Algorithmic problem sloving

1152EC256 Python Programming
Unit 1 - ALGORITHMIC PROBLEM SOLVING
Welcome
You
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Content
• Algorithms
• building blocks of algorithms (statements, state, control flow, functions),
• notation (pseudo code, flow chart, programming language)
• algorithmic problem solving
• simple strategies for developing algorithms (iteration, recursion).
• Illustrative problems:
• find minimum in a list
• insert a card in a list of sorted cards
• Guess an
• integer number in a range
• Towers of Hanoi.

PROBLEM SOLVING
• Problem solving is the systematic approach to define the
problem and creating number of solutions.
• The problem solving process starts with the problem
specifications and ends with a Correct program.

PROBLEM SOLVING TECHNIQUES
• Problem solving technique is a set of techniques that helps in
providing logic for solving a problem.
• Problem Solving Techniques:
• Problem solving can be expressed in the form of
1. Algorithms.
2. Flowcharts.
3. Pseudo codes.
4. programs

Algorithm
It is defined as a sequence of
instructions that describe a
method for solving a
problem.
In other words it is a step by step
procedure for solving a problem.
Properties of Algorithms
• Should be written in simple English
• Each and every instruction should be precise and
unambiguous.
• Instructions in an algorithm should not be
repeated infinitely.
• Algorithm should conclude after a finite number
of steps.
• Should have an end point
• Derived results should be obtained only after the
algorithm terminates.

Qualities of a good algorithm
• Time
• Memory
• Accuracy
• Time – To execute a program, the computer system takes
some amount of time. The lesser is the time required, the
better is the algorithm.
• Memory – To execute a program, computer system takes
some amount of memory space. The lesser is the memory
required, the better is the algorithm.
• Accuracy – Multiple algorithms may provide suitable or
correct solutions to a given problem, some of these may
provide more accurate results than others, and such
algorithms may be suitable.

Example
• Write an algorithm to print „Good Morning”
Step 1: Start
Step 2: Print “Good Morning”
Step 3: Stop

BUILDING BLOCKS OF ALGORITHMS
• Statements
• State
• control flow
• Functions
• Algorithms can be constructed from basic building blocks namely
• sequence,
• selection
• iteration.

Statements
• Statement is a single action in a computer.
• In a computer statements might include some of the
following actions
• input data-information given to the program
• process data-perform operation on a given input
• output data-processed result

State
• Transition from one process to another process under specified
condition with in a
• time is called state.

Control flow
• The process of executing the individual statements in a given order is
called control flow.
• The control can be executed in three ways
1. sequence
2. selection
3. iteration

Sequence
• All the instructions are executed one after another is called sequence
execution.

Selection
• A selection statement causes
the program control to be
transferred to a specific part
of the program based upon
the condition.
• If the conditional test is true,
one part of the program will
be executed, otherwise it
will execute the other part of
the program

Example
Write an algorithm to check whether he is eligible to vote?
• Step 1: Start
• Step 2: Get age
• Step 3: if age >= 18 print “Eligible to vote”
• Step 4: else print “Not eligible to vote”
• Step 6: Stop

Iteration
• In some programs, certain set of statements are executed again and
again based upon conditional test. i.e. executed more than one time.
This type of execution is called looping or iteration.

Example
Write an algorithm to print all natural numbers up to n
• Step 1: Start
• Step 2: get n value.
• Step 3: initialize i=1
• Step 4: if (i<=n) go to step 5 else go to step 7
• Step 5: Print i value and increment i value by 1
• Step 6: go to step 4
• Step 7: Stop

Functions
• Function is a sub program which consists of block of code(set of
instructions)that performs a particular task.
• For complex problems, the problem is been divided into smaller and
simpler tasks during algorithm design

Benefits of Using Functions
• Reduction in line of code
• code reuse
• Better readability
• Information hiding
• Easy to debug and test
• Improved maintainability

Example
Algorithm for addition of two numbers using function
Main function()
• Step 1: Start
• Step 2: Call the function add()
• Step 3: Stop
sub function add()
• Step 1: Function start
• Step 2: Get a, b Values
• Step 3: add c=a+b
• Step 4: Print c
• Step 5: Return

