Computational Tools 1

Computational Tools

• Structured Programming

• Spreadsheets

Computational Tools 2

Structured Programming

• Flowcharts

• Flow control

• Functions

Computational Tools 3

Start/Stop

Operation

Decision

Input/Output

Flowchart Symbols

Computational Tools 4

start

Example Flowchart

y = 4y > 4?

end

print y

y = f(x)

no

yes

read x

Computational Tools 5

start

Flowchart with Iteration

sum = 0n = 0

n=5?

end

print sum

n = n + 1sum = sum + n

noyes

Computational Tools 6

When the program represented by the following flowchart is run, what is the resulting sum?

A. 10B. 15C. 20D. 21

sum = 15 B

start

sum = 0n = 0

n=5?

end

print sum

n = n + 1sum = sum + n

noyes

n sum0 01 12 33 64 105 15

Computational Tools 7

Structured Programming

• Flowcharts

• Flow control

• Functions

Computational Tools 8

In this program, if a value of 0.5 is read for x, what value is assigned to y?

read xif x < 0 then y = 0else if x > 1 then y = 1else y = x*xend

A. 0.25B. 0.5C. 0.75D. 1

A

Computational Tools 9

In this program, what is the final value of x?

x = 1y = 2*xx = x + y*yif x > 4 then x = x/5

A. 1B. 5C. 6D. 8

x = 1y = 2x = 5x = 1

A

Computational Tools 10

In this program, if a value of 0.5 is read for x, what is the final value of x?

read xif x > -1 and x < 1 then x = 0else x = x*x

A. 0B. 0.25C. 0.5D. 1

A

Computational Tools 11

In this program, if a value of 3 is read for n, what value is assigned to x?

read nswitch n case 1 x = 2 case 2 x = 4 case 3 x = 6 otherwise x = 8end

A. 3B. 4C. 6D. 8

x = 6 C

Computational Tools 12

In this program, what is the final value of y?

x = 1y = 1for n = 1 to 3 x = x + 2 y = y*xend

A. 7B. 15C. 105D. 945

x y1 13 35 157 105

y = 105 C

Computational Tools 13

In this program, what is the final value of y?

x = 0y = 0while x 6 x = x + 2 y = y + xend

A. 8B. 10C. 12D. 20

x y0 02 24 66 128 20

y = 20 D

Computational Tools 14

read x, ms = 1t = 1for k = 1 to m t = t*x/k s = s + tend

A. s = 1 + x + x/2 + x/3 + … + x/mB. s = 1 + x/1! + x/2! + x/3! + … + x/m!C. s = 1 + x/1 + x2/2 + x3/3 + … + xm/mD. s = 1 + x/1! + x2/2! + x3/3! + … + xm/m!

s = 1 + …k = 1; t = x; s = 1 + x + …k = 2; t = x2/2; s = 1 + x + x2/2 + …k = 3; t = x3/(2·3); s = 1 + x + x2/2 + x3/3! + …

D

What formula is implemented by this program?

Computational Tools 15

Structured Programming

• Flowcharts

• Flow control

• Functions

Computational Tools 16

Function

Main Program: Function:

a = 0; x = 1; y = 2 function y = special(x)d = special(a) y = x + 1Print d return y

Notice that:• The function input is named a in the main program and x in

the function.• The function output is named d in the main program and y in

the function.• The variables x and y in the function do not affect the variables

x and y in the main program.• The only effect of the function is to set d equal to a + 1.

Computational Tools 17

The following program is run. It uses the function simplefunction, which is also shown below. What is the value of h at the end of the program?

g = 3; h = 5p = simplefunction(g)

function y = simplefunction(x)h = 7y = x + hreturn y

The function simplefunction returns 10 to the main program. The fact that the function uses h as the name of a local variable does not affect the h in the main program. The variable h in the main program remains 5. C

A. 12B. 10C. 5D. 7

Computational Tools 18

The following program is run. It uses the function squareof, which is also shown below. What is the value of s at the end of the program?

read xs = 1y = squareof(x)s = s + y

function s = squareof(x)s = x*xreturn s

A. x2 + 1B. x2

C. 2x2

D. This program will result in an error message.The function squareof returns x2 to the main program. The fact that the function uses the name s for the square does not affect the s in the main program. The assignment statement s = s + y produces x2 + 1. A

Computational Tools 19

Spreadsheets

• Formulas

• Copying and Pasting Formulas

Computational Tools 20

Formulas in Cells

A B C D

1 23 C2

2 A1

3 A1-C2

4 A1*D3

A B C D

1 23 23

2 23

3 0

4 0

Computational Tools 21

Colon

A B C D

1 10

2 2

3 3

4 SUM(B1:B3)

A B C D

1 10

2 2

3 3

4 15

A B C D

1

2

3 10 2 3 SUM(A3:C3)

