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Introduction to Computing

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Introduction to Computing ­ CS101
VU
LESSON 16
ALGORITHMS
Focus of the last Lesson was on Word Processing
First among the four lectures that we plan to have on productivity software, a sub-category of
application software
That first Lesson was on WP
We learnt about what we mean by WP and also desktop publishing
We also discussed the usage of various functions provided by common WP's
The Objective of Today's Lecture
To become familiar with the concept of algorithms:
What they are?
What is their use?
What do they consist of?
What are the techniques used for representing them?
Solving Problems (1)
When faced with a problem:
We first clearly define the problem
Think of possible solutions
Select the one that we think is the best under the prevailing circumstances
And then apply that solution
If the solution woks as desired, fine; else we go back to step 2
Solving Problems (2)
It is quite common to first solve a problem for a particular case
Then for another
And, possibly another
And watch for patterns and trends that emerge
And to use the knowledge form those patterns and trends in coming up with a general solution
Solving Problems (3)
It helps if we have experienced that problem or similar ones before
Generally, there are many ways of solving a given problem; the best problem-solvers come-up with the
most appropriate solution more often than not!
The process that can be used to solve a problem is termed as the "algorithm"
Algorithm:
Sequence of steps that can be taken to solve a given problem
sequence
steps
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Introduction to Computing ­ CS101
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Examples
Addition
Conversion from decimal to binary
The process of boiling an egg
The process of mailing a letter
Sorting
Searching
Let us write down the algorithm for a problem that is familiar to us
Converting a decimal number into binary
Convert 75 to Binary
remainder
2
75
1
1
2
37
2
18
0
2
9
1
4
2
0
2
2
0
1
1
2
0
1001011
16.1 Algorithm for Decimal-to-Binary Conversion
Write the decimal number
Divide by 2; write quotient and remainder
Repeat step 2 on the quotient; keep on repeating until the quotient becomes zero
Write all remainder digits in the reverse order (last remainder first) to form the final result
Points to Note:
The process consists of repeated application of simple steps
All steps are unambiguous (clearly defined)
We are capable of doing all those steps
Only a limited no. of steps needs to be taken
Once all those steps are taken according to the prescribed sequence, the required result will be found
Moreover, the process will stop at that point
16.2 Algorithm (Better Definition)
st
1 Definition:
Sequence of steps that can be taken to solve a problem
Better Definition:
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Introduction to Computing ­ CS101
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A precise sequence of a limited number of unambiguous, executable steps that terminates in the
form of a solution
Three Requirements:
Sequence is:
Precise
Consists of a limited number of steps
Each step is:
Unambiguous
Executable
The sequence of steps terminates in the form of a solution
16.3 Why Algorithms are Useful?
Once we find an algorithm for solving a problem, we do not need to re-discover it the next time we are
faced with that problem
Once an algorithm is known, the task of solving the problem reduces to following (almost blindly and
without thinking) the instructions precisely
All the knowledge required for solving the problem is present in the algorithm
Why Write an Algorithm Down?
For your own use in the future, so that you don't have spend the time for rethinking it
Written form is easier to modify and improve
Makes it easy when explaining the process to others
16.4 Analysis of Algorithms
Analysis in the context of algorithms is concerned with predicting the resources that re requires:
Computational time
Memory
Bandwidth
Logic functions
However, Time ­ generally measured in terms of the number of steps required to execute an algorithm -
is the resource of most interest
By analyzing several candidate algorithms, the most efficient one(s) can be identified
Selecting Among Algorithms
When choosing among competing, successful solutions to a problem, choose the one which is the least
complex
This principle is called the "Ockham's Razor," after William of Ockham - famous 13-th century English
philosopher
Early History:
Search for a Generic Algorithm
The study of algorithms began with mathematicians and was a significant area of work in the early
years
The goal of those early studies was to find a single, general algorithm that could solve all problems of a
single type
Origin of the Term "Algorithm"
The name derives from the title of a Latin book: Algoritmi de numero Indorum
That book was a translation of an Arabic book: Al-Khwarizmi Concerning the Hindu Art of Reckoning
That book was written by the famous 9-th century Muslim mathematician, Muhammad ibn Musa al-
Khwarizmi
16.5 Al-Khwarzmi
Al-Khwarizmi lived in Baghdad, where he worked at the Dar al-Hikma
Dar al-Hikma acquired and translated books on science and philosophy, particularly those in Greek, as
well as publishing original research
The word Algebra has its origins in the title of another Latin book which was a translation of yet another
book written by Al-Khwarzmi:
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Introduction to Computing ­ CS101
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Kitab al-Mukhtasar fi Hisab al-Jabr wa'l-Muqabala
Al-Khwarizmi's Golden Principle
All complex problems can be and must be solved
using the following simple steps:
Break down the problem into small, simple sub-problems
Arrange the sub-problems in such an order that each of them can be solved without effecting any other
Solve them separately, in the correct order
Combine the solutions of the sub-problems to form the solution of the original problem
That was some info on history.
