# Data Structures and Algorithms for Engineers

|CARNEGIE MELLON UNIVERSITY AFRICA|

04-630

Data Structures and Algorithms for Engineers

Core

Units: 12

Lecture/Lab/Rep hours/week: 4 hours lectures/week, 1.5 hours labs/week (two sessions), 1 hour recitation/week (two sessions)

Semester: Spring

Pre-requisites: programming skills

Students are expected to be familiar with programming in at least one programming language. Formal programming language training is not required. Students may not have any formal background in algorithms, data structures, analysis, or detailed design techniques and methods.

## Course description

Many organizations today are incorporating computer hardware and software into the products that they design and build. Most of these organizations' primary competencies are not computer science or software engineering, but rather they find that automation makes their products smarter, more capable, and more appealing in the market place. Because deep domain knowledge is needed to build these products, these organizations often hire engineers from traditional engineering disciplines to design and build the product platform, in many cases requiring them to write software to make the product actually work. These are capable engineers from many disciplines other than software engineering and unfortunately they usually learn software engineering on the job. This process typically involves considerable trial and error and often results in poorly designed and documented systems, defect laden software, bloated product development costs, unmaintainable software, and missed opportunities to leverage software development investments.

In addition to developing mere functionality, some application domains are often highly constrained and unforgiving in their quality attribute needs such as performance, safety, and availability. These systems intimately depend upon software to provide these capabilities in addition to basic functionality. Designing software intensive systems with these properties in a cost-effective way requires first-class computer science and software engineering expertise. While many practicing engineers often have many years of industrial experience writing software applications, many lack a formal background in computer science principles. These engineers may have had a few courses or technical training in specific computer languages or technologies, but in general they often lack formal training in algorithms, computing theory, data structures, and design among other key topics. The result is that many of these engineers are not fully realizing their potential as software engineers. This course is designed to bridge these gaps in formal computer science training.

## Learning objectives

The primary objective of the course is to provide engineers without formal training in computer science, a solid background in the key principles of computer science, in general, and of the algorithms and data-structures, in particular. The key purpose of this course is to complement the experience that engineers may already have in writing software with formal computer science underpinnings, making those engineers more capable in developing software intensive systems.

The course begins by considering the main phases of the software development lifecycle, from requirements elicitation, to computational modelling, system specification, software design, implementation, and software quality assurance, including various forms of testing, verification, and validation. Then, building on the concept of abstract data types, the course provides an in in-depth treatment of the key elements of algorithms and data-structures, beginning with the fundamentals of searching, sorting, lists, stacks, and queues, but quickly progressing to more advanced topics, including trees, graphs, and algorithmic strategies. It also covers the analysis of the performance and tractability of algorithms, finishing with automata theory and computability theory. A key focus of the course is on effective implementation and good design principles.

## Outcomes

After completing this course, students should be able to:

- Recognize and analyze critical computational problems, generate alternative solutions to problems, and assess their relative merits.
- Understand, analyze, and characterize those factors that influence algorithmic computational performance and memory consumption.
- Design, implement, and document appropriate, effective, and efficient data structures & algorithms for a variety of real-world problems.
- Understand detailed software structures and their underlying strengths and weaknesses.
- Perform detailed, code-level design and document the design in an understandable way.

## Content details

Refer to the
**Lecture Schedule**
for information on course delivery, including lectures, labs, assignments, and exercises.

The course will cover the following topics:

- Introduction: The Software Development Life Cycle
- Formalisms for Representing Algorithms
- Analysis of Complexity
- Searching and Sorting Algorithms
- Abstract Data Types (ADT)
- Containers, Dictionaries, and Lists
- Stacks
- Queues
- Trees
- Heaps
- Graphs
- Complex Networks
- Hashing
- Algorithmic Strategies
- Analysis of Correctness
- Automata Theory
- Computability Theory

*The detailed content for each of these topics follows.*

Introduction: The Software Development Life Cycle

- Motivation
- Goals of the course
- Syllabus and lecture schedule
- Course operation
- Software development tools for assignments
- Preview of course material
- Levels of abstraction in information processing systems
- The software development life cycle: Yourdon Structured Analysis - functional, data, and behavioural models (hierarchical decomposition trees, architecture diagrams, data flow diagrams DFD, data dictionaries, entity relationship ER diagrams, state transition diagrams)
- Software process models: waterfall, evolutionary, formal transformation, re-use, hybrid, spiral

Formalisms for Representing Algorithms

- Definition of an algorithm
- Modelling software
- Relational modelling
- State modelling
- Practical representations
- Pseudo code
- Flow charts
- Finite state machines
- UML
- Predicate logic
- Analysis

Analysis of Complexity

- Performance of algorithms, time and space tradeoff, worst case and average case performance
- Big O notation
- Recurrence relationships
- Analysis of complexity of iterative and recursive algorithms
- Recursive vs. iterative algorithms: runtime memory implications
- Complexity theory: tractable vs intractable algorithmic complexity
- Example intractable problems: travelling salesman problem, Hamiltonian circuit, 3-colour problem, SAT, cliques
- Determinism and non-determinism
- P, NP, and NP-Complete classes of algorithm

Searching and Sorting Algorithms

- Linear and binary search (iterative and recursive)
- In-place sorts: bubblesort (efficient and inefficient), selection sort, insertion sort.
- Not-in-place sorts: Quicksort, merge sort.
- Complexity analysis
- Characteristics of a good sort
- Speed, consistency, keys, memory usage, length & code complexity, stability
- Other sorts ordered by complexity

Abstract Data Types (ADT)

- Vector example exercise
- History of abstraction
- Abstract Data Types (ADT)
- Information hiding
- Types and typing
- Encapsulation
- Efficiency
- Design practices