NOTATIONS
3.1.FLOW CHART
• Flow chart is defined as graphical representation of the logic for
problem solving.
• The purpose of flowchart is making the logic of the program clear in a
visual representation

Rules for drawing a flowchart
• 1. The flowchart should be clear, neat and easy to follow.
• 2. The flowchart must have a logical start and finish.
• 3. Only one flow line should come out from a process symbol.
• 4. Only one flow line should enter a decision symbol. However,
two or three flow lines may leave the decision symbol.
• 5. Only one flow line is used with a terminal symbol.
• 6. Within standard symbols, write briefly and precisely.
• 7. Intersection of flow lines should be avoided.

Advantages of flowchart
1. Communication: - Flowcharts are better way of communicating the logic
of a system to all concerned.
2. Effective analysis: - With the help of flowchart, problem can be analyzed
in more effective way.
3. Proper documentation: - Program flowcharts serve as a good program
documentation, which is needed for various purposes.
4. Efficient Coding: - The flowcharts act as a guide or blueprint during the
systems analysis and program development phase.
5. Proper Debugging: - The flowchart helps in debugging process.
6. Efficient Program Maintenance: - The maintenance of operating program
becomes easy with the help of flowchart. It helps the programmer to put
efforts more efficiently on that part.

Disadvantages of flow chart
1. Complex logic: - Sometimes, the program logic is quite complicated.
In that case, flowchart becomes complex and clumsy.
2. Alterations and Modifications: - If alterations are required the
flowchart may require re-drawing completely.
3. Reproduction: - As the flowchart symbols cannot be typed,
reproduction of flowchart becomes a problem.
4. Cost: For large application the time and cost of flowchart drawing
becomes costly.

PSEUDO CODE
• Pseudo code consists of short, readable and formally styled English
languages used for explain an algorithm.
• It does not include details like variable declaration, subroutines.
• It is easier to understand for the programmer or non programmer
to understand
• the general working of the program, because it is not based on any
programming language.
• It gives us the sketch of the program before actual coding.
• It is not a machine readable
• Pseudo code can’t be compiled and executed.
• There is no standard syntax for pseudo code

Guidelines for writing pseudo code
• Write one statement per line
• Capitalize initial keyword
• Indent to hierarchy
• End multiline structure
• Keep statements language independent

Common keywords used in pseudocode
• The following gives common keywords used in pseudocodes.
• 1. //: This keyword used to represent a comment.
• 2. BEGIN,END: Begin is the first statement and end is the last statement.
• 3. INPUT, GET, READ: The keyword is used to inputting data.
• 4. COMPUTE, CALCULATE: used for calculation of the result of the given
expression.
• 5. ADD, SUBTRACT, INITIALIZE used for addition, subtraction and initialization.
• 6. OUTPUT, PRINT, DISPLAY: It is used to display the output of the program.
• 7. IF, ELSE, ENDIF: used to make decision.
• 8. WHILE, ENDWHILE: used for iterative statements.
• 9. FOR, ENDFOR: Another iterative incremented/decremented tested
automatically.

Advantages
• Pseudo is independent of any language; it can be used by most
programmers.
• It is easy to translate pseudo code into a programming language.
• It can be easily modified as compared to flowchart.
• Converting a pseudo code to programming language is very easy as
compared with converting a flowchart to programming language.

Disadvantages
• It does not provide visual representation of the program’s
logic.
• There are no accepted standards for writing pseudo codes.
• It cannot be compiled nor executed.
• For a beginner, It is more difficult to follow the logic or write
pseudo code as compared to flowchart.

• Addition of two numbers:
BEGIN
GET a,b
ADD c=a+b
PRINT c
END

Algorithm Flowchart Pseudo code
An algorithm is a sequence
of instructions used to
solve a problem
It is a graphical
representation of algorithm
It is a language
representation of
algorithm.
User needs knowledge to
write algorithm.
not need knowledge of
program to draw or
understand flowchart
Not need knowledge of
program language to
understand or write a
pseudo code.

