Mathematical Operations

1
Mathematical Operations
2
Average

• Accept three user input values, prompting the
  user to enter each individual value, compute the
  average value of the three input values and
  display.
• Pseudo code
• Prompt user to enter value 1
• Read in value 1
• Prompt user to enter value 2
• Read in value 2
• Prompt user to enter value 3
• Read in value 3
• Compute the average value of the entered data
• Display the average value

3
Average
alternative code (can group on one line) double
value1,value2, value3, averageValue
Coding

• / header /
• include ltiostream.hgt
• void main(void)
• double value1
• double value2
• double value3
• double averageValue
• cout ltlt "Input value 1 "
• cin gtgt value1
• cout ltlt endl ltlt "Input value 2 "
• cin gtgt value2
• cout ltlt endl ltlt "Input value 3 "
• cin gtgt value3

strings are enclosed in double quotes
user input
end of line (carriage return)
end of line (carriage return)
4
Average
Program output

• Input value 1 -1
• Input value 2 32
• Input value 3 68.3
• The average value is 33.1

5
Assignment Statements
Stepping through the code

• / header /
• include ltiostream.hgt
• void main(void)
• double value1
• double value2
• double value3
• double averageValue
• cout ltlt "Input value 1 "
• cin gtgt value1
• cout ltlt endl ltlt "Input value 2 "
• cin gtgt value2
• cout ltlt endl ltlt "Input value 3 "
• cin gtgt value3

value1 ? value2 ? value3
? averageValue ?
value1 -1 value2 ? value3
? averageValue ?
value1 -1 value2 32 value3
? averageValue ?
6
Assignment Statements
Stepping through the code

• / header /
• include ltiostream.hgt
• void main(void)
• double value1
• double value2
• double value3
• double averageValue
• cout ltlt "Input value 1 "
• cin gtgt value1
• cout ltlt endl ltlt "Input value 2 "
• cin gtgt value2
• cout ltlt endl ltlt "Input value 3 "
• cin gtgt value3

value1 -1 value2 32 value3
68.3 averageValue ?
value1 -1 value2 32 value3
68.3 averageValue 33.1
7
cin

• Two code fragments that have the same effect

double a, b, c cout ltlt Enter the sides of a
triangle cin gtgt a cin gtgt b cin gtgt c
double a, b, c cout ltlt Enter the sides of a
triangle cin gtgt a gtgt b gtgt c
Three ways to enter data values with the same
effect
Enter the sides of a triangle 17.3 12.9 9.1
Each of these three approaches is a stream of
input data containing the same three numbers
separated by blanks, tabs, and/or newline
characters (all of which are ignored when
extracting the numerical values from the input
stream
Enter the sides of a triangle 17.3 12.9 9.1
Enter the sides of a triangle 17.3 12.9 9.1
8
Operators and Expressions
9
Arithmetic Expressions

• Operators
• Addition
• Subtraction
• Multiplication
• Division /
• Modulus
• Operands
• Variables
• Constants
• Functions with output arguments (e.g. sin(3),
  pow(x,3), sqrt(y))

10
Order of Operation

• Parentheses evaluate expressions enclosed by
  parentheses first
• Precedence evaluate operators according to their
  precedence/priority (e.g. multiplication and
  division before addition or subtraction)
• Associativity if there is a sequence of two or
  more operators of the same precedence evaluate
• Unary operators from right to left (right
  associativity)
• Binary operators from left to right (left
  associativity)
• Examples
• a b c/3
• (a b c)/3
• a/-b (c 2 b)(-n 1)

11
Type Conversion

• The output of an arithmetic expression will have
  a type equal to the input type.
• Floating point example 9.0/2.0 produces
  4.5 -11.0/4.0 produces -2.75
• Integer example 9/2 produces 4 -11/4 produces
  -2
• 92 produces 1 -114 produces -3

• If there are a mixture of input types operands
  are automatically converted/promoted to the
  higher type prior to the application of the
  operator.
• 1.0 1/2 produces 1.0 (not 1.5)

high long double double float unsigned
long int long int unsigned int int low shor
t int
division produces 0, which is then converted to
0.0 prior to the addition
12
Explicit Type Conversion (aka Type Casting)

