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In a Red-Black tree, what is the maximum height of the tree in terms of the numb
In a Red-Black tree, what is the maximum height of the tree in terms of the number of nodes n?
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Q1
In a Red-Black tree, what is the maximum height of the tree in terms of the number of nodes n?
2n
n
log(n)
2 * log(n)
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The maximum height of a Red-Black tree is 2 * log(n), ensuring that the tree remains balanced.
Questions & Step-by-step Solutions
1 item
Q
Q: In a Red-Black tree, what is the maximum height of the tree in terms of the number of nodes n?
Solution:
The maximum height of a Red-Black tree is 2 * log(n), ensuring that the tree remains balanced.
Steps: 6
Show Steps
Step 1: Understand that a Red-Black tree is a type of binary search tree that maintains balance through specific properties.
Step 2: Know that the height of a tree is the number of edges on the longest path from the root to a leaf.
Step 3: Recognize that in a Red-Black tree, the properties ensure that the tree does not become too unbalanced.
Step 4: Learn that the maximum height of a Red-Black tree is related to the number of nodes (n) in the tree.
Step 5: The formula for the maximum height of a Red-Black tree is 2 * log(n), where log is the logarithm base 2.
Step 6: This means that as the number of nodes increases, the height of the tree grows at a slower rate, keeping it balanced.
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