PROGRAMMING LANGUAGE
• A programming language is a set of symbols and rules for
instructing a computer to perform specific tasks.
• The programmers have to follow all the specified rules before
writing program using programming language.
• The user has to communicate with the computer using
language which it can understand.
• Types of programming language
1. Machine language
2. Assembly language
3. High level language

Machine language
• The computer can understand only machine language which uses 0’s
and 1’s.
• In machine language the different instructions are formed by taking
different combinations of 0’s and 1’s.

Advantages
Translation free:
• Machine language is the only language which the computer
understands. For executing any program written in any
programming language, the conversion to machine language
is necessary.
• The program written in machine language can be executed
directly on computer.
• In this case any conversion process is not required.
High speed
• The machine language program is translation free. Since the
conversion time is saved, the execution of machine language
program is extremely fast

Disadvantage
• It is hard to find errors in a program written in the machine
language.
• Writhing program in machine language is a time consuming
process.
Machine dependent:
• According to architecture used, the computer differs from
each other.
• So machine language differs from computer to computer.
• So a program developed for a particular type of computer
may not run on other type of computer

Assembly language
• To overcome the issues in programming language and make
the programming process easier, an assembly language is
developed which is logically equivalent to machine language
but it is easier for people to read, write and understand.
• Assembly language is symbolic representation of machine
language.
• Assembly languages are symbolic programming language that
uses symbolic notation to represent machine language
instructions.
• They are called low level language because they are so
closely related to the machines.
• Ex: ADD a, b

• Assembler:
• Assembler is the program which translates assembly language
instruction in to a machine language.
• Advantage:
• Easy to understand and use.
• It is easy to locate and correct errors.
• Disadvantage
• Machine dependent
• Hard to learn
• Less efficient

High level language
• High level language contains English words and symbols.
• The specified rules are to be followed while writing program
in high level language.
• The interpreter or compilers are used for converting these
programs in to machine readable form.
• Translating high level language to machine language
• The programs that translate high level language in to machine
language are called interpreter or compiler.

• Compiler:
• A compiler is a program which translates the source code written in
a high level language in to object code which is in machine language
program. Compiler reads the whole program written in high level
language and translates it to machine language. If any error is found
it display error message on the screen.
• Interpreter
• Interpreter translates the high level language program in line by line
manner. The interpreter translates a high level language statement
in a source program to a machine code and executes it immediately
before translating the next statement. When an error is found the
execution of the program is halted and error message is displayed on
the screen.

Advantages
• Readability
• High level language is closer to natural language so they are easier to
learn and understand
• Machine independent
• High level language program have the advantage of being portable
between machines.
• Easy debugging
• Easy to find and correct error in high level language
• Disadvantages
• Less efficient
• The translation process increases the execution time of the program.
Programs in high level language require more memory and take
more execution time to execute.

They are divided into following categories
1. Interpreted programming languages
2. Functional programming languages
3. Compiled programming languages
4. Procedural programming languages
5. Scripting programming language
6. Markup programming language
7. Concurrent programming language
8. Object oriented programming language

Interpreted programming languages
• An interpreted language is a programming language for which
most of its implementation executes instructions directly,
without previously compiling a program into machine
language instructions.
• The interpreter executes the program directly translating each
statement into a sequence of one or more subroutines
already compiled into machine code.
• Examples:
• Pascal
• Python

Functional programming language
• Functional programming language defines every computation as a
mathematical evaluation.
• They focus on the programming languages are bound to
mathematical calculations
• Examples:
• Clean
• Haskell

Compiled Programming language
• A compiled programming is a programming language whose
implementation are typically compilers and not interpreters.
• It will produce a machine code from source code.
• Examples:
• C
• C++
• C#
• JAVA

Procedural programming language
• Procedural (imperative) programming implies specifying the
steps that the programs should take to reach to an intended
state.
• A procedure is a group of statements that can be referred
through a procedure call.
• Procedures help in the reuse of code. Procedural
programming makes the programs structured and easily
traceable for program flow.
• Examples:
• Hyper talk
• MATLAB

