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18 Terms
1
What is the AVL tree?
It is a self-balancing binary search tree where the difference in heights between left and right subtrees cannot be more than 1 for all nodes.
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2
What is a right rotation in an AVL tree?
It is a tree rotation where a node's left child becomes the new root of the subtree, and the original root becomes the right child of the new root.
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3
What is a left rotation in an AVL tree?
It is a tree rotation where a node's right child becomes the new root of the subtree, and the original root becomes the left child of the new root.
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4
What is a left-right rotation?
It is a two-step process to fix imbalance, first performing a left rotation on the left child and then a right rotation on the root.
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5
What is a right-left rotation?
It is a two-step process to fix imbalance, first performing a right rotation on the right child and then a left rotation on the root.
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6
What is the purpose of AVL balancing?
AVL balancing ensures that the height of the binary search tree remains logarithmic, which guarantees O(log n) time complexity for find, insert, and remove operations.
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7
What is the time complexity of operations in an AVL tree?
The time complexity for all operations (find, insert, delete) is O(log n).
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8
What is the primary advantage of AVL trees?
The primary advantage is that it maintains strict balance, ensuring faster operations even in the worst-case scenarios.
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9
How are balance factors calculated in AVL trees?
Balance factors are calculated by subtracting the height of the right subtree from the height of the left subtree.
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10
What happens when an AVL tree becomes unbalanced?
It will perform rotations (left or right) to restore balance and maintain logarithmic height.
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11
What is a Red-Black Tree?
It is a self-balancing binary search tree with an extra property where each node has a color (red or black) and ensures balancing via a set of rules.
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12
What are the properties of a Red-Black Tree?
The properties include: 1) Every node is either red or black. 2) The root is black. 3) Red nodes cannot have red children. 4) Every path from a node to a null pointer has the same number of black nodes.
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13
What is the time complexity of operations in a Red-Black Tree?
O(log n) for insertion, deletion, and search operations.
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14
What is the primary advantage of Red-Black Trees over AVL Trees?
Red-Black trees have simpler balancing rules, making insertion and deletion faster in practice compared to AVL trees.
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15
What is the color flip operation in Red-Black Trees?
The color flip operation changes the colors of a node's children and parent to maintain the Red-Black properties.
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16
How does the insertion operation work in a Red-Black Tree?
Insertion in a Red-Black Tree involves adding the node as red, followed by balancing the tree to restore Red-Black properties if necessary.
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17
What is the time complexity for insertion in a Red-Black Tree?
O(log n) due to the need for rebalancing and re-coloring the tree after insertion.
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18
What is the purpose of the "recoloring" operation in a Red-Black Tree?
Recoloring helps maintain the Red-Black Tree properties, especially during insertions and deletions, to prevent violations of balance rules.
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