1. Problem Solving Concepts
Dr. Munesh Singh

2. POINTS TO BE DISCUSSED:
What is mean by data, information, data structure
What is a problem?-Types of problems
Problem Solving in everyday life.
Six steps for general problem solving
Problem solving concepts for computers
Organising Problems
Problem Analysis Charts
Structure/Interactivity Charts, IPO Chart
Algorithm, Flowcharts, Internal and External documentation

3. Review of Data Structure
Data is raw
Unorganized facts that needs to be processed
Data can be simple and seamlessly random
Useless until it is organized
Example: Student record is one piece of data
Information
When data is processed
Organized or structured
Presented in a given context to make it useful

4. Review of Data Structure
Data Type: a data type or simply type is a classification identifying one of various types of data:
Real-valued
Integer
Boolean
determines the possible values for that type
the operations that can be done on values of that type
the meaning of the data
the way values of that type can be stored.
Data Structure: a data structure is a particular way of storing and organizing data in a computer so that it can be used efficiently.

5. Types of Data Structures

6. What is a Problem? A state of difficulty that needs to be resolved
Problems exist where goals need to be attained and there is uncertainty about solution
A Problem is an opportunity for improvement
A problem is the difference between your current state and your goal state

7. Problem Faced in Everyday in Life
People make decisions everyday
Examples:
Should I wear casual or formal today?
Should I watch TV or go out to cinema?
what career?
what course?
What shoes?
Everything needs a DECISION AS A SOLUTION TO THE PROBLEM

8. What happens when bad decisions are made?
WASTAGE OF TIME AND RESOURCES

9. Six steps to ensure a Best decision in PROBLEM SOLVING
Identify the problem
Understand the problem
Identify alternative ways to solve the problem
Select the best way to solve the problem from the list of alternative solutions
List instructions that enable you to solve the problem using selected solution
Evaluate the solution

10. Take the problem of what to do to get solution
A Water Jug Problem: You are given two jugs, a 4-gallon one and a 3-gallon one, a pump which has unlimited water which you can use to fill the jug, and the ground on which water may be poured. Neither jug has any measuring markings on it.
How can you get exactly 2 gallons of water in the 4-gallon jug?

11. Problem Steps
To solve this we have to make some assumptions not mentioned in the problem. They are
1. We can fill a jug from the pump.
2. we can pour water out of a jug to the ground.
3. We can pour water from one jug to another.
4. There is no measuring device available.

12. What I am Expecting
How to approach this problem in terms traditional way.
Hint. Input, output, and logic
How to Map this problem in computer language
Which kind of Data Structure you need to Solve this problem efficiently
This problem is heuristic or Algorithmic.
how many solution of this problem.
And which one is the best solution with reason

13. First Solutions of the Problem

14. Second and Third Solution

15. Data structure for above problem
Graph will be the data structure to solve this problem
BFS (Breadth first search)
DFS (Depth first search)

16. Another Problem
On one bank of a river are three missionaries and three cannibals. There is one boat available that can hold up to two people and that they would like to use to cross the river. If the cannibals ever outnumber the missionaries on either of the river’s banks, the missionaries will get eaten.  How can the boat be used to safely carry all the missionaries and cannibals across the river?

17. TIC-TAC-TOE Problem

18. Approaches to solve a problem:
Algorithmic :
Solutions that can be solved with a series of known actions are called
Algorithmic Solutions
Heuristic :
Employing a self-learning approach to the solution of a problems is known as
Heuristic Solutions

19. Examples Algorithmic solution: To make a cup of coffee
To find largest of three numbers
Heuristic solutions:
how to buy the best stock?
How to play chess?

20. Problem solving with computers
Computers use algorithmic solutions
Program – set of instructions that make up solution to a problem
Results – outcome of running the program
Testing – Are the outcomes what you expected and correct
Documentation – two types
manual documentation
instructions telling users how to use the program

21. Problem solving with computers involves several steps
Clearly define the problem.
Analyze the problem and formulate a method to solve it (see also .validation.).
Describe the solution in the form of an algorithm.
Draw a flowchart of the algorithm.
Write the computer program.
Compile and run the program (debugging).
Test the program (debugging) (see also verification.).
Interpretation of results.

