lecture notes of algorithms design techniques and analysis

Faculty of Science for Women, University of Babylon, Iraq

[email protected]

By

Ass. Prof. Dr. Samaher Al_Janabi

LECTURE NOTES OF ALGORITHMS

DESIGN TECHNIQUES AND

ANALYSIS

Department of Computer Science The University of Babylon

22 February 2017

Why Study Algorithms?

• important for all other branches of computer science

• plays a key role in modern technological innovation– “Everyone knows Moore’s Law – a prediction made in 1965 by Intel co-

founder Gordon Moore that the density of transistors in integrated circuits would continue to double every 1 to 2 years….in many areas, performance gains due to improvements in algorithms have vastly exceeded even the dramatic performance gains due to increased processor speed.”• Excerpt from Report to the President and Congress: Designing a Digital Future,

December 2010 (page 71).

• provides novel “lens” on processes outside of computer

science and technology

– quantum mechanics, economic markets, evolution

• challenging (i.e., good for the brain!)

• fun

Dr. Samaher Hussein AliNotes of Lecture #1

22 February 2017

Course Objectives

Dr. Samaher Hussein Ali Notes of Lecture #122 February 2017

Algorithms are the heart of computer science, and the subject has

countless practical applications as well as intellectual depth. This specialization is

an introduction to algorithms for learners with at least a little programming

experience.

The specialization is rigorous but emphasizes the big picture and

conceptual understanding over low-level implementation and mathematical details.

After completing this specialization, you will be well-positioned to ace your

technical interviews and speak fluently about algorithms with other programmers

and computer scientists.

Specific topics in the course include: "Big-oh" notation, sorting and

searching, divide and conquer (master method, integer and matrix multiplication,

closest pair), randomized algorithms (QuickSort, contraction algorithm for min

cuts), data structures (heaps, balanced search trees, hash tables, bloom filters),

graph primitives (applications of BFS and DFS, connectivity, shortest paths).

Course DescriptionCourse Topics


• Vocabulary for design and analysis of algorithms

E.g., “Big-Oh” notation

“sweet spot” for high-level reasoning about algorithms

• Divide and conquer algorithm design paradigm

Will apply to: Integer multiplication, sorting, matrix

multiplication, closest pair

General analysis methods (“Master Method/Theorem”)

• Randomization in algorithm design

Will apply to: QuickSort, primality testing, graph partitioning,

hashing.

• Primitives for reasoning about graphs

Connectivity information, shortest paths, structure of

information and social networks.

• Use and implementation of data structures

Heaps, balanced binary search trees, hashing and some variants

(e.g., bloom filters)

Topics in Sequel Course


• Greedy algorithm design paradigm

• Dynamic programming algorithm design paradigm

• NP-complete problems and what to do about them

• Fast heuristics with provable guarantees

• Fast exact algorithms for special cases

• Exact algorithms that beat brute-force search

Skills Student will Learn


• Become a better programmer

• Sharpen your mathematical and analytical skills

• Start “thinking algorithmically”

• Literacy with computer science’s “greatest hits”

• Ace your technical interviews

Supporting Materials


• Kleinberg/Tardos, Algorithm Design, 2005.

• Dasgupta/Papadimitriou/Vazirani, Algorithms, 2006.

• Cormen/Leiserson/Rivest/Stein, Introduction to Algorithms,

2009 (3rd edition).

• Mehlhorn/Sanders, Data Structures and Algorithms: The Basic

Toolbox, 2008.

• “Mathematics for Computer Science”, by Eric Lehman and

Tom Leighton

Supporting Materials

MSc Course Weekly Outline


Week Date Topics Covered

1 19/2/2017 General Introduction of design and analysis algorithm, explained the

topics of course.

2 26/2/2017 Introduction; "big-oh" notation and asymptotic analysis; divide-and-

conquer basics.

3 5/3/2017 The master method for analyzing (divide and conquer) algorithms; the

Quick Sort algorithm and its analysis; probability review

4 12/3/2017 Linear-time selection; graphs, cuts, and the contraction algorithm.

5 19/3/2017 Breadth-first and depth-first search; computing strong components;

applications.

6 26/3/2017 Dijkstra's shortest-path algorithms; heaps; balanced binary search

trees.

7 2/4/2017 Hashing; bloom filters.

8 9/4/2017 First Exam

9 16/4/2017 Two motivating applications; selected review; introduction to greedy

algorithms; a scheduling application; Prim's MST algorithm.

MSc Course Weekly Outline


Week Date Topics Covered

10 23/4/2017 Kruskal's MST algorithm and applications to clustering; advanced

union-find (optional); Huffman codes.

11 30/4/2017 Dynamic programming: introduction, the knapsack problem, sequence

alignment, and optimal binary search trees

12 7/5/2017 The Bellman-Ford algorithm; all-pairs shortest paths.

13 14/5/2017 NP-complete problems and exact algorithms for them

14 21/5/2017 Approximation and local search algorithms for NP-complete problems;

the wider world of algorithms

15 28/5/2017 Second Exam

Algorithms


Algorithm vs Program


Program = Algorithm+ Data Structure

T(P)=Const. + TP

S(P)=Const. + SP

Time Complexity of


Time Complexity of


Space Complexity

Time Complexity of


Note: The above relation accept if m <=n otherwise must used the relation :

lecture notes of algorithms design techniques and analysis

Documents