Containers, Dictionaries, and Lists

- Basic operations
- Implementation with arrays and linked lists
- Singly linked lists
- Doubly linked lists
- Performance considerations

Stacks

- Stack (LIFO): push, pop, peek, size, numItems operations
- Array implementation (directly and array of pointers to data)
- Stack applications, including evaluation of infix, prefix, and postfix expressions

Queues

- Queue (FIFO): enqueue, dequeue, peek, size, numItems operations
- Array implementation (directly and array of pointers to data)
- Linked list implementation
- Circular queues
- Performance considerations

Trees

- Concepts and terminology: level, height, external and internal nodes, skinny, fat, complete, left-complete, perfect, multi-way, d-ary
- Types of tree: binary, binary search, B-tree, 2-3 tree, AVL, Red-Black
- Binary trees and binary search trees
- Tree traversals: inorder, preorder, postorder
- Fixed-length codes, variable length codes, optimal code trees, Huffman's algorithm and implementation
- Height-balanced trees: AVL Trees, RR, RL, LR, LL rotations
- Height-balanced trees: Red-Black Trees, single promotion, zig-zag promotion, recolouring and restructuring

Heaps

- Heap basics
- Types of heap: min heaps and max heap
- Heap characteristics
- Heap operations: delete max/min, down heap, up heap, merge, construct, heapify; complexity of operations
- Priority queues
- Operating systems heaps
- Implementation of heap
- Heap sort

Graphs

- Types of graphs: directed, undirected, weighted, unweighted, cyclic, acyclic, directed acyclic, simple, non-simple, implicit, explicit, embedded, topological
- Adjacency matrix representation,
- Adjacency list representation
- Topological sort
- Euler's theorem
- Graph traversal: breadth-first and depth-first, uses of
- Depth-first search and maze traversal
- Spanning trees and minimum spanning trees, Kruskal's algorithm, Prim's algorithm
- Dijkstra's shortest path algorithm
- Floyd-Warshall's all-pairs algorithm

Complex Networks

- The importance of complex networks and network science
- Euler's theorem: the Bridges of Königsberg
- Networks vs. graphs
- Degree, average degree, and degree distribution
- Bipartite networks
- Path length, BFS, Connectivity, Components
- Clustering coefficient
- Random graph model
- Small world phenomena
- Scale free networks
- Communities
- Fundamental Hypothesis
- Connectedness and Density Hypothesis
- Strong and weak communities
- Graph partitioning
- Community detection
- Hierarchical clustering
- Girvan-Newman Algorithm
- Modularity
- Random Hypothesis
- Maximum Modularity Hypothesis
- Greedy algorithm for community detection by maximizing modularity
- Overlapping communities
- Clique percolation algorithm and CFinder

Hashing

- Using keys to address data
- Mappings: injection, surjection, bijection
- Map ADT
- Hash functions
- Hash tables: current value tables, direct access tables
- Managing collisions: chaining, overflow areas, re-hashing, linear probing, quadratic probing
- Example application: dictionaries

Algorithmic Strategies

- Classes of algorithms
- Brute force
- Divide and conquer
- Greedy algorithms
- Dynamic programming
- Combinatorial search and backtracking
- Branch and bound

Analysis of Correctness

- Types of software defects
- Code module design
- Syntactic, semantic, logical defects
- (Semi-)formal verification: partial vs. total correctness
- Invariant assertion method
- Simple proof strategies: by contradiction, counterexample, induction
- Dynamic testing: unit tests, test harness, stubs, drivers, integration testing, regression testing.
- Static tests: reviews, walkthroughs, inspections, reviewing algorithms and software
- Pair programming
- Verification and validation strategies

Automata Theory

- Regular Languages
- Finite Automata
- Nondeterminism
- Regular Expressions
- Nonregular Languages
- Context-free Languages
- Context-free Grammars
- Pushdown Automata
- Deterministic Context-Free Languages

Computability Theory

- The Church-Turing Thesis
- Turing Machines
- Variants of Turing Machines
- The Definition of Algorithm
- Decidability
- Decidable Languages
- Undecidability
- Reducibility

## Lecture Schedule

Refer to the Lecture Schedule for information on course delivery, including lectures, labs, assignments, and exercises.

## Faculty

## Delivery

Face-to-face.

## Student assessment

This course includes several hands-on programming and analysis assignments. Students will program in C/C++. The programming assignments include seven individual assignments. In addition to programming assignments, students will be assigned readings to support the lecture material.

Marks will be awarded as follows.

Best six of seven individual assignments: 60%. Mid-semester examination: 10%. Final examination: 30%.

## Software tools

We will use Microsoft Visual C++ Express compiler, version 10.0 (also known as Visual C++ 2010) and CMake running on Windows 7 (64 bit).

Please follow the instructions provided in the Software Development Environment installation guide.

## Course texts

David Harel and Yishai Feldman, *Algorithmics: The Spirit of Computing*, Third Edition.

Alfred V. Aho, Jeffrey D. Ullman, and John E. Hopcroft, *Data Structures and Algorithms*.

A selection of examples will be taken from Steven Skiena, "The Algorithm Design Manual", Second Edition.

A selection of papers and readings will be provided to complement these required textbooks.

## Acknowledgments

This syllabus is based mainly on Course 04-630 Computer Science Principles for Practicing Engineers given by Mel Rosso-Llopart and Anthony J. Lattanze at Carnegie Mellon University, USA, Course CS-CO-412 Algorithms and Data Structures given by David Vernon at Innopolis University, Russia, and Course IT706A Scientific Theory in Informatics given by David Vernon and others at the University of Skövde, Sweden.