Algorithms and Flowcharts II

ALGORITHMS AND

FLOWCHARTS

Part #2

Three Constructs

Flowcharts for Three Constructs

Pseudocode for Three Constructs

Examples-1 calculate 12 + 22 + ... + n2

Pseudocode

Input: n

sum 0

i 1

Repeat the following

three steps while i n:

sq i * i

sum sum + sq

i i + 1

Output: sum

A B

Set A to the

value of B

Examples-1:

Flowchart

n

sum 0

i 1

i n ?

sq i * i

sum sum + sq

i i + 1

sum

No

Yes

Input / output

Processing step

Decision

Examples-2:

1. Start at pos0, facing dir0

2. If wall in front,

turn 90º clockwise

else

go forward

3. If not back to initial

position / direction

proceed to Step 2

else

stop

dir dir + 90º

pos = pos0

and dir = dir0?

Yes No

Yes

No

pos pos0

dir dir0

Step forward

Input:

pos0, dir0

Stop

Wall in front?

Examples-3:

Sort the following objects based on their

heights

Output

Expected result

Strategy

There are many strategies for solving this

problem. We demonstrate a simple one:

Repeat the following steps while the list is un-sorted:

Start with the first object in the list

Swap it with the one next to it if they are in the wrong order

Repeat the same with the next to the first object

Keep on repeating until you reach the last object in the list

Back to The Objects to be Sorted

12

Q: Is the list sorted?

A: No

13

Sorting: Step A1

14

Sorting: Step A1

Swap? Yes

15

Sorting: Step A2

16

Sorting: Step A2

Swap? Yes

17

Sorting: Step A3

18

Sorting: Step A3

Swap? No

19

Sorting: After Step A7

20

Q: Is the list sorted?

A: No

21

Sorting: Step B1

22

Sorting: Step B1

Swap? Yes

23

Sorting: Step B2

24

Sorting: Step B2

Swap? No

25

Sorting: After Step B7

26

Q: Is the list sorted?

A: No

27

Sorting: Step C1

28

Sorting: Step C1

Swap? No

29

Sorting: After Step C7

30

Q: Is the list sorted?

A: Yes

31

32

Start

n = n+1

Get list

list

sorted?

Stop

SWAP

list[n], list[n+1]

list is an array containing the heights

N is the total number of objects in the list

Flowchart for the Sorting Process

No

Yes

n = 0 list[n] >

list[n+1]?

Yes No n>N ?

Yes

No

Variables

Algorithms usually work with variables

A variable is a “named container”

A variable is like a slate on which a

value can be written and later erased

and replaced with another value

sum sum + sq

sum

Properties of Algorithm

Compactness: an algorithm can use

iterations or recursion to repeat the

same steps multiple times

Generality: the same algorithm applies

to any “size” of task or any input values

Abstractness: an algorithm does not

depend on a particular computer

language or platform (although it may

depend on the general computing

model)

Properties of Algorithm

Input: n

sum 0

i 1

Repeat the following

three steps while i n:

sq i * i

sum sum + sq

i i + 1

Output: sum

Compact: the same length regardless

of n, thanks to iterations the

algorithm repeats the same

instructions many times, but with

different values of the variables

(The “running time” depends on n, of course)

General: works for any n

Properties of Algorithm

function addSquares(n : integer)

: integer;

var

i, sum : integer;

begin

sum := 0;

for i := 1 to n do begin

sum := sum + i * i

end;

addSquares := sum;

end;

Abstract:

Pascal

C/C++

Java

public class MyMath

{

public static int

addSquares(int n)

{

int sum = 0;

for (int i = 1; i <= n; i++)

sum += i * i;

return sum;

}

}

int addSquares(int n)

{

int i, sum = 0;

for (i = 1; i <= n; i++)

sum += i * i;

return sum;

}

Iterations

Repeat the same sequence of

instructions multiple times

Start with initial values of variables

Values of some of the variables

change in each cycle

Stop when the tested condition

becomes false

Supported by high-level

programming languages

Iterations: while Loop in Java

For example:

while (<this condition holds>)

{

... // do something

}

while (i <= n)

{

sum += i * i; // add i * i to sum

i++; // increment i by 1

}

Iterations: while Loop in Java

for (<initial setup>; <as long as this condition holds>;

<adjust variable(s) at the end of each iteration>)

{

... // do something

}

for ( int i = 1; i <= n; i++)

{

sum += i * i; // add i * i to sum

}

For example: Increment i

by 1

Assignments

Write an algorithm in pseudocode that finds

the average of two numbers

Write an algorithm to change a numeric grade

to a letter grade.

Write an algorithm to find the largest of a set

of numbers. You do not know the number of

numbers.

Write an algorithm to find the largest of 1000

numbers.