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C++ Data Structures and Algorithm Design Principles
C++ Data Structures and Algorithm Design Principles

C++ Data Structures and Algorithm Design Principles: Leverage the power of modern C++ to build robust and scalable applications

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C++ Data Structures and Algorithm Design Principles

2. Trees, Heaps, and Graphs

Learning Objectives

By the end of this chapter, you will be able to:

  • Analyze and identify where non-linear data structures can be used
  • Implement and manipulate tree structures to represent data and solve problems
  • Traverse a tree using various methods
  • Implement a graph structure to represent data and solve problems
  • Represent a graph using different methods based on a given scenario

In this chapter, we will look at two non-linear data structures, namely trees and graphs, and how they can be used to represent real-world scenarios and solve various problems.

Introduction

In the previous chapter, we implemented different types of linear data structures to store and manage data in a linear fashion. In linear structures, we can traverse in, at most, two directions – forward or backward. However, the scope of these structures is very limited, and they can't be used to solve advanced problems. In this chapter, we'll explore a more advanced class of problems. We will see that the solutions we implemented previously are not good enough to be used directly. Due to this, we'll expand upon those data structures to make more complex structures that can be used to represent non-linear data.

After looking at these problems, we'll discuss basic solutions using the tree data structure. We'll implement different types of trees to solve different kinds of problems. After that, we'll have a look at a special type of tree called a heap, as well as its possible implementation and applications. Following that, we'll look...

Non-Linear Problems

Two main categories of situations that cannot be represented with the help of linear data structures are hierarchical problems and cyclic dependencies. Let's take a closer look at these cases.

Hierarchical Problems

Let's look at a couple of examples that inherently have hierarchical properties. The following is the structure of an organization:

Figure 2.1: Organization structure

Figure 2.1: Organization structure

As we can see, the CEO is the head of the company and manages the Deputy Director. The Deputy Director leads three other officers, and so on.

The data is inherently hierarchical in nature. This type of data is difficult to manage using simple arrays, vectors, or linked lists. To solidify our understanding, let's look at another use case; that is, a university course's structure, as shown in the following figure:

Figure 2.2: Course hierarchy in a university course structure

The preceding figure shows the course dependencies for some courses...

Tree – It's Upside Down!

As we discussed in the previous section, a tree is nothing but some objects or nodes connected to other nodes via a relationship that results in some sort of hierarchy. If we were to show this hierarchy in a graphical way, it would look like a tree, while the different edges would look like its branches. The main node, which is not dependent on any other node, is also known as a root node and is usually represented at the top. So, unlike an actual tree, this tree is upside down, with the root at its top!

Let's try to construct a structure for a very basic version of an organizational hierarchy.

Exercise 7: Creating an Organizational Structure

In this exercise, we will implement a basic version of the organizational tree we saw in the introduction to this chapter. Let's get started:

  1. First, let's include the required headers:

    #include <iostream>

    #include <queue>

  2. For simplicity, we'll assume that any person can have, at...

Variants of Trees

In the previous exercises, we've mainly looked at the binary tree, which is one of the most common kinds of trees. In a binary tree, each node can have two child nodes at most. However, a plain binary tree doesn't always serve this purpose. Next, we'll look at a more specialized version of the binary tree, called a binary search tree.

Binary Search Tree

A binary search tree (BST) is a popular version of the binary tree. BST is nothing but a binary tree with the following properties:

  • Value of the parent node ≥ value of the left child
  • Value of the parent node ≤ value of the right child

In short, left child ≤ parent ≤ right child.

This leads us to an interesting feature. At any point in time, we can always say that all the elements that are less than or equal to the parent node will be on the left side, while those greater than or equal to the parent node will be on the right side. So, the problem of searching an element keeps...

Heaps

In the previous chapter, we had a brief look at heaps and how C++ provides heaps via STL. In this chapter, we'll take a deeper look at heaps. Just to recap, the following are the intended time complexities:

  • O(1): Immediate access to the max element
  • O(log n): Insertion of any element
  • O(log n): Deletion of the max element

To achieve O(log n) insertion/deletion, we'll use a tree to store data. But in this case, we'll 'use a complete tree. A complete tree is defined as a tree where nodes at all the levels except the last one have two children, and the last level has as many of the elements on the left side as possible. For example, consider the two trees shown in the following figure:

Figure 2.14: Complete versus non-complete tree
Figure 2.14: Complete versus non-complete tree

Thus, a complete tree can be constructed by inserting elements in the last level, as long as there's enough space there. If not, we will insert them at the leftmost position on the new level. This gives...

Graphs

Although a tree is a pretty good way to represent hierarchical data, we can't represent circular or cyclic dependencies in a tree because we always have a single and unique path to go from one node to another. However, there are more complex scenarios that have a cyclic structure inherently. For example, consider a road network. There can be multiple ways to go from one place (places can be represented as nodes) to another. Such a set of scenarios can be better represented using graphs.

Unlike a tree, a graph has to store data for the nodes, as well as for the edges between the nodes. For example, in any road network, for each node (place), we have to store the information about which other nodes (places) it connects to. This way, we can form a graph with all the required nodes and edges. This is called an unweighted graph. We can add weights, or more information, to each of the edges. For our road network example, we can add the distance of each edge (path) from one node (place...

Summary

In this chapter, we looked at a more advanced class of problems compared to the previous chapter, which helped us to describe a wider range of real-world scenarios. We looked at and implemented two major data structures – trees and graphs. We also looked at various types of trees that we can use in different situations. Then, we looked at different ways of representing data programmatically for these structures. With the help of this chapter, you should be able to apply these techniques to solve real-world problems of similar kinds.

