Introduction to Java Programming and Data Structures, Comprehensive Version (11th Edition)
11th Edition
ISBN: 9780134670942
Author: Y. Daniel Liang
Publisher: PEARSON
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Expert Solution & Answer
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.
Expert Solution & Answer
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Check out a sample textbook solutionStudents have asked these similar questions
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Chapter 26 Solutions
Introduction to Java Programming and Data Structures, Comprehensive Version (11th Edition)
Ch. 26.2 - Prob. 26.2.1CPCh. 26.2 - Prob. 26.2.2CPCh. 26.2 - Prob. 26.2.3CPCh. 26.3 - Prob. 26.3.1CPCh. 26.3 - Prob. 26.3.2CPCh. 26.3 - Prob. 26.3.3CPCh. 26.4 - Prob. 26.4.1CPCh. 26.4 - Prob. 26.4.2CPCh. 26.4 - Prob. 26.4.3CPCh. 26.4 - Prob. 26.4.4CP
Ch. 26.5 - Use Listing 26.2 as a template to describe the...Ch. 26.6 - Prob. 26.6.1CPCh. 26.6 - Prob. 26.6.2CPCh. 26.6 - Prob. 26.6.3CPCh. 26.6 - Prob. 26.6.4CPCh. 26.7 - Prob. 26.7.1CPCh. 26.7 - Prob. 26.7.2CPCh. 26.7 - Prob. 26.7.3CPCh. 26.7 - Prob. 26.7.4CPCh. 26.8 - Prob. 26.8.1CPCh. 26.8 - Prob. 26.8.2CPCh. 26.8 - Prob. 26.8.3CPCh. 26.9 - Prob. 26.9.1CPCh. 26.9 - Prob. 26.9.2CPCh. 26.9 - Prob. 26.9.3CPCh. 26 - Prob. 26.5PE
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Similar questions
- Draw a KD Tree in the space below with these points inserted in the following order: (7,2), (6,4), (9,6), (8,1), (4,9), and (2,3). Assume the first level of the KD Tree is split along the x-axis. What point (from the KD Tree ) is the nearest neighbor of the point (1,4)?arrow_forwardConsider the values 19, 10, 4, 30, 55, 24, 9, 13, 11 and 22: Draw the 2-3-4 tree that results from inserting these values in that order into an initially empty 2-3-4 tree. Show your workings.arrow_forwardTrace the construction of an AVL tree using the insertion sequence:BOX IN YOUR FINAL AVL ANSWER50, 25, 10, 5, 7, 3, 30, 20, 8, 15arrow_forward
- Show the results of inserting the keys: F, L, O, R, I, D, A, U, N, V, M, Y, C, S in order into an empty B-tree with minimal degree 2. Draw only the configurations of the tree just before some node being split, and also draw the final configuration. Please make sure your tree configurations are drawn neatly and are easy to read and understand.arrow_forwardProblem 1. Insert the following set of keys {1, 7, 6, 8, 0, 5, 2, 12, 3, 18} in an empty red-black tree in the order they are listed.arrow_forwardBuild an AVL tree with the following values: 15, 20, 24, 10, 13, 7, 30, 36, 25arrow_forward
- Show the results of inserting the keys Q,S,F,K,H,I,F,T,V,P,M,R,N,W,A in oder to empty an B- tree with minimum degree 2. Only draw the configuration ot the tree just before some node must split and also draw the final configuration.arrow_forwardFor AVL tree in above, now what is the node X which causes the tree to be imbalanced with the alpha node at the root? Show inserting and balancing the tree. What type of imbalance is it?arrow_forwardGiven the following LLRB tree What is the problem of this tree? How to fix this problem?arrow_forward
- Trace the construction of an A VL tree using the insertion sequence:BOX IN YOUR FINAL A VL ANSWER57, 15, 80, 32, 17, 45, 25, 61, 48, 15arrow_forwardConsider a B-Tree with order as 3. Which of the following will be the correct B-tree for the given key value sequence? 12, 13, 7, 16, 19, 20, 25, 3, 6arrow_forwardAssume that we have the BST tree as shown in Figure 10. Change the tree to an AVLtree.arrow_forward
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