must be in the right subtree of the root. In this case, the first number to be inserted in the tree will be 1. Therefore, the answer is n - p - 1 = n - (n - 1) - 1 = 1.
Case 3: 0 < p="" />< n="" -="" />
If the right subtree of the root contains p nodes (0 < p="" />< n="" -="" 1),="" it="" means="" that="" there="" are="" some="" elements="" greater="" than="" the="" root="" and="" some="" elements="" smaller="" than="" the="" root.="" in="" this="" case,="" the="" first="" number="" to="" be="" inserted="" in="" the="" tree="" will="" be="" the="" (p="" +="" 1)th="" element,="" as="" it="" will="" be="" the="" first="" element="" to="" be="" inserted="" in="" the="" right="" subtree.="" therefore,="" the="" answer="" is="" p="" +="" />
Conclusion:
From the above analysis, we can conclude that the correct answer is option 'C', which states that the first number to be inserted in the tree is n - p - 1 when p = 0, 1 when p = n - 1, and p + 1 when 0 < p="" />< n="" -="" 1.="" n="" -="" />
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The numbers 1 , 2 .... n are inserted in a binary search tree in some order, In the resulting tree, the right subtree of the root contains p nodes. The first number to be inserted in the tree must bea)pb)p + 1c)n - pd)n - p + 1Correct answer is option 'C'. Can you explain this answer?
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