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Balancing Binary Search Trees: Rotations and Height Adjustments

This document presents a series of illustrations and explanations regarding unbalanced and balanced binary search trees (BSTs). It shows how different types of rotations—single and double—can transform an unbalanced BST into a balanced one, thereby optimizing search and insertion operations. Figures depict scenarios before and after rotations, emphasizing the effects on the tree's height. Key concepts include violations of the BST properties and methods for correcting them to maintain balance. Understanding these operations is crucial for efficient tree management.

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Balancing Binary Search Trees: Rotations and Height Adjustments

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  1. Figure 12-37 (a) An unbalanced binary search tree; (b) a balanced tree after rotation; (c) a balanced tree after insertion

  2. Figure 12-38 (a) An unbalanced binary search tree; (b) a balanced tree after a single left rotation

  3. Figure 12-39 Before and after a single left rotation and decreases the tree’s height

  4. Figure 12-40 (a) An unbalanced binary search tree; (b) a balanced tree after a single left rotation

  5. Figure 12-41 Before and after a single left rotation that does not affect the tree’s height Note, however, that the violation has been corrected. If T3 had had a height of h, the violation would not have been corrected. -tjr

  6. Figure 12-42 (a) Before; (b) during; and (c) after a double rotation

  7. Figure 12-43 Before and after a double rotation that decreases the tree’s height

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