Introduction to Java Programming and Data Structures, Comprehensive Version (11th Edition)
Introduction to Java Programming and Data Structures, Comprehensive Version (11th Edition)
11th Edition
ISBN: 9780134670942
Author: Y. Daniel Liang
Publisher: PEARSON
Expert Solution & Answer
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Chapter 26.8, Problem 26.8.1CP

Explanation of Solution

AVL tree: It is a self-balancing binary search tree. If the tree is not balanced, the tree performs rotation operation.

Insertion of the nodes 1, 2, 3, 4, 10, 9, 7, 5, 8, 6:

Insertion of 1 and 2:

  • First the value 1 is inserted as the node.
  • The value 2 is greater than 1 and it becomes the right child of 1.

Insertion of 3:

  • Next the value 3 is greater than 1 and it goes to the right of 1.
  • The value 3 is again greater than 3 and it goes to the right of 2.

  • Now the tree gets rebalanced.
  • After inserting 3, the tree becomes,

Insertion of 4:

  • The value 4 is greater than 1 and it goes to the right of 1.
  • The value 4 is greater than 3 and it goes to the right of 3.

Insertion of 10:

  • The value 10 is greater than 1 and it goes to the right of 1.
  • The value 10 is greater than 3 and it goes to the right of 3.
  • The value 10 is greater than 4 and it goes to the right of 4.

  • Now the tree gets rebalanced.
  • After inserting 10, the tree becomes,

Insertion of 9:

  • The value 9 is greater than 2 and it goes to the right of 2.
  • The value 9 is greater than 4 and it goes to the right of 4.
  • The value 9 is lesser than 10 and it goes to the left of 10.

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Students have asked these similar questions
For the AVL Tree what values could you insert to cause a right-left imbalance and at which node does the imbalance occur? Please show and explain based on the tree provided.
The following items are inserted into an AVL tree: 1, 2, 3, 8, and 9. How many rotations are performed in total to maintain an AVL tree?
please help with drawing the binary tree
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