Now that we've looked at linear and non-linear data structures, in the next chapter, we'll look at a very specific but widely used concept called lookup, where the goal is to store values in a container so that searching is super fast. We will also look at the fundamental idea behind hashing and how can we implement such a container.

Left arrow icon Right arrow icon

Key benefits

  • Explore data structures such as arrays, stacks, and graphs with real-world examples
  • Study the trade-offs between algorithms and data structures and discover what works and what doesn't
  • Discover how techniques such as bloom filters and multi-way heaps boost real-world applications

Description

C++ is a mature multi-paradigm programming language that enables you to write high-level code with a high degree of control over the hardware. Today, significant parts of software infrastructure, including databases, browsers, multimedia frameworks, and GUI toolkits, are written in C++. This book starts by introducing C++ data structures and how to store data using linked lists, arrays, stacks, and queues. In later chapters, the book explains the basic algorithm design paradigms, such as the greedy approach and the divide-and-conquer approach, which are used to solve a large variety of computational problems. Finally, you will learn the advanced technique of dynamic programming to develop optimized implementations of several algorithms discussed in the book. By the end of this book, you will have learned how to implement standard data structures and algorithms in efficient and scalable C++ 14 code.

Who is this book for?

This book is for developers or students who want to revisit basic data structures and algorithm design techniques. Although no mathematical background is required, basic knowledge of complexity classes and Big O notation along with a qualification in an algorithms course will help you get the most out of this book. Familiarity with C++ 14 standard is assumed.

What you will learn

  • Build applications using hash tables, dictionaries, and sets
  • Explore how modern hardware affects the actual run-time performance of programs
  • Apply common algorithms such as heapsort and merge sort for string data types
  • Use C++ template metaprogramming to write code libraries
  • Implement a URL shortening service using a bloom filter
  • Use appropriate modern C++ idioms such as std:: array instead of C-style arrays
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Table of Contents

9 Chapters
1. Lists, Stacks, and Queues Chevron down icon Chevron up icon
2. Trees, Heaps, and Graphs Chevron down icon Chevron up icon
3. Hash Tables and Bloom Filters Chevron down icon Chevron up icon
4. Divide and Conquer Chevron down icon Chevron up icon
5. Greedy Algorithms Chevron down icon Chevron up icon
6. Graph Algorithms I Chevron down icon Chevron up icon
7. Graph Algorithms II Chevron down icon Chevron up icon
8. Dynamic Programming I Chevron down icon Chevron up icon
9. Dynamic Programming II Chevron down icon Chevron up icon

Customer reviews

Rating distribution
Full star icon Full star icon Half star icon Empty star icon Empty star icon 2.3
(4 Ratings)
5 star 25%
4 star 0%
3 star 0%
2 star 25%
1 star 50%
CT Jan 21, 2020
Full star icon Full star icon Full star icon Full star icon Full star icon 5
This book gives a pretty thorough overview of many of the most famous algorithm paradigms and data structures. The first part is sort of a "refresher", giving a general tour of how to implement typical data structures (linked lists, stacks, heaps, etc.) in C++, first by using STL and then from scratch. This section contains a decent amount of useful tidbits for quick reference, in much plainer english than a lot of the technical documentation out there. The rest of the chapters delve into more advanced topics, like graphs, greedy technique, and dynamic programming. The explanations of a lot of the tougher stuff tend to be pretty easy to follow, and each chapter contains a 5 or so exercises with step by step descriptions. A lot of the activities that are included are pretty interesting, though i did find with a few of them that I was having trouble understanding what the problem description was asking.There are definitely some issues with the formatting in some of the code snippets (brackets not aligned), and i did spot a few typos and other little glitches in the text, but nothing too serious. Also, though the illustrations were quite helpful overall, some of them were meant to be color-coded despite the fact that the book is printed in black and white.it's also worth saying though that the miniature programs contained in the exercises don't really touch upon a lot of really important aspects of c++ programming, particularly proper memory allocation. A lot of code examples contain things that are considered somewhat verbotten among most c++ developers (global variables, raw pointers, etc.). Thankfully, the authors do point out these sections and give a very general explanation about why they're "evil". Its clear they did it this way to make the code easier to read and understand for students, especially cause the book is about algorithms much more that it is about c++, but someone who is very unfamiliar with c++ best practices should be aware that there's a lot more to it when youre working on a full fledged application.These are really minor gripes, though. overall i'm quite happy with this book. I'd recommend it primarily for upper-intermediate programmers wanting to expand their general knowledge of algorithms, or anyone who wants a straightforward explanation of most of the common techniques for reference or technical interviews.
Amazon Verified review Amazon
b Jan 12, 2020
Full star icon Full star icon Empty star icon Empty star icon Empty star icon 2
Beyond the fact that this book is riddled with typos and poor code alignment, it also is full of non-idiomatic C++11 code snippets. It contains all of the low-quality examples you expect to find on internet forums posted by non-experts. It demonstrates all sorts of bad programming habits and lazy coding techniques.Find a better book from a better publisher.
Amazon Verified review Amazon
Felix Mar 08, 2021
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There are sooooooo many typos in this book. It makes the information completely tedious to navigate, essentially useless. The typos also exist in the code examples. All in all, this book is a huge waste of money.
Amazon Verified review Amazon
Francesco Feb 23, 2021
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Very bad C++Full of mistakes which confuse the readerFull of repeated code which is not needed
Amazon Verified review Amazon
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