Scripting language
• Scripting language are programming languages that control an
application.
• Scripts can execute independent of any other application.
They are mostly embedded in the application that they
control and are used to automate frequently executed tasks
like communicating with external program.
• Examples:
• Apple script
• VB script

Markup languages:
• A markup language is an artificial language that uses annotations to
text that define hoe the text is to be displayed.
• Examples:
• HTML
• XML

Concurrent programming language:
• Concurrent programming is a computer programming technique that
provides for the execution of operation concurrently, either with in a
single computer or across a number of systems.
• Examples:
• Joule
• Limbo

Object oriented programming language:
• Object oriented programming is a programming paradigm based on
the concept of objects which may contain data in the form of
procedures often known as methods
• Examples:
• Lava
• Moto

ALGORITHMIC PROBLEM SOLVING
• Algorithmic
problem
solving is
solving
problem that
require the
formulation of
an algorithm
for the
solution.

SIMPLE STRATEGIES FOR DEVELOPING
ALGORITHMS
• 1. iterations
• 2. Recursions

Iterations
• A sequence of statements is executed until a specified
condition is true is called iterations.
• 1. for loop
• 2. While loop

Recursions
• A function that calls itself is known as recursion.
• Recursion is a process by which a function calls itself
repeatedly until some specified condition has been satisfied.

Algorithm :
Step 1: Start
Step 2: Get a list “a”
step 3: assign the first element of the list as min
Step 4: for each element(i) in “a” go to step5 else go to step 6
Step 5: if(i<min) then min=i else go to step 4
step 6: print min value
Step 8: Stop
Minimum element in a list

step 1: Start
Step 2: get a list a
Step 3: for each element (i) in a go to step4 else go to step 8
step 4: get the index of i assign it to j and go to step 5
Step 5: while (j>0) got to step6 else go to step3
Step 6: if(a[j-1]>a[j]) then swap a[j],a[j-1] and go to step7
else go to step7
step 7:decrement j value and go to step 5
Step 8: Print the list a
Step 9: Stop
Insert a card in a list of sorted cards

step 1: Start
Step 2: Assign computer generated number as num
Step 3: Get guess value from user
Step 4: if(guess== num) then print “well-done” and got o step 8
else go to step 5
Step 5: if(guess> num) then print “too high” and go to step 7
step 6: else print “too low” and go to step 7
Step 7: if you want to guess again go to step 3 else go to step 9
Step 8: if you want to play again go to step 2 else go to step 9
Step 9: stop
Guess a integer number in a range

• A tower of Hanoi is a mathematical puzzle with three rods
and n number of discs.
• The mission is to move all the disks to some another tower
without violating the
• sequence of arrangement.
• A few rules to be followed for Tower of Hanoi are −
• Only one disk can be moved among the towers at any given
time.
• Only the "top" disk can be removed.
• No large disk can sit over a small disk.
Towers of Hanoi

• Steps for algorithm:
Step 1 − Move n-1 disks from source to aux
Step 2 − Move nth disk from source to dest
Step 3 − Move n-1 disks from aux to dest
• Pseudocode for tower of Hanoi
• BEGIN
• Function Hanoi (n, source, dest, aux)
• IF n == 1, THEN
• move n from source to dest
• ELSE
• Hanoi (n - 1, source, aux, dest) // Step 1
• move n from source to dest // Step 2
• Hanoi (n - 1, aux, dest, source) // Step 3
• END IF
• END Function
• END

# Recursive Python function to solve tower of hanoi
def TowerOfHanoi(n , from_rod, to_rod, aux_rod):
if n == 1:
print "Move disk 1 from rod",from_rod,"to rod",to_rod
return
TowerOfHanoi(n-1, from_rod, aux_rod, to_rod)
print "Move disk",n,"from rod",from_rod,"to rod",to_rod
TowerOfHanoi(n-1, aux_rod, to_rod, from_rod)
# Driver code
n = 4
TowerOfHanoi(n, 'A', 'C', 'B')
# A, C, B are the name of rods

Algorithmic problem sloving

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