Rotation Flashcards
Left Rotation
What is a left rotation in a Red-Black tree?
A left rotation is an operation that changes the structure of a Red-Black tree by rotating a node to the left around its right child.
True or False: A left rotation increases the height of the subtree.
False.
Fill in the blank: In a left rotation, the ______ child of a node becomes the new root of the subtree.
right
What is the main purpose of performing a left rotation in Red-Black trees?
To maintain the balancing properties of the tree after insertions or deletions.
After a left rotation, what happens to the left child of the original root?
It becomes the left child of the new root.
In a left rotation, which node becomes the parent of the original root?
The original right child of the root.
Multiple Choice: What is the time complexity of performing a left rotation in a Red-Black tree? A) O(1) B) O(log n) C) O(n)
A) O(1)
True or False: A left rotation can be performed on any node in a Red-Black tree.
True.
What adjustment is needed for the children of the nodes involved in a left rotation?
The children need to be re-assigned appropriately to maintain the tree structure.
Fill in the blank: A left rotation is typically performed after an ______ insertion that causes a violation of Red-Black properties.
unbalanced
What happens to the original left child of the subtree after a left rotation?
It remains the left child of the subtree and does not change position.
Multiple Choice: Which of the following is a potential result of a left rotation? A) Increase in tree height B) Change in node colors C) None of the above
C) None of the above
What is the relationship between left rotation and right rotation?
Left rotation is a mirror operation to right rotation, used to rebalance the tree.
What node is temporarily removed during a left rotation?
The original right child of the root.
True or False: Left rotations can only be performed on Red nodes.
False.
What property of Red-Black trees does a left rotation help maintain?
The balanced height property.
Fill in the blank: After a left rotation, the original right child becomes the new ______.
root
What is a common scenario that necessitates a left rotation in a Red-Black tree?
When a node is inserted into the right subtree of a right child.
Multiple Choice: Which of the following operations may require a left rotation? A) Insertion B) Deletion C) Both A and B
C) Both A and B
What happens to the color of the nodes involved in a left rotation?
The colors may need to be adjusted to maintain Red-Black properties.
True or False: A left rotation is a local operation affecting only a small part of the tree.
True.
Fill in the blank: The left rotation operation is denoted by the symbol ______.
↻
Short Answer: Describe the steps involved in performing a left rotation.
- Identify the node to rotate. 2. Set its right child as the new root. 3. Reassign the left child of the new root to be the original right child’s left child. 4. Set the original node as the left child of the new root.
What is the impact of a left rotation on the overall structure of the Red-Black tree?
It helps to restore balance and maintain the properties of the tree.
Fill in the blank: A left rotation is often used in conjunction with ______ rotations to maintain balance.
right
Multiple Choice: Which of the following best describes a left rotation? A) A restructuring of the tree B) A color change C) A node deletion
A) A restructuring of the tree
True or False: The left rotation operation can lead to a violation of the Red-Black tree properties.
False.
