You know now that the 2-4 tree allows 2,3, and 4-nodes that hold more than a...

You know now that the 2-4 tree allows 2,3, and 4-nodes that hold more than a single data element, 'squeezing' the tree to shorter heights, and the B tree is the generalized category of search tree that allows an arbitrary number of data elements in each node. The 2-4 tree is one specific type of B tree.

The red black tree is a binary search tree (only one data element per node, the data elements are maintained in order), but it adds a color attribute to each node that allows a way to force adjacent nodes (parent-child) to be of different colors. This means we can rely on the nodes to also be able to be divided into two 'categories' separated by edges.

Come up with an example of a situation in which the data can benefit from being stored in the 2-4, B tree or red black tree.

Expert Solution

In a database, items that are stored aren't usually sorted. This means that if you're looking for "Machine Gun Kelly" and you're currently at "Kanye West", it's not guaranteed that "Machine Gun Kelly" will follow "Kanye West". Thus, the search time in a non-indexed database is linear in the size of the input because in the worst case, you will have to scan for each and every entry to find "Machine Gun Kelly".

But, if we switch to a red-black tree or 2-4 tree implementation, i.e we index the database, we can achieve logarithmic time complexity () in terms of n (size of the input). The worst-case height of a red-black tree is which means that the search would take logarithmic time. The tree traversal is a very efficient operation in an indexed DB, because it works near-instantly, even if the size of n is very large. A tree of n = 10,000 nodes will have a depth of 26.5757132836 (= 27 approx) in case of a RB tree. Whereas, if it is stored as a skewed Binary Search Tree, it will have a depth of 10,000 (which is huge). You can yourself notice the speedup when we shift to a RB tree implementation (because it is height-balanced).

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venereology answered 5 months ago

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