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FlowChart & Algorithm
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1 Decision Support System Hemant Kumar Jain : [email protected]
Algorithms and Flowcharts
Hemant Jain B.Sc (PCM), M.Sc (Phy), B. Tech (Telcom & Elec), MDBA , MS (Comp. Sc.) USA
Tuesday, November 12, 2013
2 Decision Support System Hemant Kumar Jain : [email protected]
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
3 Decision Support System Hemant Kumar Jain : [email protected]
Steps in Problem Solving
First produce a general algorithm (one can use pseudocode)
Refine the algorithm successively to get step by step detailed algorithm that is very close to a computer language.
Pseudocode is an artificial and informal language that helps programmers develop algorithms. Pseudocode is very similar to everyday English.
4 Decision Support System Hemant Kumar Jain : [email protected]
Pseudocode & Algorithm
Example 1: Write an algorithm to determine a students final grade and indicate whether it is passing or failing. The final grade is calculated as the average of four marks.
5 Decision Support System Hemant Kumar Jain : [email protected]
Pseudocode & Algorithm
Pseudocode:
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
6 Decision Support System Hemant Kumar Jain : [email protected]
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
7 Decision Support System Hemant Kumar Jain : [email protected]
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.
8 Decision Support System Hemant Kumar Jain : [email protected]
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
9 Decision Support System Hemant Kumar Jain : [email protected]
Flowchart Symbols
Basic
Oval
Parallelogram
Rectangle
Diamond
Hybrid
Name Symbol Use in Flowchart
Denotes the beginning or end of the program
Denotes an input operation
Denotes an output operation
Denotes a decision (or branch) to be made.
The program should continue along one of
two routes. (e.g. IF/THEN/ELSE)
Denotes a process to be carried out
e.g. addition, subtraction, division etc.
Flow line Denotes the direction of logic flow in the program
10 Decision Support System Hemant Kumar Jain : [email protected]
Example
PRINT PASS
Step 1: Input M1,M2,M3,M4 Step 2: GRADE (M1+M2+M3+M4)/4 Step 3: if (GRADE
11 Decision Support System Hemant Kumar Jain : [email protected]
Example 2
Write an algorithm and draw a flowchart to convert the length in feet to centimeter.
Pseudocode:
Input the length in feet (Lft)
Calculate the length in cm (Lcm) by multiplying LFT with 30
Print length in cm (LCM)
12 Decision Support System Hemant Kumar Jain : [email protected]
Example 2
Algorithm
Step 1: Input Lft
Step 2: Lcm Lft x 30
Step 3: Print Lcm
START
Input Lft
Lcm Lft x 30
Print Lcm
STOP
Flowchart
13 Decision Support System Hemant Kumar Jain : [email protected]
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
14 Decision Support System Hemant Kumar Jain : [email protected]
Example 3
Algorithm
Step 1: Input W,L
Step 2: A L x W
Step 3: Print A
START
Input W, L
A L x W
Print A
STOP
15 Decision Support System Hemant Kumar Jain : [email protected]
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
2 0ax bx c 2 4b ac
16 Decision Support System Hemant Kumar Jain : [email protected]
Example 4
Pseudocode:
Input the coefficients (a, b, c) of the quadratic equation
Calculate d
Calculate x1
Calculate x2
Print x1 and x2
17 Decision Support System Hemant Kumar Jain : [email protected]
Example 4
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)
4b b a c
18 Decision Support System Hemant Kumar Jain : [email protected]
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
19 Decision Support System Hemant Kumar Jain : [email protected]
DECISION STRUCTURES
is A>B
Print B Print A
Y N
20 Decision Support System Hemant Kumar Jain : [email protected]
IFTHENELSE STRUCTURE
The structure is as follows
If condition then
true alternative
else
false alternative
endif
21 Decision Support System Hemant Kumar Jain : [email protected]
IFTHENELSE STRUCTURE
The algorithm for the flowchart is as follows:
If A>B then
print A
else
print B
endif
is A>B
Print B Print A
Y N
22 Decision Support System Hemant Kumar Jain : [email protected]
Relational Operators
Relational Operators
Operator Description
> Greater than
< Less than
= Equal to
Greater than or equal to
Less than or equal to
Not equal to
23 Decision Support System Hemant Kumar Jain : [email protected]
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
24 Decision Support System Hemant Kumar Jain : [email protected]
Example 5
MAX VALUE1
Print The largest value is, MAX
STOP
Y N
START
Input VALUE1,VALUE2
MAX VALUE2
is VALUE1>VALUE2
25 Decision Support System Hemant Kumar Jain : [email protected]
NESTED IFS
One of the alternatives within an IFTHENELSE statement
may involve further IFTHENELSE statement
26 Decision Support System Hemant Kumar Jain : [email protected]
Example 6
Write an algorithm that reads three numbers and prints the value of the largest number.