Now, let us to take a look at several types of algorithms & algorithmic strategies
16.6 Greedy Algorithm
An algorithm that always takes the best immediate, or local solution while finding an answer
Greedy algorithms may find the overall or globally optimal solution for some optimization problems,
but may find less-than-optimal solutions for some instances of other problems
KEY ADVANTAGE: Greedy algorithms are usually faster, since they don't consider the details of
possible alternatives
Greedy Algorithm: Counter Example
During one of the international cricket tournaments, one of the teams intentionally lost a match, so that
they could qualify for the next round
If they had won that particular match, some other team would have qualified
This is an example of a non-greedy algorithm
Greedy Algorithm: Example
A skier skiing downhill on a mountain wants to get to the bottom as quickly as possible
What sort of an algorithm should the skier be using?
The greedy-algorithm approach will be to always have the skies pointed towards the largest downhill
slope (dy/dx), at all times
What is the problem with that approach?
In what situations that will be the best algorithm?
In which situations would it perform poorly?
16.7 Deterministic Algorithm (1)
An algorithm whose behavior can be completely predicted from the inputs
That is, each time a certain set of input is presented, the algorithm gives the same results as any other
time the set of input is presented.
16.8 Randomized Algorithm (1)
Any algorithm whose behavior is not only determined by the input, but also values produced by a
random number generator
These algorithms are often simpler and more efficient than deterministic algorithms for the same
problem
Simpler algorithms have the advantages of being easier to analyze and implement.
16.9 Randomized Algorithm (2)
These algorithm work for all practical purposes but have a theoretical chance of being wrong:
Either in the form of incorrect results
Or in the form of impractically long running time
Example: Monte Carlo algorithms.
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Introduction to Computing ­ CS101
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16.10 Deterministic Algorithm (2)
There can be degrees of deterministic behavior: an algorithm that also uses a random number generator
might not be considered deterministic
However, if the "random numbers" come from a pseudo-random number generator, the behavior may be
deterministic
Most computing environments offer a "pseudo random number generators," therefore, most randomized
algorithms, in practice, behave deterministically!
16.11 Heuristic
A procedure that usually, but not always, works or that gives nearly the right answer
Some problems, such as the traveling salesman problem, take far too long to compute an exact, optimal
solution. A few good heuristics have been devised that are fast and find a near-optimal solution more
often than not
Is a heuristic, an algorithm? Yes? No? Why?
The Traveling Salesman Problem
A salesman needs
A possible sequence for n =
6
to visit each of the n
3
cities one after the
other and wants to
5
finish the trip where
1
it was started
2
Determine the
4
sequence of cities
such that the
traveling distance is
6
minimized
A Few Questions
Is that the best possible sequence?
How do you know?
How do I determine the best sequence?
16.12 The Brute Force Strategy (1)
A strategy in which all possible combinations are examined and the best among them is selected
What is the problem with this approach?
A: Doesn't scale well with the size of the problem
How many possible city sequences for n=6? For n=60? For n=600?
16.13 The Brute Force Strategy (2)
However, with the relentless increase in computing power, certain problems that ­ only a few years ago
- were impossible to solve with brute force, are now solvable with this technique
16.14 A Selection of Algorithmic Application Areas
Search
Sort
Cryptography
Parallel
Numeric
Graphical
Quantum computing
Combinatory
We'll now talk about the various ways of representing algorithms.
But, before we do that please allow me to say a few words about ...
