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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?
Verified Answer
The numbers 1, 2, .... n are inserted in a binary search tree in some ...
Binary Search Tree, is a node-based binary tree data structure which has the following properties:
  • The left subtree of a node contains only nodes with keys less than the node’s key.
  • The right subtree of a node contains only nodes with keys greater than the node’s key.
  • The left and right subtree each must also be a binary search tree. There must be no duplicate nodes.
So let us say n=10, p=4. According to BST property the root must be 10-4=6 (considering all unique elements in BST)
And according to BST insertion, root is the first element to be inserted in a BST.
Therefore, the answer is (n-p).
 
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The numbers 1, 2, .... n are inserted in a binary search tree in some ...
Explanation:

  • A Binary Search Tree (BST) is a tree data structure in which each node has at most two children, which are referred to as the left child and the right child.

  • In a BST, all elements in the left subtree are smaller than the root node, and all elements in the right subtree are greater than the root node.

  • The first number to be inserted in the tree must be the root node.

  • Let the total number of nodes in the tree be n.

  • Since the right subtree of the root contains p nodes, the left subtree of the root contains (n-1)-p = n-p-1 nodes.

  • For the first number to be inserted to become the root node, it must be greater than all the elements in its left subtree and less than all the elements in its right subtree.

  • Therefore, the first number to be inserted must be the (n-p)th element in the sequence of numbers.

  • Thus, the answer is option C: n-p-1.

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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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