27 Decision Support System Hemant Kumar Jain : [email protected]
Example 6
Step 1: Input N1, N2, N3 Step 2: if (N1>N2) then if (N1>N3) then MAX N1 [N1>N2, N1>N3] else MAX N3 [N3>N1>N2] endif else if (N2>N3) then MAX N2 [N2>N1, N2>N3] else MAX N3 [N3>N2>N1] endif endif Step 3: Print The largest number is, MAX
28 Decision Support System Hemant Kumar Jain : [email protected]
Example 6
Flowchart: Draw the flowchart of the above Algorithm.
29 Decision Support System Hemant Kumar Jain : [email protected]
Example 7
Write and algorithm and draw a flowchart to
a) read an employee name (NAME), overtime hours worked (OVERTIME), hours absent (ABSENT) and
b) determine the bonus payment (PAYMENT).
30 Decision Support System Hemant Kumar Jain : [email protected]
Example 7
Bonus Schedule
OVERTIME (2/3)*ABSENT Bonus Paid
>40 hours
>30 but 40 hours
>20 but 30 hours
>10 but 20 hours
10 hours
$50
$40
$30
$20
$10
31 Decision Support System Hemant Kumar Jain : [email protected]
Step 1: Input NAME,OVERTIME,ABSENT
Step 2: if (OVERTIME(2/3)*ABSENT > 40) then PAYMENT 50
else if (OVERTIME(2/3)*ABSENT > 30) then PAYMENT 40
else if (OVERTIME(2/3)*ABSENT > 20) then PAYMENT 30
else if (OVERTIME(2/3)*ABSENT > 10) then PAYMENT 20
else
PAYMENT 10
endif
Step 3: Print Bonus for, NAME is $, PAYMENT
32 Decision Support System Hemant Kumar Jain : [email protected]
Example 7
Flowchart: Draw the flowchart of the above algorithm?
33 Decision Support System Hemant Kumar Jain : [email protected]
Four Flowchart Structures
Sequence
Decision
Repetition
Case
34 Decision Support System Hemant Kumar Jain : [email protected]
Sequence Structure
a series of actions are performed in sequence
The pay-calculating example was a sequence flowchart.
35 Decision Support System Hemant Kumar Jain : [email protected]
Decision Structure
One of two possible actions is taken, depending on a condition.
36 Decision Support System Hemant Kumar Jain : [email protected]
Decision Structure
A new symbol, the diamond, indicates a yes/no question. If the answer to the question is yes, the flow follows one path. If the answer is no, the flow follows another path
YES NO
37 Decision Support System Hemant Kumar Jain : [email protected]
Decision Structure
In the flowchart segment below, the question is x < y? is asked. If the answer is no, then process A is performed. If the answer is yes, then process B is performed.
YES NO
x < y?
Process B Process A
38 Decision Support System Hemant Kumar Jain : [email protected]
Decision Structure
The flowchart segment below shows how a decision structure is expressed in C++ as an if/else statement.
YES NO
x < y?
Calculate a as x times 2.
Calculate a as x plus y.
if (x < y)
a = x * 2;
else
a = x + y;
Flowchart C++ Code
39 Decision Support System Hemant Kumar Jain : [email protected]
Decision Structure
The flowchart segment below shows a decision structure with only one action to perform. It is expressed as an if statement in C++ code.
if (x < y)
a = x * 2;
Flowchart C++ Code
YES NO
x < y?
Calculate a as x times 2.
40 Decision Support System Hemant Kumar Jain : [email protected]
Repetition Structure
A repetition structure represents part of the program that repeats. This type of structure is commonly known as a loop.
