Gain insights into array and linked list-based implementations, delve into advanced structures like skiplists and trees, and explore template-based collections for efficient data optimization 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 C++

# Additional notes
Red-black trees were first introduced by #key# Guibas and Sedgewick: L. Guibas and R. Sedgewick. A dichromatic framework for balanced trees. In 19th Annual Symposium on Foundations of Computer Science, Ann Arbor, Michigan, 16–18 October 1978, Proceedings, pages 8–21. IEEE Computer Society, 1978. #key#. Despite their high implementation complexity they are found in some of the most commonly used libraries and applications. Most algorithms and data structures textbooks discuss some variant of red-black trees.


#key# Andersson: A. Andersson. Balanced search trees made simple. In F. K. H. A. Dehne, J.-R. Sack, N. Santoro, and S. Whitesides, editors, Algorithms and Data Structures, Third Workshop, WADS ’93, Montre ́al, Canada, August 11–13, 1993, Proceedings, volume 709 of Lecture Notes in Computer Science, pages 60–71. Springer, 1993. #key# describes a left-leaning version of balanced trees that is similar to red-black trees but has the additional constraint that any node has at most one red child. This implies that these trees simulate 2-3 trees rather than 2-4 trees. They are significantly simpler, though, than the `RedBlackTree` structure presented in this chapter.


#key# Sedgewick: R. Sedgewick. Left-leaning red-black trees, September 2008. URL: http://www.cs.princeton.edu/ ̃rs/talks/LLRB/LLRB.pdf [cited 2011-07-21]. #key# describes two versions of left-leaning red-black trees. These use recursion along with a simulation of top-down splitting and merging in 2-4 trees. The combination of these two techniques makes for particularly short and elegant code.


A related, and older, data structure is the #key# AVL tree: G. Adelson-Velskii and E. Landis. An algorithm for the organization of information. Soviet Mathematics Doklady, 3(1259-1262):4, 1962. #key#. AVL trees are height-balanced: At each node `u`, the height of the subtree rooted at `u.left` and the subtree rooted at `u.right` differ by at most one. It follows immediately that, if $F(h)$ is the minimum number of leaves in a tree of height `h`, then $F(h)$ obeys the Fibonacci recurrence

$$
F(h) = F(h-1) + F(h-2)
$$

with base cases $F(0) = 1$ and $F(1) = 1$. This means $F(h)$ is approximate $\varphi^h / \sqrt{5}$
, where $\varphi = (1 + \sqrt{5})/2 \approx 1.61803399$ is the golden ratio. (More precisely, $|\varphi^h / \sqrt{5} - F(h)| \leq 1 / 2$.) Arguing as in the proof of #key# lemma: A 2-4 tree with n leaves has height at most log n. #key#, this implies

$$h \leq \log_{\varphi}\ n \approx 1.440420088 \log n$$

so AVL trees have smaller height than red-black trees. The height balancing can be maintained during `add(x)` and `remove(x)` operations by walking back up the path to the root and performing a rebalancing operation at each node `u` where the height of `u`’s left and right subtrees differ by two.




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 Red-Black Trees

Additional notes