1. UNIT- I General Problem Solving Concepts

2. Contents Introduction General Problem Solving Concepts
Types of Problems
Problem solving with computers
Difficulties with problem solving
Problem solving Aspect
Problem Solving Concepts for Computer
Constants and variables
Data types
Functions
Operators
Expressions and equations
Programming Concepts
Communicating with computers
Organizing the problem
Using the tools
Testing the solution
Coding the program
Time & Space complexity
Sorting Problem

3. problem A perceived gap between the existing state and a desired state
Definition
A perceived gap between the existing state and a desired state

5. Introduction -Einstein
“If I have one hour to save the world I would spend fifty- five minutes defining the problem and only five minutes finding the solution.
-Einstein

6. Six steps for problem Solving
Identify the problem
Understand the problem
Identify alternative ways to solve the problem
Select the best way to solve the problem
List instructions that enable you to solve the problem using the selected solution
Evaluate the solution

7. Example: Problem what to do this evening
Indentify the Problem: How do the Individuals wish to spend the evening?
Understand the problem: The knowledge base of the participants must be considered. The only solutions that should be selected are ones that everyone would know how to do. You probably would not select as a possible solution playing a game of chess if the participants do not know hot to play chess.
Identify Alternatives:
Watch Television
Invite friends over
Play games
Go to the movie
Play miniature golf
Go to a friends party
Go to the amusement park
List is complete only when you can think of no more alternatives
Select best way to solve the problem
Cut out alternatives that are not acceptable
Specify pros and Cons of each Remaining alternative
Compare pros and cons to make final decision
Prepare a list of steps that will result in a fun evening.
Evaluate the solution. Are we having fun yet?

8. E.G. Chitti The Robot
(From: PS&PC by Maureen Sprankle -pg no:463-Appendix A)

9. General Problem-Solving Concepts

10. Types of Problems Problems can be solved with series of actions
Algorithmic Solution
Problems do not always have straightforward solutions
Heuristic solutions
Problem solver can use six steps for both algorithmic and heuristic solutions
Evaluating correctness and Appropriateness of heuristic solutions are far less certain.
Most problems require a combination of the two kinds of solutions

11. Problem solving with computers
Results means the outcome or the completed computer assisted answer
Program means the set of instructions that make up the solution using programming language
Computers are built to deal with algorithmic solutions
Difficulty lies in Programming
Solutions must be transformed into an algorithmic format

12. Difficulties with Problem Solving
People have many problems with problem solving
Afraid to make decisions
People go through one or more steps inadequately
Problem solving process is not easy
Problem solving on computer
Difficult task of writing instructions
Computer has specific system of communication

13. Problem Solving Aspect
There is no universal method for problem solving
Phases
Problem Definition Phase
Getting started on a problem
The use of Specific Examples
Similarities among problems
Working backwards from the solution
General Problem Solving Strategies

14. Problem Definition Phase
What must be done?
We must try to extract set of precisely defined tasks.
E.g. Finding Square root, Greatest Common Divisor
Getting Started on a Problem
Sometimes, even after problem definition people do not know where to start?
What can we do?

15. The use of Specific Examples
Best approach when we are stuck is to make a start on a problem is to pick a specific example
Geometrical and graphical representing certain aspect of a problem can be useful
Similarities among problems
Bring as much as past experiences as possible
New problem cannot be completely different
Sometimes it blocks us from discovering a new thing
In the first instance try to independently solve the problem

16. Greedy method Branch and Bound Backtracking
Working Backwards from the solution
In some cases we assume that we already have solution and then try to work backwards
Whatever attempts we make that we make to get started on a problem we should write it down
General Problem Solving Strategies
Divide and Conquer
Binary doubling
Dynamic Programming
Greedy method
Branch and Bound
Backtracking

17. Problem Solving Concepts for the Computer

18. Constants and Variables
The Computer uses constants and variables to solve problems
Constants is a value that never changes during processing of all instructions
Can be numeric, alphabetic or special Symbol
Constant is given a value and then referred to by its name
In contrast, the value of a variable may change during processing
In many languages variables are called Identifiers

19. Rules for naming and Using Variables
Name a variable according to what it represent
Do not use spaces in variable name
Start variable with a letter
Do not use dash(-) in a program
After introduces variable name, exact variable name must be used where data item is used
Be consistent while using UPPERCASE and lowercase variables
Use naming conventions specified by your company

20. Data Types To process solutions computer must have data.
Data are unorganized facts
Computer Must be told the data types of each variable and constant
DATA
Data Processed into information
Report
Checks
Deposits
Bk Charges
Calculates the Balance
Balance Sheet
Fig. Processing Data: How a computer Balances a Checkbook

21. Surrounded by quotation mark All letters, Numbers and Special Symbols
Data Type
Data Sets
Examples
Numeric:
Integer
All whole numbers
3400
-34
Real
All real Numbers
(Whole + Decimal)
Character :
Surrounded by quotation mark
All letters, Numbers and Special Symbols
“a”, “1”, “A”, “F”, “%”, “&”
“$”
String:
Combination of more than one character
“Rahul”
“343443”
“ ”
Logical
True, False

22. Rules for Data Types
The data that define the value of a variable or a constant will be of numeric, character, logical
Computer then associate variable with desired data type
Data types can not be mixed
Each of the data types uses what is called a data sets
Any numeric item that must be used in calculations resulting in a numeric result must be of numeric type

23. Functions
Functions are small set of instructions that perform specific task and return values
By using functions programmers can shorten the problem solving time and improves readability
Each language has set of functions within it
Most languages allows programmers to write their own functions
Functions can be
Mathematical functions
String functions
Conversion Functions
Statistical functions
Utility functions

24. Operators Mathematical + - / * % ^
Operators are the data connectors within expressions
They tell the computer how to process data
Operators
Mathematical + - / * % ^
Relational < > <= >= != [<>]
Logical && || !
Operand and resultant are two concepts related to operator
The data type of Operands and resultant depends on the operator

25. Expressions and Equations
Expressions and Equations make a part of instructions in the solution
An Expressions processes data, operands using operators e.g. length * breadth
An Equation stores the resultant of an expression e.g. area=length*breadth
Setting up /Evaluating
Numeric Expression
Mathematical equations
Relational Expression
Logical expression

26. Programming Concepts

27. Communicating with the computer
We have to learn system of communication or Computer language
System of communication requires instructions governed by specific rules.
Syntax are the rules governing the computer operating system
An error is called a bug
Bug must be found and corrected, a process is called Debugging
Computers are exact machines but the people working with them are not.

