Gain insights into array-based and linked list-based data structures, explore advanced structures like skiplists and hashing, and discover template-based collections for efficient data storage and retrieval.

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Data structures and algorithms are essential in computer science since they play a crucial role in efficient information retrieval and processing, dealing with files, storing contacts on phones, social networks and web searches.

In this course, you’ll learn about the array-based implementation of various linear data structures, stack, and queues. You’ll also learn about linked list-based implementation. Next, you’ll explore advanced data structures like skiplists and hashing. You’ll learn how to implement a variety of trees and graphs, and data structures related to bits of an integer. Toward the end of the course, you’ll learn the implementation of structures based on external storage.

After completing this course, you’ll be able to create reusable programs with template-based collections that can efficiently analyze how to optimize the storage and retrieval of very large amounts of data. Overall, this course will enhance your productivity and performance as a software developer.

Data Structures with Generic Types in Python

# Additional notes
Random binary search trees have been studied extensively. #key# Devroye: L. Devroye. Applications of the theory of records in the study of random trees. Acta Informatica, 26(1):123–130, 1988. #key# gives a proof of the #key# lemma: The lemma is about the length of search path in a binary search tree. #key# and related results. There are much stronger
results in the literature as well, the most impressive of which is due to #key# Reed: B. Reed. The height of a random binary search tree. Journal of the ACM, 50(3):306–332, 2003. #key#, who shows that the expected height of a random binary search
tree is

$$
\alpha\ln n - \beta\ln\ln n + O(1)
$$

where $a \approx 4.31107$ is the unique solution on the interval $[2,\infty)$ of the equation $\alpha\ln((2e/\alpha)) = 1$ and $\beta = \frac{3}{2 \ln(\alpha/2)} .$ Furthermore, the variance of
the height is constant.

The name `Treap` was coined by #key# Seidel and Aragon: R. Seidel and C. Aragon. Randomized search trees. Algorithmica, 16(4):464–497, 1996. #key# who discussed
`Treap`s and some of their variants. However, their basic structure was
studied much earlier by #key# Vuillemin: J. Vuillemin. A unifying look at data structures. Communications of the ACM, 23(4):229–239, 1980. #key# who called them Cartesian trees.


One possible space-optimization of the `Treap` data structure is the elimination of the explicit storage of the priority `p` in each node. Instead, the priority of a node, `u`, is computed by hashing `u`’s address in memory. Although a number of hash functions will probably work well for this in
practice, for the important parts of the proof of Lemma 7.1 to remain
valid, the hash function should be randomized and have the _min-wise independent property_: For any distinct values $x_1,..., x_k$
, each of the hash values $h(x_1),..., h(x_k
)$ should be distinct with high probability and, for each
$i \in \left\{1,...,k\right\}$,

$$\Pr\left\{h(x_i)=\min\{h(x_1),\ldots,h(x_k)\}\right\}\leq c/k
$$

for some constant $c$. One such class of hash functions that is easy to implement and fairly fast is tabulation hashing.

Discover more aspects regarding random binary search trees.


Overview

Array-Based Lists

Linked Lists

Skiplists

Hash Tables

Binary Trees

Random Binary Search Trees

Scapegoat Trees

Red-Black Trees

Heaps

Sorting Algorithms

Graphs

Data Structures for Integers

External Memory Searching

Wrap Up

Discussion on Random Binary Search Trees

Additional notes