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Deriving time complexity of Binary tree and AVL tree, step
by step.
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Answer / tilak chandan
Lemma: A subtree rooted at node v has at least 2bh(v) − 1 internal nodes.
Proof of Lemma (by induction height):
Basis: h(v) = 0
If v has a height of zero then it must be null, therefore bh(v) = 0. So:
2bh(v) − 1 = 20 − 1 = 1 − 1 = 0
Inductive Step: v such that h(v) = k, has at least 2bh(v) − 1 internal nodes implies that v' such that h(v') = k+1 has at least 2bh(v') − 1 internal nodes.
Since v' has h(v') > 0 it is an internal node. As such it has two children each of which have a black-height of either bh(v') or bh(v')-1 (depending on whether the child is red or black, respectively). By the inductive hypothesis each child has at least 2bh(v') − 1 − 1 internal nodes, so v' has at least:
2bh(v') − 1 − 1 + 2bh(v') − 1 − 1 + 1 = 2bh(v') − 1
internal nodes.
Using this lemma we can now show that the height of the tree is logarithmic. Since at least half of the nodes on any path from the root to a leaf are black (property 4 of a red black tree), the black-height of the root is at least h(root)/2. By the lemma we get:
Therefore the height of the root is O(log(n)).
| Is This Answer Correct ? | 2 Yes | 1 No |
Answer / pudwallis gudzinsky
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tots?" Indeed the answer would be a resounding Yes and I
am 100 percent certain that this answer is correct.
If there are girls available in the room, I would not like
strike with them.
| Is This Answer Correct ? | 5 Yes | 22 No |
Answer / haresh
Actually i was searching for the same answer as i dont know
what the answer is.. But yah if there are girls in ur room i
will be happy striking with them lol
| Is This Answer Correct ? | 1 Yes | 19 No |
Answer / ssss ss
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not my friend .However I do not the answer.But you do not
know the answer.You have already told me that i have already
strike with the girls available in the room.
| Is This Answer Correct ? | 6 Yes | 34 No |
Perform the functionality of 2-D array through 1-D array and in it the functions to be performed were: (1) Display the array in 2-D format (2) Display a particular element (3) Display a particular row (4) Display a particular column
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0 Answers Nagarro, Wollega University,
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