Practice Efficient Height Management (18.7) - AVL Tree Rotations - Design & Analysis of Algorithms

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8 questions

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Exercise
6 questions · about 4 min · pass mark 70%. Hints available.
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2 questions · about 1 min · pass mark 70%. Hints available.
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6 sample questions

Question 1.
What does a slope of -1 indicate in a binary search tree?
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Think about the definition of slope.
Question 2.
What is the main purpose of performing rotations in BSTs?
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Consider why tree operations can slow down.
3Question 3.
What action do we take if the slope of a tree node is -2?
- Perform a left rotation
- Perform a right rotation
- Rotate at the child first
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Think about which direction needs to be adjusted first.
4Question 4.
True or False: A slope of 0 means both the left and right subtrees are of equal height.
- True
- False
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Consider the definition of slope.
Question 5.
Given a series of insertions into a binary search tree, track the changes in slopes and the necessary rotations needed after each insertion.
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Document each step with a simple tree diagram.
Question 6.
Create a balanced binary search tree with a specific set of nodes and explain how to maintain its balance through rotations during subsequent operations.
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Focus on tree height and slopes after each alteration.

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