Chapter 4 Methods

1
Chapter 4 Methods

• Introducing Methods
• Benefits of methods, Declaring Methods, and
  Calling Methods
• Passing Parameters
• Pass by Value
• Overloading Methods
• Ambiguous Invocation
• Scope of Local Variables
• Method Abstraction
• The Math Class
• Case Studies
• Recursion (Optional)

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Introducing Methods
Method Structure
A method is a collection of statements that are
grouped together to perform an operation.
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Introducing Methods, cont.

• parameter profile refers to the type, order, and
  number of the parameters of a method.
• method signature is the combination of the method
  name and the parameter profiles.
• The parameters defined in the method header are
  known as formal parameters.
• When a method is invoked, its formal parameters
  are replaced by variables or data, which are
  referred to as actual parameters.

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Declaring Methods

• public static int max(int num1, int num2)
• if (num1 gt num2)
• return num1
• else
• return num2

5
Calling Methods
Example 4.1 Testing the max method This program
demonstrates calling a method max to return the
largest of the int values
TestMax
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Calling Methods, cont.
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Calling Methods, cont.
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CAUTION

• A return statement is required for a nonvoid
  method. The following method is logically
  correct, but it has a compilation error, because
  the Java compiler thinks it possible that this
  method does not return any value.
• public static int xMethod(int n)
• if (n gt 0) return 1
• else if (n 0) return 0
• else if (n lt 0) return 1
• To fix this problem, delete if (nlt0) in the code.

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Passing Parameters

• public static void nPrintln(String message, int
  n)
• for (int i 0 i lt n i)
• System.out.println(message)

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Pass by Value
Example 4.2 Testing Pass by value This program
demonstrates passing values to the methods.
TestPassByValue
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Pass by Value, cont.
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Overloading Methods

• Example 4.3 Overloading the max Method
• public static double max(double num1, double
  num2)
• if (num1 gt num2)
• return num1
• else
• return num2

TestMethodOverloading
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Ambiguous Invocation

• Sometimes there may be two or more possible
  matches for an invocation of a method, but the
  compiler cannot determine the most specific
  match. This is referred to as ambiguous
  invocation. Ambiguous invocation is a compilation
  error.

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Ambiguous Invocation

• public class AmbiguousOverloading
• public static void main(String args)
• System.out.println(max(1, 2))
•  
• public static double max(int num1, double num2)
  
• if (num1 gt num2)
• return num1
• else
• return num2
• public static double max(double num1, int num2)
  
• if (num1 gt num2)
• return num1
• else
• return num2

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Scope of Local Variables

• A local variable a variable defined inside a
  method.
• Scope the part of the program where the variable
  can be referenced.
• The scope of a local variable starts from its
  declaration and continues to the end of the block
  that contains the variable. A local variable must
  be declared before it can be used.

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Scope of Local Variables, cont.

• You can declare a local variable with the same
  name multiple times in different non-nesting
  blocks in a method, but you cannot declare a
  local variable twice in nested blocks.

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Scope of Local Variables, cont.
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Scope of Local Variables, cont.

• // Fine with no errors
• public static void correctMethod()
• int x 1
• int y 1
• // i is declared
• for (int i 1 i lt 10 i)
• x i
• // i is declared again
• for (int i 1 i lt 10 i)
• y i

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Scope of Local Variables, cont.
// With no errors public static void
incorrectMethod() int x 1 int y 1
for (int i 1 i lt 10 i) int x 0
x i
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Method Abstraction

• You can think of the method body as a black box
  that contains the detailed implementation for the
  method.

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Benefits of Methods

• Write a method once and reuse it anywhere.
• Information hiding. Hide the implementation from
  the user.
• Reduce complexity.

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The Math Class

• Class constants
• PI
• E
• Class methods
• Trigonometric Methods
• Exponent Methods
• Rounding Methods
• min, max, abs, and random Methods

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Trigonometric Methods

• sin(double a)
• cos(double a)
• tan(double a)
• acos(double a)
• asin(double a)
• atan(double a)

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Exponent Methods

• exp(double a)
• Returns e raised to the power of a.
• log(double a)
• Returns the natural logarithm of a.
• pow(double a, double b)
• Returns a raised to the power of b.
• sqrt(double a)
• Returns the square root of a.