4

A B C D

1

2

3 10 2 3 15

4

Computational Tools 22

Spreadsheets

• Formulas

• Copying and Pasting Formulas

Computational Tools 23

Absolute and Relative Addresses

A B C D

1 8 A1

2 $A$1

3 $A1

4 A$1

A B C D

1 8 8

2 8

3 8

4 8

Computational Tools 24

Copy and Paste a Cell: $A$1

A B C D

1 8 7

2 5 4

3 $A$1

4

A B C D

1 8 7

2 5 4

3 $A$1

4 $A$1

A B C D

1 8 7

2 5 4

3 8

4 8

Computational Tools 25

Copy and Paste a Cell: A1

A B C D

1 8 7

2 5 4

3 A1

4

A B C D

1 8 7

2 5 4

3 A1

4 C2

A B C D

1 8 7

2 5 4

3 8

4 4

Computational Tools 26

Copy and Paste a Cell: $A1

A B C D

1 8 7

2 5 4

3 $A1

4

A B C D

1 8 7

2 5 4

3 $A1

4 $A2

A B C D

1 8 7

2 5 4

3 8

4 5

Computational Tools 27

Copy and Paste a Cell: A$1

A B C D

1 8 7

2 5 4

3 A$1

4

A B C D

1 8 7

2 5 4

3 A$1

4 C$1

A B C D

1 8 7

2 5 4

3 8

4 7

Computational Tools 28

Copy and Paste a Column

A B C D

1 8 5 A1

2 $A$1

3 $A1

4 A$1

A B C D

1 8 5 A1 B1

2 $A$1 $A$1

3 $A1 $A1

4 A$1 B$1

A B C D

1 8 5 8 5

2 8 8

3 8 8

4 8 5

Computational Tools 29

Copy and Paste a Row

A B C D

1 8

2 5

3 A1 $A$1 $A1 A$1

4

A B C D

1 8

2 5

3 A1 $A$1 $A1 A$1

4 A2 $A$1 $A2 A$1

A B C D

1 8

2 5

3 8 8 8 8

4 5 8 5 8

Computational Tools 30

In a spreadsheet, the number in cell A3 is 4. Cell A4 contains the formula A3 + $A$3. This formula is copied into cells A5 and A6. What is the value of cell A6?

A. 4B. 8C. 16D. 32

A

3 4

4

5

6

A

3 4

4 8

5

6

A

3 4

4 8

5 12

6

A

3 4

4 8

5 12

6 16 C

Computational Tools 31

In a spreadsheet, the formula $A$3 + $B3 + D2 is entered into cell C2. The contents of cell C2 are copied and pasted into cell D5. The formula in cell D5 is:

A. $A$3 + C$2 + C4B. $B$6 + $C4 + C4C. $A$3 + $B6 + E5D. $A$3 + $B2 + B2

cell C2: $A$3 + $B3 + D2

cell D5: $A$3 + $B6 + E5 C

Computational Tools 32

A spreadsheet contains the series of numbers 5,10,15,… in cells C2:C7. Cell D3 contains the formula (2*C2)+7. If the formula is copied and pasted into cells D4:D8, what is the numeric value in cell D8?

A. 67B. 55C. 93D. 77

The formula (2*C2)+7 in cell D3 employs the number in the cell one column to the left and one row up.

C2 53 104 155 206 257 30

A

In cell D8, this formula employs the number in the cell one column to the left and one row up (cell C7). This number is 30. (2*30)+7 = 67

Computational Tools 33

In this spreadsheet, the contents of column B are copied and pasted into columns C and D. What numeric value will cell D4 have?

A B C D

1 2 $A$1

2 4 A2

3 0 A3+B2

4 5 A$3*B3

A B C D

1 2 $A$1 $A$1 $A$1

2 4 A2 B2 C2

3 0 A3+B2 B3+C2 C3+D2

4 5 A$3*B3 B$3*C3 C$3*D3

A B C D

1 2 2 2 2

2 4 4 4 4

3 0 4 8 12

4 5 0 32 96

A. 32B. 64C. 96D. 128

C

Computational Tools 34

In this spreadsheet, the cell D1 contains the formula (A1+B1+C1)/3.This formula is copied into the range of cells D2:D3. Cell D4 contains the formula SUM(D1:D3). What is the numeric value in cell D4?

A B C D

1 1 2 3

2 4 5 6

3 7 8 9

4

A. 15B. 12C. 14D. 18

A B C D

1 1 2 3 2

2 4 5 6

3 7 8 9

4

A B C D

1 1 2 3 2

2 4 5 6 5

3 7 8 9 8

4 15 A