GATE | Gate IT 2005 | Question 12

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

Answer: (C)


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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