AVL tree is a binary tree for which a special condition holds throughout the tree, namely, that at every node the height of the left and right subtrees differ by at most 1. A binary tree can be defined in terms of 2 predicates: empty, the empty binary tree bt(N,T1,T2) that is true if N is the root of a binary tree with left subtree T1 and right subtree T2, where all the items in T1 are less than or equal to N and all the items in T2 are greater than N. Write a Prolog program that implements the following predicates for an AVL tree: insert(I,T1,T2) is true if T2 is the AVL tree resulting from I being inserted into an AVL tree T1. display(T) is always true prints the AVL tree to the display.

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An AVL tree is a binary tree for which a special condition holds throughout the tree, namely, that at every node the height of the left and right subtrees differ by at most 1. A binary tree can be defined in terms of 2 predicates:

  • empty, the empty binary tree
  • bt(N,T1,T2) that is true if N is the root of a binary tree with left subtree T1 and right subtree T2, where all the items in T1 are less than or equal to N and all the items in T2 are greater than N.

Write a Prolog program that implements the following predicates for an AVL tree:

  • insert(I,T1,T2) is true if T2 is the AVL tree resulting from I being inserted into an AVL tree T1.
  • display(T) is always true prints the AVL tree to the display.

 

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