Questions tagged [b-tree]

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Is deletion and insertion easier in B+ trees compared to B trees?

I saw this question in test. It says that insertion and deletion is easier in B+ tree compared to B tree. The given reason for this was the key to be deleted must be present in leaf node in B+ tree ...
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1answer
85 views

Databases and B-Trees: What are Keys and how are they related

I confused about the description & definition of "key" occuring as terminology for databases and b-trees. In first case dealing with theory of databases a key is defined as a choice for ...
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Inserting numbers into B-Tree

I need to insert these numbers from left to right into a B-Tree where $t=2$ Am I right? I am not sure as $t=2$ means you can hold at most 3 keys per node, and here I have only 2. I used this site: ...
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27 views

Finding minimal degree for a B-Tree

We are given 44,000,000 elements. We want to store them in a B-Tree so that his height is 5 (no more than 5). We are asked: "What is the minimal t we can choose?" ($t$ is the minimal degree, in ...
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25 views

Enhance B-Tree with find(k) function

I have a question to enhance a B-Tree and add a function called find(k) which gets a key - k and returns the index of it in the sorted keys of the tree, using $O(N)$ space complexity, and it needs to ...
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Minimal t needed in B tree for the lowest reading time

I've got an assignment, which I was asked to calculate the minimal t needed in a B tree, to have the optimal searching time. So here it is: We've been told that in a specific B tree, with unknown t, ...
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17 views

Why do b*trees partition 2 nodes into 3?

I'm writing a b*tree library in Rust. I'm thinking it might be better to make the purposeful decision to only implement half of the b* optimizations. (And not because it is easier, although it is.) ...
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1answer
221 views

Max no. of keys of B-Tree of height h

I am reading about B-Tree through CLRS. One of the exercise problem is to express maximum number of keys in a BTree of height $h$ and minimum degree $t$. Properties of BTree of $t$: $t\ge 2$ Min. no ...
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1answer
142 views

Splitting a node in B+ tree with odd number of keys

This and several other resources suggest to "Always a node that gets the middle key from bottom splits, should drop one item for a new middle key". To illustrate with an example. For 5-way B+-tree, ...
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1answer
75 views

What is the minimal degree $d$ required for a B tree with $44*10^6 $ keys so that it's height is less than or equal to $5$

What is the minimal degree $d$ required so a B - tree with $44*10^6$ keys will have a height $h$, such that $h\leq 5$ My attempt was to build the tallest tree possible with minimum degree $d$ and $n =...
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2answers
79 views

Why is it that Btrees most of the times have a degree that is odd? What happens if they are even?

I was watching a lecture video and the Professor states that it would be very rare to see the order of a Btree to be even. I was hoping for an explanation but he cut it off there and moved on with the ...
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1answer
142 views

How to delete an element from a B-tree

There is a lot of information online on this specific topic, but I still don't quite understand how to delete elements from a B-tree. For example, given the following tree, how would we delete 26 and ...
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190 views

Calculating maximum number of splits that can occur during insertion of $n$ keys in B Tree of order $m$

I can calculate this by trying out manually inserting $n$ keys in $m$ order B Tree as follows: Assume median to be selected for split be left biased. That is $m/2$. For example, if $m=4$, then a ...
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239 views

Maximum node splits in B-tree in terms of insertions and branching order

Is there any algorithm to calculate maximum number of node splits that can occur in given number of insertions and highest branching order? Lets say I want to insert 10 elements to an empty B-tree ...
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260 views

Time complexity of inorder run on B+ tree (without leavesa link)

I quite sure that it should be $O(n)$, but I didn't found any information about it and I'm not sure how to prove it. Maybe in 2-3 tree the max number of node (include the leaves) is $2n$ and in each ...
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1answer
34 views

Doubt regarding deletion from a B-tree

After deleting an element from a B-tree,I could rearrange the tree in several ways,that would still complies to the rules of B-trees.But,we are supposed to follow a certain set of rules for ...
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1answer
384 views

Deletion of record from B+ tree

I was going through the B+ tree deletion operation from the book Database System Concepts, 6th Edition by Henry F. Korth. One particular thing caught my attention. A B+ tree is given. We have to ...
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1answer
4k views

How many node does the final B-tree have?

I'm currently studying the B-Trees chapter of Introduction to Algorithms. One of the question from the chapter is: Suppose that we insert the keys $\{1,2,...,n\}$ into an empty B-tree with minimum ...
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1answer
323 views

Understanding B tree key deletion step from CLRS algorithm

CLRS explains B tree key deletion as follows: If the key $k$ is in node $x$ and $x$ is a leaf, delete the key $k$ from $x$. If the key $k$ is in node $x$ and $x$ is an internal node, do the ...
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342 views

return a key of a node with maximum value within a range of keys in B+ tree

I've been asked a question about B+ Tree. The question is: Suppose we have object of the following type: ...