Operator precedence

Operator precedence

Evaluate a + b * c – multiplication first? a + (b * c) – addition first? (a + b) * c

Java solves this problem by assigning priorities to operators (operator precedence)

– operators with high priority are evaluated before operators with low priority

– operators with equal priority are evaluated left to right

Operator priority(highest to lowest)

1. ( ) 2. * / % 3. + - 4. =

When in doubt, use parentheses

a + b * c = a + (b * c) – because * has higher priority than +

To first perform the + operation we need to use parentheses – (a + b) * c

If in any doubt use extra parentheses to ensure the correct order of evaluation– parentheses are free!– cause no extra work for the computer when the

program is executing– only make it easier for you to work out what is

happening

Examples

Java adheres to traditional order of operations * and / have higher priority than + and –

int x = 3 + 5 * 6; (x = 33)int y = (3 + 5) * 6; (y = 48)

Parentheses are free, use them liberallyint z = ((3 + 5) * (6)); (z = 48)

Equal priority operations are evaluated left-to-right in the absence of parenthesesint w = 3 * 4 / 2 * 6; (w = 36)int x = 3 * 4 / (2 * 6); (x = 1)int y = 3 * 4 + 2 * 6; (y = 24)int z = 3 * (4 + 2) * 6; (z = 108)

Syntax and semantics

Addition, subtraction: + and –, int and doubleint x = 21+4; (x = 25) double y = 14.1-2; (y = 12.1)

Multiplication: *, int and double int x = 21*4; (x = 84)

double y = 14.1*2.5; (y = 35.25) Division: /, different for int and double

int x = 21/4; (x = 5)double y = 21/4; (y = 5.0)double y = 21/4.0; (y = 5.25)

Modulus: %, only for intint x = 21%4; (x = 1)

Automatic type conversion

Mixed type expressions are converted to a “higher” compatible type as part of the computation process

Rules: – if both operands are of

type int then the result is of type int

– if either operand, or both, are of type double then the result is of type double

Cannot convert to a “lower” type

Example: Convert Fahrenheit to Celsius

Given the following Java statements:

double F = 41.0;double C = (F-32.0)*(5/9);

Question: What is the value of C?a. 5b. 0.0c. 5.0d. 0.5e. error

More expressions

int g = 12 + 2.5;What is the value of g?a. 0b. 12c. 14d. 14.5e. error

int x = 8 * (7 – 6 + 5) % (4 + 3 / 2) – 1;What is the value of x?a. -1b. 0c. 2d. 3e. none of the above

int n = 1 – 2 * 3 – (4 + 5); What is the value of n?a. -4b. -2c. 2d. 4e. none of the above

Arrays

Arrays

Aggregate data type– collection of elements stored in one unit

Arrays store collections of identically typed elements– not a primitive data type (but can store them)– behavior is similar to objects

Analogies– mailboxes in post office– CD racks with slots

Advantages– Simplifies naming– Allows use of loops– Holds multiple elements

Accessing array elements

Example: an array A of integers

3 is the element of array A at index 1 Access:

int w = A[0] ; (w = 5)int x = A[3] ; (x = 3)int y = A[2]+A[5]; (y = -5)int z = A[10]; error

5 -703230 1 2 3 4 5

arrayelementsarrayindices

A =

Declaring arrays

Declare an array of 5 integersint[] A = new int[5];

Size must be knownint[] A = new int[n];– error if n has not been assigned a value!

Size must be integer valuedouble n = 5;int[] A = new int[n];– error: n is not of type int !

Correct:int n = 5;int[] A = new int[n];

Assigning array values

Declare an array of 5 integersint[] A = new int[5];

Assign values to array elementsA[0] = 2;A[1] = 4;A[2] = -9;A[3] = 0;A[4] = 2;

Variable initializer syntaxint[] A = {2, 4, -9, 0, 2};– use when you know what values you want to

initially store in the array

Using arrays

Subroutine sumArray computes the sum of the elements in an array– size of an array (number of elements) is given by

the length property

double sumArray(double[] A){

double sum = 0.0;for(int k = 0; k < A.length; k++)

sum = sum + A[k];return sum;

}

Exercises

Write a Java subroutine minArray that takes an array of doubles as input and returns the minimum value in the array– for example, if the input array is

your subroutine should return 1.99 Write a Java subroutine reverseArray that takes an

array of ints as input and returns the array of ints in reverse order– for example, if the input array is

your subroutine should return the array

3.5 2.4 2.0 1.99 3.1

3.1 1.99 2.0 2.4 3.5

3.5 2.4 2.0 1.99 3.1

Exercises

Write a Java subroutine numGreater that takes as input a double d and an array A of doubles and returns the number of elements in A greater than d – the declaration of your subroutine should be

int numGreater(double d, double[] A){

/* you do this part! */}

– example: if d=1 and the input array is

your subroutine should return 3

-3.1 6.5 -0.7 2.9 2.3

Recursion

Triangular numbers

Write a recursive Java subroutine to compute the nth triangular number

Base case– the first triangular number is 1

Recursive case– the nth triangular number is equal to

n + the (n-1)st triangular number

The 4th triangular number is 6+4 = 10

The 5th triangular number is 10+5 = 15

The 6th triangular number is 15+6 = 21

Recursive solution

int TriNumber( int n ){

if( n==1 )return 1;

elsereturn n + TriNumber( n-1 );

}

Square numbers

Write a recursive Java subroutine to compute the nth square number

Base case– the first square number is 1

Recursive case– the nth square number is equal to

2n-1 + the (n-1)st square number

The 4th square number is 9+2*4-1 = 16

The 5th square numberis 16+2*5-1 = 25

The 6th square numberis 25+2*6-1 = 36

Recursive solution

int SquareNumber( int n ){

if( n==1 )return 1;

elsereturn 2*n-1 + SquareNumber( n-1 );

}

Exercise

The following statements call the subroutine given belowx = something(2,7);y = something(8,2);

What is the value of x? What is the value of y?

int something( int a, int b ){

if( a < b )return a+b;elsereturn 1 + something( a-b, b);

}