• We can explicitly convert a value from one type
  to another.
• Syntax
• lttype to cast togt (ltvariable/expressiongt)
• or
• (lttype to cast togt) ltvariable/expressiongt
• Note that type casting simply performs a
  conversion prior to the variable/expression being
  used. It does not change the content of the
  variable.
• Example
• 1.0 (double)1/2 produces 1.5

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Explicit Type Conversion (aka Type Casting)

• int totalScore 23
• int numStudents 4
• double average
• average (double) totalScore/(double)
  numStudents
• or
• average double (totalScore)/double
  (numStudents)
• or
• average double (totalScore)/numStudents
• All these computations of average are equivalent
  and produce a value of 5.75. Note, as shown in
  the last line that only a single casting is
  required as the second casting would be done
  automatically.

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Explicit Type Conversion (aka Type Casting)

• Type casting can also be performed from a higher
  data type to a lower data type. For example, we
  could type cast a double to an int, which has the
  effect of truncation.
• double a 17.9
• double b 22.1
• cout ltlt a ltlt " rounds to " ltlt (int) a ltlt " and
  ltlt
• b ltlt " rounds to " ltlt int (b)
• Produces
• 17.9 rounds to 17 and 22.1 rounds to 22

15
Assignment Shortcuts

• Short form Long form equivalent
• counter counter counter 1
• counter counter counter 1
• index-- index index 1
• --index index index 1
• index 2 index index 2
• index / counter index index/counter
• index 5 index index 5 index
• index index 1
• index 5 --index index index - 1
• index 5 index
• --index 5 index index - 1
• index 5 index
• Although these short forms produce more compact
  code ensure that the readability of your code
  remains intact!

16
Boolean (True/False)

• In C false is related to the value zero and
  true is related to any other value other than
  zero. When a boolean expression is evaluated in
  C, a true value will be represented by a value
  of one. Borland C provides a boolean variable
  type called bool and the constants true and
  false.
• Note Some compilers, including Borland C
  version 4.2 or earlier do not have the bool
  variable type, and the constants true and false
  do not exist. In these cases you can define them
  yourself using the line
• typedef enum false 0, true 1 bool
• after your include directives.

17
Relational and Logical Operators

• Relational operators Action
• gt Greater than
• gt Greater than or equal to
• lt Less than
• lt Less than or equal to
• Equal to
• ! Not equal to
• Logical operators Action
• AND
• OR
• ! NOT

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Precedence

• Relational and logical operators have lower
  precedence than arithmetic operators (e.g. , ,
  ).
• The relative precedence of the relational and
  logical operators are
• Highest !
• gt gt lt lt
• !
• Lowest

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Examples

• Expression Evaluates to
• 9 gt 5 true
• 9 lt 5 false
• 13 4 true
• ((57) gt 0) ((-17) lt 0) true
• 57 gt 0 -17 lt 0 true
• true !0 1 true
• true !(0 1) false
• 9 true true

20
Problem 1 Area and volume of a sphere
Write a program that accepts a user input for the
sphere, and computes and displays the surface
area and volume of a sphere. Use float data types
for your variables radius, area, and volume. See
sample output below. What happens when you change
your variables to type int. Note that you will
have to use the directive include ltmath.hgt to
have access if you want to use the function
pow(x,y), You should also define the constant
M_PI, using the code const double M_PI 2.0
asin(1.0) After your include statements (note
Borland defines M_PI in ltmath.hgt so doesnt
require this code)

• Enter the radius of the sphere 15.5
• The area of the sphere is 3019.07 and the volume
  is 15598.5

21
Problem 2 Long equation
Write a program that accepts three user inputs x,
y, and z. The program should then compute and
display the result for the following
formula See sample outputs below. Use data
type float for your variables x, y, z, and
f. Change your variables x, y, and z to data type
int. Does the value of f change? Use type casting
so that f is evaluated correctly. Try to use as
few type casts as possible (it can be done with
only three type casts for sure)

• Enter the values for x, y, and z 3 5 7
• f(x,y,z) 3.47142

Enter the values for x, y, and z 5 9 3 f(x,y,z)
24.067