I know that randomisation in quick sort input may help into avoiding the worst case scenario which is an already sorted list. But how is this helping to improve into an insertion in a binary search tree?
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Can anyone explain the difference between binary search and binary search tree with example?Are they the same?Reading the internet it seems the second is only for trees and binary search does not follow this rule.And how to check the presence of a number in O(log(n)) time?
Binary search is an algorithm used on straightforward sorted arrays, which runs in O(log n).
Updating a sorted array is O(n).
A binary tree is a data structure that has both O(log n) search and update (Ignoring problems of balancing).
An interesting comparison is at the end of this chapter.
Since splay tree is a type of unbalanced binary search tree (brilliant.org/wiki/splay-tree), it cannot guarantee a height of at most O(log(n)). Thus, I would think it cannot guarantee a worst case search time of O(log(n)).
But according to bigocheatsheet.com:
Splay Tree has worst case search time of O(log(n))???
You’re correct; the cost of a lookup in a splay tree can reach Θ(n) for an imbalanced tree.
Many resources like the big-O cheat sheet either make simplifying assumptions or just have factually incorrect data in them. It’s unclear whether they were just wrong here, or whether they were talking amortized worst case, etc.
It’s always best to know the internals of the data structures you’re working with so that you can understand where the runtimes come from.
I've searched online everywhere and can't seem to find an answer to this. Given a sorted list of frequencies, what is the most efficient algorithm for creating a huffman tree and what would its big O worst case be?
If you have the list of ordered frequencies then the basic greedy algorithm runs in linear time. You can't beat that (from an asymptotic perspective) since you have to process each node at least once.
If I have 5 million records, then which searching algorithm will be better from linear search, binary search, b tree search algorithm?
Every data structure has it's value.
For instance, you'd use a binary tree most likely if you had numerically sorted data because your complexity would be really low (I.e. O(logn)).
You would use a linear search only if you have a few records because the complexity is O(n) or linear (go figure!).
You'll have to do research on the value of various structures and the knowledge of how your data is stored to get a better feel!
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Red-Black Trees
I started watching a lecture at mit on red-black trees and after 15 minutes gave up.
Sure, I have not watched the previous 10 lectures but why no real world example before going into the theory?
Can someone give an example and explain why red-black trees are an essential data structure?
Red-black trees are self-balancing, and so can insert, delete, and search in O(log n) time. Other types of balanced trees (e.g. AVL trees) are often slower for insert and delete operations.
In addition, the code for red-black trees tends to be simpler.
They are good for creating Maps or associative arrays, and special-purpose data stores. I used one in a high speed telecom application to implement a least-cost routing system.
Note: I haven't seen the lecture.
Red-black trees are binary search trees that are self-balancing when an item is added or removed. This feature guarantees that every search within this tree has O(logn) complexity.
If you construct a tree without balancing it, it is possible to create a degenrated tree that is effectively a linked list with O(n) complexity.
Wikipedia says "self-balancing binary search tree".
"Put very simply, a red–black tree is a binary search tree that inserts and deletes in such a way that the tree is always reasonably balanced."
Which helps when data happens to be sorted. Without the balancing the tree devolves to a linked list.
Wikipedia provides an explanation and an important example.
Red-black trees provide worst-case guarantees for insertion time, deletion time and search time. This can be very useful for real time applications.
A real world example is the Completely Fair Scheduler in the Linux kernel.