22. ALGORITHMS AND FLOWCHARTS
A typical programming task can be divided into two phases:
Problem solving phase
produce an ordered sequence of steps that describe solution of problem
this sequence of steps is called an algorithm
Implementation phase
implement the program in some programming language

23. Steps in Problem Solving
First produce a general algorithm (one can use pseudo code)
Refine the algorithm successively to get step by step detailed algorithm that is very close to a computer language.
Pseudo code is an artificial and informal language that helps programmers develop algorithms. Pseudo code is very similar to everyday English.

24. Pseudo code & Algorithm
Example 1: Write an algorithm to determine a student’s final grade and indicate whether it is passing or failing. The final grade is calculated as the average of four marks.

25. Pseudo code & Algorithm
Input a set of 4 marks
Calculate their average by summing and dividing by 4
if average is below 50
Print “FAIL”
else
Print “PASS”

26. Pseudocode & Algorithm
Detailed Algorithm
Step 1: Input M1,M2,M3,M4
Step 2: GRADE  (M1+M2+M3+M4)/4
Step 3: if (GRADE < 50) then
Print “FAIL”
else
Print “PASS”
endif

27. The Flowchart
(Dictionary) A schematic representation of a sequence of operations, as in a manufacturing process or computer program.
(Technical) A graphical representation of the sequence of operations in an information system or program.
Information system flowcharts show how data flows from source documents through the computer to final distribution to users.
Program flowcharts show the sequence of instructions in a single program or subroutine.
Different symbols are used to draw each type of flowchart.

28. The Flowchart A Flowchart shows logic of an algorithm
emphasizes individual steps and their interconnections
e.g. control flow from one action to the next

29. Flowchart Symbols
Basic

30. Example 1 START Input M1,M2,M3,M4 GRADE(M1+M2+M3+M4)/4 IS GRADE<50
PRINT
“FAIL”
STOP Y N
PRINT
“PASS”

31. Example 2
Write an algorithm and draw a flowchart to convert the length in feet to centimeter.
Pseudo code:
Input the length in feet (Lft)
Calculate the length in cm (Lcm) by multiplying LFT with 30
Print length in cm (LCM)

32. Flowchart

33. Example 3
Write an algorithm and draw a flowchart that will read the two sides of a rectangle and calculate its area.
Pseudocode
Input the width (W) and Length (L) of a rectangle
Calculate the area (A) by multiplying L with W
Print A

34. Algorithm
Step 1: Input W,L
Step 2: A  L x W
Step 3: Print A

35. Example 4
Write an algorithm and draw a flowchart that will calculate the roots of a quadratic equation
Hint: d = sqrt ( ), and the roots are: x1 = (–b + d)/2a and x2 = (–b – d)/2a

36. Pseudo code:
Input the coefficients (a, b, c) of the quadratic equation
Calculate d
Calculate x1
Calculate x2
Print x1 and x2

37. Algorithm: Step 1: Input a, b, c Step 2: d  sqrt ( )
Step 3: x1  (–b + d) / (2 x a)
Step 4: x2  (–b – d) / (2 x a)
Step 5: Print x1, x2
START
Input
a, b, c
d  sqrt(b x b – 4 x a x c)
Print
x1 ,x2
STOP
x1 (–b + d) / (2 x a)
X2  (–b – d) / (2 x a)

38. DECISION STRUCTURES The expression A>B is a logical expression
it describes a condition we want to test
if A>B is true (if A is greater than B) we take the action on left
print the value of A
if A>B is false (if A is not greater than B) we take the action on right
print the value of B

39. DECISION STRUCTURES

40. IF–THEN–ELSE STRUCTURE
The structure is as follows:
If condition then
true alternative
else
false alternative
endif

41. IF–THEN–ELSE STRUCTURE
The algorithm for the flowchart is as follows:
If A>B then
print A
else
print B
endif

42. Relational Operators

43. Example 5
Write an algorithm that reads two values, determines the largest value and prints the largest value with an identifying message.
ALGORITHM
Step 1: Input VALUE1, VALUE2
Step 2: if (VALUE1 > VALUE2) then
MAX  VALUE1
else
MAX  VALUE2
endif
Step 3: Print “The largest value is”, MAX

45. NESTED IFS One of the alternatives within an IF–THEN–ELSE statement
may involve further IF–THEN–ELSE statement

46. Example 6
Write an algorithm that reads three numbers and prints the value of the largest number.

48. A program that is easy to read & understand, and therefore, easy to maintain & enhance
readable program?

49. A program with correct syntax & semantics
correct program?

50. PPT you will get on the link https://shodhkarya.blogspot.in/
Queries ?
PPT you will get on the link

51. ThanksYou