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Rounding Methods

• double ceil(double x)
• x rounded up to its nearest integer. This integer
  is returned as a double value.
• double floor(double x)
• x is rounded down to its nearest integer. This
  integer is returned as a double value.
• double rint(double x)
• x is rounded to its nearest integer. If x is
  equally close to two integers, the even one is
  returned as a double.
• int round(float x)
• Return (int)Math.floor(x0.5).
• long round(double x)
• Return (long)Math.floor(x0.5).

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min, max, abs, and random

• max(a, b)and min(a, b)
• Returns the maximum or minimum of two parameters.
• abs(a)
• Returns the absolute value of the parameter.
• random()
• Returns a random double valuein the range 0.0,
  1.0).

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Example 4.4 Computing Taxes with Methods

• Example 3.1, Computing Taxes, uses if
  statements to check the filing status and
  computes the tax based on the filing status.
  Simplify Example 3.1 using methods. Each filing
  status has six brackets.
• The code for computing taxes is nearly same for
  each filing status except that each filing status
  has different bracket ranges. For example, the
  single filer status has six brackets 0, 6000,
  (6000, 27950, (27950, 67700, (67700, 141250,
  (141250, 307050, (307050, ?), and the married
  file jointly status has six brackets 0, 12000,
  (12000, 46700, (46700, 112850, (112850,
  171950, (171950, 307050, (307050, ?).

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Example 4.4 Computing Taxes with Methods

• The first bracket of each filing status is taxed
  at 10, the second 15, the third 27, the fourth
  30, the fifth 35, and the sixth 38.6. So you
  can write a method with the brackets as arguments
  to compute the tax for the filing status. The
  signature of the method is
• public static double computeTax(double income,
• int r1, int r2, int r3, int r4, int r5)

ComputeTaxWithMethod
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Example 4.5 Computing Mean and Standard Deviation

• Generate 10 random numbers and compute the mean
  and standard deviation

ComputeMeanDeviation
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Example 4.6 Obtaining Random Characters

• Write the methods for generating random
  characters. The program uses these methods to
  generate 175 random characters between !' and
  ' and displays 25 characters per line. To find
  out the characters between !' and ', see
  Appendix B, The ASCII Character Set.

RandomCharacter
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Example 4.6 Obtaining Random Characters, cont.
Appendix B ASCII Character Set
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Case Studies

• Example 4.7 Displaying Calendars
• The program reads in the month and year and
  displays the calendar for a given month of the
  year.

PrintCalendar
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Design Diagram
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Recursion (Optional)

• Example 4.8 Computing Factorial
• factorial(0) 1
• factorial(n) nfactorial(n-1)
• Factorial(3) 3 factorial(2) 3 (2
  factorial(1)) 3 ( 2 (1 factorial(0)))
• 3 ( 2 ( 1 1))) 3 ( 2 1) 3 2 6

ComputeFactorial
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Example 4.8 Computing Factorial, cont.
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Example 4.8 Computing Factorial, cont.
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Fibonacci Numbers

• Example 4.8 Computing Finonacci Numbers
• 0 1 1 2 3 5 8 13 21 34 55 89
• f0 f1
• fib(0) 0
• fib(1) 1
• fib(n) fib(n-1) fib(n-2) ngt2

fib(3) fib(2) fib(1) (fib(1) fib(0))
fib(1) (1 0) fib(1) 1 fib(1) 1 1 2
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Fibonacci Numbers, cont
ComputeFibonacci
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Fibonnaci Numbers, cont.
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Towers of Hanoi

• Example 4.10 Solving the Towers of Hanoi Problem
• Solve the towers of Hanoi problem.

TowersOfHanoi
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Towers of Hanoi, cont.
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Exercise 4.11 GCD

• gcd(2, 3) 1
• gcd(2, 10) 2
• gcd(25, 35) 5
• gcd(205, 301) 5
• gcd(m, n)
• Approach 1 Brute-force, start from min(n, m)
  down to 1, to check if a number is common divisor
  for both m and n, if so, it is the greatest
  common divisor.
• Approach 2 Euclids algorithm
• Approach 3 Recursive method

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Approach 2 Euclids algorithm

• // Get absolute value of m and n
• t1 Math.abs(m) t2 Math.abs(n)
• // r is the remainder of t1 divided by t2
• r t1 t2
• while (r ! 0)
• t1 t2
• t2 r
• r t1 t2
•  
• // When r is 0, t2 is the greatest common divisor
  between t1 and t2
• return t2

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Approach 3 Recursive Method

• gcd(m, n) n if m n 0
• gcd(m, n) gcd(n, m n) otherwise