28. Organizing the problem
Organizational tools will help us to solve problems on the computer
Tools
Problem Analysis Chart
Structure Chart or Interactivity Chart
IPO chart
Algorithms
Flowcharts

29. Analyzing the Problem The given data The required Results
First programmer has to understand and analyze the requirements of the problem
Good way to analyze problem is to separate it into four parts
The given data
The required Results
The processing that required in the problem
A list of solution alternatives
PAC allows problem solver to eliminate the words and separate the facts from the problem

30. 4. Solution Alternatives
1. Given Data
2. Required Results
3. Processing Required
4. Solution Alternatives
Fig: Problem Analysis Chart

31. Grosspay=Hours*Payrate 4. Solution Alternatives
Given Data
Hours
Pay rate
2. Required Results
Grosspay
3. Processing Required
Grosspay=Hours*Payrate
4. Solution Alternatives
Define the hours worked and Payrate as constants
Define the hours worked and payrate as input values
Fig: Problem Analysis Chart

32. Developing the Interactivity(Structure) Chart
Next task in organizing the solution is to divide the processing into subtasks called modules
Connect these modules to show interaction of processing between modules
Each module should contain the task to accomplish one function
There will be one module that controls the flow of most of the other module[Control or Main module]

33. Control Module 1 Module 3 Module 2 Module 6 Module 7 Module 4 Module 5
Interactivity Chart
Interactivity Chart for Payroll Problem
Payrollcontrol
Read
Calc
Print
Until No Employee

34. Module 7
Module 6
Module 3
Module 2
Module 3
Module 1
CONTROL
Module 5
Module 4
Interactivity Chart
[Object Oriented Solution]

35. Object Oriented Solution
Read
PayrollControl
Print
Calc
Interactivity Chart for Payroll Problem
Object Oriented Solution

36. Developing the IPO chart
The input-processing-output chart extends and organizes the information in the PAC
IPO also shows that where in the solution processing takes place
Sections
Input
The processing
Module Reference
Output

37. Input
Processing
Module reference
Output
All data input [From section 1 of PAC]
All processing in step [From Section 3 and 4]
Module reference from the interactivity chart
All output requirement
[from section1 and 2 from PAC]
The IPO Chart
Input
Processing
Module reference
Output
Hours worked
Pay Rate
Enter Hours Worked
Enter Pay Rate
Calculate Pay
Print Pay
End
Read
Calc
Print
Payrollcontrol
Gross pay
The IPO Chart for the Payroll Problem

38. e.g
Joe would like to build several bookcases that are different heights and widths. All will be 12 inches in depth. The bookcases will have 3 shelves, in addition to the bottom and top. Write a solution to print the no. of feet of 12 –inch-wide boards that Joe need to complete a bookcase, given the height and width.
Bob would like to know what percentage of his income his rent is. Write a solution that would calculate and print this percentage. (Hint: Percentage=Number/Total)

39. Writing the Algorithms
Next steps in organizing the solution is to develop set of instructions for the computer called algorithm
Pseudo code is similar to algorithms
Programmer writes a separate instructions for each module in the structure chart
Hardest part of problem solving
The instructions cannot assume anything
Cannot skip Steps
Must be executable one step at a time
Must be complete

40. Drawing Flowchart
From the algorithms programmer develops the flowcharts
Flowcharts are the graphical representation of the algorithms
Flowcharts can show errors in logic not readily visible in the other charts
A flowchart shows the flow of the processing from the beginning to the end of a solution

41. Rules for drawing flowcharts
You should write instructions inside the blocks
If there is something you need to remember you can write a note besides a block
A flowchart always start at the top of the page and flows to the bottom
Use flowchart template to draw the symbols and flow lines
Make the blocks big enough to write instructions so they can be easily read
Final copy of the flowchart may not be the first draft

42. Testing the Solutions
When a solution is complete it is important to test it
To test a solution programmers select test data, a set of values
A solution should never be assumed correct.
If bug is detected, the solution has to be modified it and then the testing process starts once again

43. Coding the Program
Next step is writing the solution into a computer language
If programmer follows the proper steps in developing solution there should be few logic errors in the program

44. Pointers of structuring program
Use modules
4 Logic structures
Sequential structure
Decision structure
Loop structure
Case structure

45. Modules Rules for designing modules
Solution breaks always in modules
Rules for designing modules
Each module is an entity itself with entrance and exit
It should not jump in between
Only with Single function or task
Easily readable and modified
No. of instructions to complete the function should be governed by functions
Order of processing

46. Types of modules Control module Initialization module Process module
Calculation modules
Print modules
Read and data validation modules
Wrap up modules
Event module in OOP( mouse up/dw etc…)

47. Cohesion and coupling Cohesion: independent of each other Module 1
Coupling allows to share data with some interface
Module 3

48. Solution development -6 steps
The problem analysis chart
The interactivity chart
The IPO chart
Coupling diagram with design of data flow
Algorithm writing
Flowchart

49. PART I END