This course introduces data structures and algorithms, focusing on practical implementation in Python.

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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

`ScapegoatTree` keeps itself balanced by total rebuilding operations.

`ScapegoatTree` has an upper-bound on the number of nodes, `q`.

A call to `rebuild(u)` takes $O(n)$ time.

The resulting subtree of `rebuild(u)` has a maximum height.

Which statement is *true* about `ScapegoatTree`?

Which statement is true about <code>ScapegoatTree</code>?

A `ScapegoatTree` always maintains a perfectly balanced structure without any rebuilding operations.

The `rebuild()` method reconstructs an entire subtree into a perfectly balanced subtree.

The height of a `ScapegoatTree` is always smaller than the logarithm of the number of nodes.

The `add(x)` operation in a `ScapegoatTree` can increase the height of the tree.

Which statement is true?

What is the running time of rebuilding the subtree rooted at a scapegoat node `w` during a call to `add(x)` in a `ScapegoatTree`?

What is the running time of rebuilding the subtree rooted at a scapegoat node <code>w</code> during a call to <code>add(x)</code> in a <code>ScapegoatTree</code>?

**(True or False)** During a call to `add(x)` in a `ScapegoatTree`, the cost of finding the scapegoat `w` and rebuilding the subtree rooted at `w` is $O(\text{size}(w))$.

(True or False) During a call to <code>add(x)</code> in a <code>ScapegoatTree</code>, the cost of finding the scapegoat <code>w</code> and rebuilding the subtree rooted at <code>w</code> is <math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>O</mi><mo stretchy="false">(</mo><mtext>size</mtext><mo stretchy="false">(</mo><mi>w</mi><mo stretchy="false">)</mo><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">O(\text{size}(w))</annotation></semantics></math>O(size(w)).

Test yourself on what you've learned about scapegoat 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

Quiz on Scapegoat Trees