LECTURE:
Arithmetic Expressions and Math Class
Purpose:
Work with and modify variables, assignments , increment/decrement,
Casting and modulus. Math API
Resources:
Deitel & Deitel “Java How to Program” Chapter 2
Litvin, “Java Methods” Chapter 6
C++ Class Notes Chapter 4
Lambert Comprehensive Chapter 3
Handouts:
1.
ArithmeticExpressions.java
Java application with var expression examples
C:\Dave Java\Lecture Code Examples\
Arithmetic Expressions and Math Class\
ArithmeticExpressions \
Intro:
We will modify primitive datatypes using simple math operations. We will also examine the math API in
Java (java.lang.Math).
Arithmetic Operators and Assignments:
+ - * / %
Order of operations is determined by ( ) and by the rank of the operators.
Mult and division are performed 1st (LEFT TO RIGHT)
Followed by addition and subtraction
ORDER:
()
evaluate from the inside out
*, /, % evaluate LEFT to RIGHT
+, evaluate LEFT to RIGHT
the minus can also be used for negation
Example:
x = -(y + 2 * z) / 5;
a = -a;
Examples:
avg = (grade1 + grade2 + grade3 + grade4 + grade5) / numGrades;
INTEGER MATH a = 25 b = 10 c = 20 d = 30 e = 0
int e = 0; // compile error if not initialized
System.out.println(a + b / c * d); // ANS 25 b/c = 0 0 * 30 = 0 + a = 25
System.out.println((a + b) / c + d); // ANS 31 a+b=35 35/20 = 1 Truncates 1.75
// 1+30=31
System.out.println(a * (c / b) * d); // ANS 1500 c/b=2 a*2 = 50 50*30=1500
System.out.println((a + b) / (c * d)); // ANS 0 a+b=35 c*d=600 35/600 = 0 Tr .058
System.out.println(e + a); // ANS 25
// System.out.println(e + A); UNDEFINED VAR A – compile error
DOUBLE MATH a = 25.0 b = 10.0 c = 20.0 d = 30.0 e = .0
double e = .0; // compile error if not initialized
System.out.println(a + b / c * d); // 40.0
System.out.println((a + b) / c + d); // 31.75
System.out.println(a * (c / b) * d); // 1500.0
System.out.println((a + b) / (c * d)); // 0.0583
System.out.println(e + a); // 25.0
// System.out.println(e + A); UNDEFINED VAR A – compile error
addition is performed first because ( ) are executed first, addition is done L to R
division is performed second
the result is Assigned to the LVALUE variable avg
modulus % --- remainder (or remainder of partial units of b given a)
int a = 7, b = 22;
a%b=7
b%a=1
modulus is used to determine if a number is evenly divisible by another
if (b % 2 == 0)
is true if b is an EVEN number
Other Examples:
z = p * r % q + w / x - y;
6
1 2
4
3 5
3 + 5 * 3 = 18
-3 + 5 * 3 = 12
3 + 5 * -3 = -12
3+5%3 =5
(3 + 5) % 3 = 2
Type Casting:
Java allows variables of different types to be used in an expression
The type of the result depends on the type of the operands NOT THEIR VALUES
Operands of the same type results in an answer of that same type (int + int = int)
Example:
Int a = 7, b = 2;
System.out.println(a / b);
The result is 3 and NOT 3.5
If you have integers but wish a NON INTEGER result of an expression use type casting
You can temporarily cast an integer into a double, for example
Example:
int a = 7, b = 2;
double ratio;
ratio = (double)a / (double)b;
system.out.println(ratio);
The result is 3.5
However, the following code STILL produces 3 and NOT 3.5
ratio = a / b;
as the RVALUE is performed as an integer !!!
If you have 2 variables of DIFFERENT types, the smaller type is “promoted” to that of the larger one
Example:
ratio = (double)a / b;
ratio = a / (double)b;
The results will be 3.5
However, ratio = (double) a / b;
Results in 3 and NOT 3.5 as a/b is still performed as an integer
You may also cast from a larger to a smaller data type, from a double to an integer
Example:
Int ptsOnDie = 1 + (int)(Math.random() * 6);
// 0.0 <= Mah.random() < 1.0
here, the (int) cast truncates the number in the direction of 0
(int) 1.99 = 1
(int) –1.99 = -1
You can ROUND a double value to the nearest integer by adding or subtracting .5 AND THEN cast that
result into an integer
Example:
int value = (int) ((double)count / totalCount * 360 + .5);
Compound Assignment Operators:
Instead of coding the following:
a = a + b;
a = a – b;
a = a * b;
a = a / b;
a = a % b;
You can use compound assignments:
a += b;
a -= b;
a *= b;
a /= b;
a %= b;
the compound method enforces the concept that thr RVALUE is being processed in a temporary workspace
and that result is the ASSIGNED to the RVALUE variable
Increment & Decrement:
Shorthand for incrementing or decrementing a variable by 1
Instead of the following:
a = a + 1;
a = a - 1;
You can write:
a++;
a--;
++a;
--a;
There is an important difference between the two types of increment and decrement when they are used in
expressions
Increment, a++, increments the variable, a, AFTER it has been used in an expression
Increment, ++a, increments the variable, a, BEFORE, it is used in an expression
Math Class:
Java.lang.Math
Inherited from java.lang.Object (all java classes originate from java.lang.Object)
absolute value
sin
cos
log
max
min
pow
floor
Examples:
double a = 81, answer = 0.0;
int b = 50, c = 67;
System.out.println("NOW ILLUSTRATING Math Methods: ");
// LOG
answer = Math.log(a);
System.out.println("Log " + answer);
// Square Root
answer = Math.sqrt(a);
System.out.println("Sqr " + answer);
// Power
answer = Math.pow(10, 2);
System.out.println("Pwr " + answer);
//Sin
answer = Math.sin(90);
System.out.println("Sin " + answer);
//absolute value
answer = Math.abs(-67);
System.out.println("Abs " + answer);
//min
answer = Math.min(b, c);
System.out.println("Min " + answer);
//max
answer = Math.max(b, c);
System.out.println("Max " + answer);
NOW ILLUSTRATING Math Methods:
Log 4.394449154672439
Sqr 9.0
Pwr 100.0
Sin 0.8939966636005579
Abs 67.0
Min 50.0
Max 67.0
Projects:
Math
Fahrenheit to/from Celsius:
Jogging Distance
Square Meters to Mow
Pathageorin theorum
Population Growth
BMI litvin p.169
Dog years to human years lit p.170
Pound to/from kilos
Income tax calculator lit p.72