41 Decision Support System Hemant Kumar Jain : [email protected]
Repetition Structure
Notice the use of the diamond symbol. A loop tests a condition, and if the condition exists, it performs an action. Then it tests the condition again. If the condition still exists, the action is repeated. This continues until the condition no longer exists.
42 Decision Support System Hemant Kumar Jain : [email protected]
Repetition Structure
In the flowchart segment, the question is x < y? is asked. If the answer is yes, then Process A is performed. The question is x < y? is asked again. Process A is repeated as long as x is less than y. When x is no longer less than y, the repetition stops and the structure is exited.
x < y? Process A
YES
43 Decision Support System Hemant Kumar Jain : [email protected]
Repetition Structure
The flowchart segment below shows a repetition structure expressed in C++ as a while loop.
Flowchart
x < y? Add 1 to x
YES
44 Decision Support System Hemant Kumar Jain : [email protected]
Controlling a Repetition Structure
The action performed by a repetition structure must eventually cause the loop to terminate. Otherwise, an infinite loop is created.
In this flowchart segment, x is never changed. Once the loop starts, it will never end.
QUESTION: How can this flowchart be modified so it is no longer an infinite loop?
x < y? Display x
YES
45 Decision Support System Hemant Kumar Jain : [email protected]
Controlling a Repetition Structure
ANSWER: By adding an action within the repetition that changes the value of x.
x < y? Display x
Add 1 to x
YES
46 Decision Support System Hemant Kumar Jain : [email protected]
A Pre-Test Repetition Structure
This type of structure is known as a pre-test repetition structure. The condition is tested BEFORE any actions are performed.
x < y? Display x
Add 1 to x
YES
47 Decision Support System Hemant Kumar Jain : [email protected]
A Pre-Test Repetition Structure
In a pre-test repetition structure, if the condition does not exist, the loop will never begin.
x < y? Display x
Add 1 to x
YES
48 Decision Support System Hemant Kumar Jain : [email protected]
A Post-Test Repetition Structure
This flowchart segment shows a post-test repetition structure.
The condition is tested AFTER the actions are performed.
A post-test repetition structure always performs its actions at least once.
Display x
Add 1 to x
YES x < y?
49 Decision Support System Hemant Kumar Jain : [email protected]
A Post-Test Repetition Structure
The flowchart segment below shows a post-test repetition structure expressed in C++ as a do-while loop.
Flowchart
Display x
Add 1 to x
YES x < y?
50 Decision Support System Hemant Kumar Jain : [email protected]
Case Structure
One of several possible actions is taken, depending on the contents of a variable.
51 Decision Support System Hemant Kumar Jain : [email protected]
Case Structure
The structure below indicates actions to perform depending on the value in years_employed.
CASE years_employed
1 2 3 Other
bonus = 100 bonus = 200 bonus = 400 bonus = 800
52 Decision Support System Hemant Kumar Jain : [email protected]
Case Structure
CASE years_employed
1 2 3 Other
bonus = 100 bonus = 200 bonus = 400 bonus = 800
If years_employed = 1, bonus is set to 100
If years_employed = 2, bonus is set to 200
If years_employed = 3, bonus is set to 400
If years_employed is any other value, bonus is set to 800
53 Decision Support System Hemant Kumar Jain : [email protected]
Connectors
Sometimes a flowchart will not fit on one page.
A connector (represented by a small circle) allows you to connect two flowchart segments.
A
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Connectors
A
A
START
END
The A connector indicates that the second flowchart segment begins where the first segment ends.
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Modules
A program module (such as a function in C++) is represented by a special symbol.
56 Decision Support System Hemant Kumar Jain : [email protected]
Modules
The position of the module symbol indicates the point the module is executed.
A separate flowchart can be constructed for the module.
START
END
Read Input.
Call calc_pay function.
Display results.
57 Decision Support System Hemant Kumar Jain : [email protected]
Combining Structures
Structures are commonly combined to create more complex algorithms.
The flowchart segment below combines a decision structure with a sequence structure.
x < y? Display x
Add 1 to x
YES
58 Decision Support System Hemant Kumar Jain : [email protected]
This flowchart segment shows two decision structures combined.
Combining Structures
Display x is within limits.
Display x is outside the limits.
YES NO x > min?
x < max?
YES
NO
Display x is outside the limits.
59 Decision Support System Hemant Kumar Jain : [email protected]
Thanks