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ALGORITHMS &

FLOWCHARTING II

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LOOPS

Computers are particularly well suited to

applications in which operations are

repeated many times. If the same task is repeated over and over

again a loop can be used to reduce

program size and complexity

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Iteration (Loops)

Loops repeat a set of instructions

Two types of loops:

Definite loops ( for) perform instructions

explicit number of times

Indefinite loops ( while) perform instructions

an indefinite number of times (until a certaintest fails)

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Questions for You

take 2 minutes and draw a situation on

paper that would necessitate that you use

a while loop to solve the problem

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forLoops

General form:for ( ;

; )

{

}

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forLoops (cont.)

sets avariable/identifier to a certain value

(variable is usually count, i, j) is a test that is evaluated each

time the body is about to be executed(when false, loop is exited)

changes the loop controlvariable (usually x++or x--)

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forLoops (cont.)

Example:for (int x=1; x

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forLoops (cont.)

Flow of forloops:

1. Initialization statement executes

2. If test is true, proceed to step 3; if test isfalse, go to step 6

3. Instructions in body of loop are executed

4. Increment statement executes5. Return to step 2

6. Program proceeds to statements after loop

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whileLoops

General form:while ( )

{

}

Loop continues until test is false

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whileLoops (cont.)

Example:while (rebot.frontIsClear ())

{rebot.move ();

}

Causes rebot to move continuously untilthere is a wall in front of it

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whileLoops (cont.)

Flow of whileloops

1. If test is true, proceed to step 2; if test is

false, go to step 42. Instructions in body of loop are executed

3. Go to step 1

4. Statements after loop are executed

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Building a While Loop

Formalizing (making easier) the ad-hoc way youve been writing while

loops to this point..

Step 1Identify what is true when the

loop is finished (this is always easierthan determining what is false while it is

still executing)

Step 2Use the opposite form of step1s result as the for the loop. You

just need to negate the entire thing.

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Building a While Loop (contd)

Step 3make progress toward the goal

(completion of the loop) within the loop

Step 4Do whatever is required beforeand/or after the loop to ensure that we

solve the given problem

Example: Pick all beepers from a cornerwithout knowing how many there are.

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Your try the while condition

You may use &&and ||for this

Write a loop that moves a robot forwarduntil it is either next to a robot, next to abeeper, or there is no wall on its right

while ( ??? ) {

???

}

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Infinite Loops

In a foror while loop, it is possible for

the test to never be false

When this happens, the loop continuesinfinitely

Depending on the compiler, application,

and other circumstances, an error mayoccur or the app may crash

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Example 8: Write an algorithm and

draw a flowchart to calculate 24

. Algorithm:

Step 1: Base 2

Step 2: Product Base Step 3: Product Product * Base

Step 4: Product Product * Base

Step 5: Product Product * Base Step 6: Print Product

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FlowchartSTART

ProductBase

Print

Product

STOP

ProductProduct * Base



Base2

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Question: What happens if you want tocalculate 2 to the power of 1000?

Answer: Use a LOOP (repeated execution

of the same set of instructions)

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Example 9: Write an algorithm and draw a

flowchart to calculate 24using a loop

approach? Verify your result by a tracetable.

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Algorithm:

Step 1: Base2

Step 2: Power 4

Step 3: Product Base

Step 4: Counter 1

Step 5: While Counter < PowerRepeat Step 5 through step 7

Step 6: Product Product * Base

Step 7: Counter Counter +1

Step 8: Print Product

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START

ProductBaseCounter1

Print

Product

STOP

Y

is

Counter < Power


CounterCounter + 1

N

Base2

Power4

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TRACING

BASE POWER PRODUCT COUNTERCOUNTER < POWER

STEP 1: 2 ? ? ? ?

STEP 2: 2 4 ? ? ?

STEP 3: 2 4 2 ? ?

STEP 4: 2 4 2 1 T

STEP 5: 2 4 2 1 T

STEP 6: 2 4 2x2=4 1 T

STEP 7: 2 4 4 1+1=2 T

STEP 5: 2 4 4 2 T

STEP 6: 2 4 4x2=8 2 T

STEP 7: 2 4 8 2+1=3 T

STEP 5: 2 4 8 3 T

STEP 6: 2 4 8x2=16 3 T

STEP 7: 2 4 16 3+1=4 F

STEP 5: 2 4 16 4 F

STEP 8: print 16.

Step 1: Base 2

Step 2: Power 4

Step 3: Product Base

Step 4: Counter 1

Step 5: While Counter < Power

Repeat Step 5 through

step 7

Step 6: Product Product *

Base

Step 7: Counter Counter +1

Step 8: Print Product

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Example 10:Write down an algorithm and

draw a flowchart to find and print the

largest of three numbers. Read numbersone by one. Verify your result by a trace

table. (Use 5, 7, 3 as the numbers read)

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Algorithm

Step 1: InputN1

Step 2: MaxN1

Step 3: InputN2

Step 4: If (N2>Max) then

Max = N2endif

Step 5: InputN3

Step 6: If (N3>Max) then

Max = N3

endif Step 7: Print The largest number is:,Max

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Flowchart &

Tracing

START

INPUT

N1

MAXN1

INPUT

N2

N2>MAX

MAXN2

INPUT

N3

MAXN3

Print

Largest

Number is,

MAX

STOP

N3>MAX

N

Y

N

Y

N1 N2 N3 Max N2>Max N3>Max

Step1: 5 ? ? ? ? ?

Step 2: 5 ? ? 5 ? ?

Step 3: 5 7 ? 5 T ?

Step 4: 5 7 ? 7 T ?

Step 5: 5 7 3 7 F F

Step 6: 5 7 3 7 F F

Step 8: Print Largest Number is 7

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Example 11: Write down an algorithm and

draw a flowchart to find and print the

largest of N (N can be any number)numbers. Read numbers one by one.

Verify your result by a trace table.

(Assume N to be 5 and the following set tobe the numbers {1 4 2 6 8 })

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Algorithm:

Step 1: InputN

Step 2: Input Current

Step 3: MaxCurrent

Step 4: Counter1

Step 5: While (Counter < N)Repeat steps 5 through 8

Step 6: CounterCounter + 1

Step 7: InputNext

Step 8: If (Next > Max) then

MaxNextendif

Step 9: Print Max

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START

InputN, Current

Max Current

Print

Max

STOP

Y

Counter < NN

Counter 1

Counter Counter +1

InputNext

Next

>Max

Y

N

Max Next

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TracingN Current Max Counter Counter < N Next Next > Max

Step 1

Step 2

Step 3

Step 4

Step 5

Step 6

Step 7

Step 8

Step 5

Step 6

Step 7

Step 8

Step 5

Step 6

Step 7

Step 8

Step 5

Step 6

Step 7

Step 8

Step 5

Step 9

5

5

5

5

5

5

5

5

5

5

5

5

5

5

5

5

5

5

5

5

5

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

4

4

4

4

4

4

4

4

6

6

6

6

8

8

8 output

1

1

2

2

2

2

3

3

3

3

4

4

4

4

5

5

5

5

T

T

T

T

T

T

T

T

T

T

T

T

T

T

F

F

F

F

4

4

4

4

2

2

2

2

6

6

6

6

8

8

8

T

F

F

F

F

F

F

T

T

F

F

T

T

F

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Examples

Write an algorithm and draw a flowchartto print the multiplication table for 6's. i.e.

---- 1

6 = 6 ---- 2 6 = 12

---- 12 6 = 72

lect 8 and9

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