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Introduction to Computing ­ CS101
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Syntax & Semantics
An algo. is "correct" if its:
WARNINGS:
­
1. An algo. can be
Semantics are
syntactically correct, yet
correct
semantically incorrect ­
­
very dangerous
situation!
Syntax is correct
2. Syntactic correctness
Semantics:
is easier to check as
The concept embedded in
compared with semantic
an algorithm (the soul!)
Syntax:
The actual representation
of an algorithm (the body!)
Now onto Algorithm Representation
We have said enough about algorithms ­ their definition, their types, etc.
But, how do we actually represent them?
Generally, SW developers represent them in one of three forms:
Pseudo code
Flowcharts
Actual code
Pseudo Code
Language that is typically used for writing algorithms
Similar to a programming language, but not as rigid
The method of expression most suitable for a given situation is used:
At times, plain English
At others, a programming language like syntax
16.15 Flowchart
A graphical representation of a process (e.g. an algorithm), in which graphic objects are used to indicate
the steps & decisions that are taken as the process moves along from start to finish
Individual steps are represented by boxes and other shapes on the flowchart, with arrows between those
shapes indicating the order in which the steps are taken
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Introduction to Computing ­ CS101
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Flowchart
Start or stop
Elements
Process
Input or output
Decision
Flow line
Connector
Off-page connector
In Today's Lecture, We ...
Became familiar with the concept of algorithms:
What they are?
What is their use?
What do they consist of?
What are the techniques used for representing them?
Next Lecture: Algorithms II
We will continue our discussion on algorithms during the next lecture
In particular, we will discuss the pseudo code and flowcharts for particular problems
We will also discuss the pros and cons of these two algorithm representation techniques i.e. pseudo code
and flow charts
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Table of Contents:
  1. INTRODUCTION
  2. EVOLUTION OF COMPUTING
  3. World Wide Web, Web’s structure, genesis, its evolution
  4. Types of Computers, Components, Parts of Computers
  5. List of Parts of Computers
  6. Develop your Personal Web Page: HTML
  7. Microprocessor, Bus interface unit, Data & instruction cache memory, ALU
  8. Number systems, binary numbers, NOT, AND, OR and XOR logic operations
  9. structure of HTML tags, types of lists in web development
  10. COMPUTER SOFTWARE: Operating Systems, Device Drivers, Trialware
  11. Operating System: functions, components, types of operating systems
  12. Forms on Web pages, Components of Forms, building interactive Forms
  13. APPLICATION SOFTWARE: Scientific, engineering, graphics, Business, Productivity, Entertainment, Educational Software
  14. WORD PROCESSING: Common functions of word processors, desktop publishing
  15. Interactivity to Forms, JavaScript, server-side scripts
  16. ALGORITHMS
  17. ALGORITHMS: Pseudo code, Flowcharts
  18. JavaScript and client-side scripting, objects in JavaScript
  19. Low, High-Level, interpreted, compiled, structured & object-oriented programming languages
  20. Software Design and Development Methodologies
  21. DATA TYPES & OPERATORS
  22. SPREADSHEETS
  23. FLOW CONTROL & LOOPS
  24. DESIGN HEURISTICS. Rule of thumb learned through trial & error
  25. WEB DESIGN FOR USABILITY
  26. ARRAYS
  27. COMPUTER NETWORKS: types of networks, networking topologies and protocols
  28. THE INTERNET
  29. Variables: Local and Global Variables
  30. Internet Services: FTP, Telnet, Web, eMail, Instant messaging, VoIP
  31. DEVELOPING PRESENTATIONS: Effective Multimedia Presentations
  32. Event Handlers
  33. GRAPHICS & ANIMATION
  34. INTELLIGENT SYSTEMS: techniques for designing Artificial Intelligent Systems
  35. Mathematical Functions in JavaScript
  36. DATA MANAGEMENT
  37. DATABASE SOFTWARE: Data Security, Data Integrity, Integrity, Accessibility, DBMS
  38. String Manipulations:
  39. CYBER CRIME
  40. Social Implications of Computing
  41. IMAGES & ANIMATION
  42. THE COMPUTING PROFESSION
  43. THE FUTURE OF COMPUTING
  44. PROGRAMMING METHODOLOGY
  45. REVIEW & WRAP-UP of Introduction to Computing