Copyright © 2005 Pearson Addison-Wesley. All rights reserved. 13-1 Balancing Binary Trees There are many approaches to balancing binary trees One method.

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Copyright © 2005 Pearson Addison-Wesley. All rights reserved Balancing Binary Trees There are many approaches to balancing binary trees One method is brute force – Write an inorder traversal to a file – Use a recursive binary search of the file to rebuild the tree

Copyright © 2005 Pearson Addison-Wesley. All rights reserved Balancing Binary Trees Better solutions involve algorithms such as red-black trees and AVL trees that persistently maintain the balance of the tree Most all of these algorithms make use of rotations to balance the tree Lets examine each of the possible rotations

Copyright © 2005 Pearson Addison-Wesley. All rights reserved Right Rotation Right rotation will solve an imbalance if it is caused by a long path in the left sub-tree of the left child of the root

Copyright © 2005 Pearson Addison-Wesley. All rights reserved FIGURE Unbalanced tree and balanced tree after a right rotation

Copyright © 2005 Pearson Addison-Wesley. All rights reserved Left Rotation Left rotation will solve an imbalance if it is caused by a long path in the right sub-tree of the right child of the root

Copyright © 2005 Pearson Addison-Wesley. All rights reserved FIGURE Unbalanced tree and balanced tree after a left rotation

Copyright © 2005 Pearson Addison-Wesley. All rights reserved Rightleft Rotation Rightleft rotation will solve an imbalance if it is caused by a long path in the left sub-tree of the right child of the root Perform a right rotation of the left child of the right child of the root around the right child of the root, and then perform a left rotation of the resulting right child of the root around the root

Copyright © 2005 Pearson Addison-Wesley. All rights reserved FIGURE A rightleft rotation

Copyright © 2005 Pearson Addison-Wesley. All rights reserved Leftright Rotation Leftright rotation will solve an imbalance if it is caused by a long path in the right sub-tree of the left child of the root Perform a left rotation of the right child of the left child of the root around the left child of the root, and then perform a right rotation of the resulting left child of the root around the root

Copyright © 2005 Pearson Addison-Wesley. All rights reserved FIGURE A leftright rotation