04-Math_Functions.pptx data structure and algo

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Chapter 4
Mathematical Functions,
Characters, and Strings

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Outline
1. Java Class Library
2. Class Math
3. Character Data Type
4. Class String
5. printf Statement

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1. Java Class Library
• A class library is a collection of classes that we use
when developing programs
• The Java standard class library is part of any Java
development environment
• The library classes are not part of the Java language
per se, but we rely on them heavily
• Various library classes we've already used in our
programs, such as System, Scanner, and Random
• Other class libraries can be obtained through third
party vendors, or you can create them yourself
• Classes must be imported into the program

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Packages
• The classes of the Java standard class library are
organized into packages
• Some of the packages in the standard class library are:
Package
java.lang
java.util
java.applet
java.awt
javax.swing
java.net
javax.xml.parsers
Purpose
General support (Character, Math, System, Number, …)
Utilities (Date, Random, Calendar, …)
Creating applets for the web
Graphics and graphical user interfaces
Additional graphics capabilities
Network communication
XML document processing

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import Declaration
• When you want to use a class from a package, you
could use its fully qualified name
java.util.Scanner
• Or you can import the class, and then use just the
class name
import java.util.Scanner;
• To import all classes in a particular package, you
can use the * wildcard character
import java.util.*; // wildcard

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import Declaration
• All classes of the java.lang package are
imported automatically into all programs
• It's as if all programs contain the following line:
import java.lang.*;
• That's why we didn't have to import the System or
String classes explicitly in earlier programs
• The Scanner class, on the other hand, is part of
the java.util package, and therefore must be
imported

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2. Class Math
• The Math class is part of the java.lang package
• The Math class contains methods (called class methods)
that perform various mathematical functions:
 PI constant
 E (base of natural logarithms) constant
 Trigonometric Methods
 Exponent Methods
 Rounding Methods
 min, max, abs, and random Methods
• Methods in the Math class are called static methods
• Static methods can be invoked through the class name –
no object of the Math class is needed
Double value = Math.cos(90) + Math.sqrt(delta);

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Example
public class Quadratic
{
public static void main (String[] args)
{
int a, b, c; // ax^2 + bx + c
double discriminant, root1, root2;
Scanner scan = new Scanner (System.in);
System.out.print ("Enter the coefficient of x squared: ");
a = scan.nextInt();
System.out.print ("Enter the coefficient of x: ");
b = scan.nextInt();
System.out.print ("Enter the constant: ");
c = scan.nextInt();
// Use quadratic formula to compute the roots.
discriminant = Math.pow(b, 2) - (4 * a * c);
root1 = ((-1 * b) + Math.sqrt(discriminant)) / (2 * a);
root2 = ((-1 * b) - Math.sqrt(discriminant)) / (2 * a);
System.out.println ("Root #1: " + root1);
System.out.println ("Root #2: " + root2);
}
}

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Example
Output:
Enter the coefficient of x squared: 3
Enter the coefficient of x: 8
Enter the constant: 4
Root #1: -0.6666666666666666
Root #2: -2.0
Enter the coefficient of x squared: 2
Enter the coefficient of x: 4
Enter the constant: 8
Root #1: NaN
Root #2: NaN
NaN indicates undefined root due to square root of negative
value (sqrt of b^2-4ac)

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Trigonometric Methods
• sin(double a)
• cos(double a)
• tan(double a)
• acos(double a)
• asin(double a)
• atan(double a)
Examples:
Math.sin(0) returns 0.0
Math.sin(Math.PI/6) returns 0.5
Math.sin(Math.PI/2) returns 1.0
Math.cos(0) returns 1.0
Math.cos(Math.PI/2) returns 0
Math.cos(Math.PI/6) returns 0.866

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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.
• log10(double a)
Returns the 10-based 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.
Examples:
Math.exp(1) returns 2.71
Math.log(2.71) returns 1.0
Math.pow(2,3) returns 8.0
Math.pow(3,2) returns 9.0
Math.pow(3.5,2.5) returns
22.91765
Math.sqrt(4) returns 2.0
Math.sqrt(10.5) returns 3.24

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Rounding Methods
• double ceil(double x)
x is 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)
returns (int)Math.floor(x+0.5)
• long round(double x)
returns (long)Math.floor(x+0.5)

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Rounding Methods Examples
Math.ceil(2.1) returns 3.0
Math.ceil(2.0) returns 2.0
Math.ceil(-2.0) returns –2.0
Math.ceil(-2.1) returns -2.0
Math.floor(2.1) returns 2.0
Math.floor(2.0) returns 2.0
Math.floor(-2.0) returns –2.0
Math.floor(-2.1) returns -3.0
Math.rint(2.1) returns 2.0
Math.rint(2.0) returns 2.0
Math.rint(-2.0) returns –2.0
Math.rint(-2.1) returns -2.0
Math.rint(2.5) returns 2.0 //returns even value as double
Math.rint(-2.5) returns -2.0
Math.round(2.6f) returns 3 //round returns integers
Math.round(2.0) returns 2
Math.round(-2.0f) returns -2
Math.round(-2.6) returns -3

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Min(), max(), and abs()
• max(a,b)and min(a,b)
Returns the maximum or
minimum of two parameters.
• abs(a)
Returns the absolute value of the
parameter.
Examples:
Math.max(2,3) returns 3
Math.max(2.5,3) returns 3.0
Math.min(2.5,3.6) returns 2.5
Math.abs(-2) returns 2
Math.abs(-2.1) returns 2.1

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Method random()
Generates a random double value greater than or equal to 0.0 and
less than 1.0 (0.0 <= Math.random() < 1.0)
Examples:
(int)(Math.random() * 10)
Returns a random integer
between 0 and 9.
50 + (int)(Math.random() * 50)
Returns a random integer
between 50 and 99.
In general,
a + Math.random() * b
Returns a random number between
a and a + b, excluding a + b.

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Generating Random Characters
Each character has a unique Unicode between 0 and FFFF in
hexadecimal (65535 in decimal).
To generate a random character is to generate a random integer
between 0 and 65535 using the following expression:
(int)(Math.random() * (65535 + 1))
Note:
Since 0.0 <= Math.random() <1.0, you have to add 1 to 65535

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Generating Random Characters
Lowercase letter: The Unicode for lowercase letters are consecutive
integers starting from the Unicode for 'a', 'b', 'c', ..., and 'z'.
The Unicode for 'a' is (int)'a'
A random integer between (int)'a' and (int)'z‘ is
(int)((int)'a'+ Math.random()*((int)'z'-(int)'a'+1)
So, a random lowercase letter is:
(char)('a' + Math.random() * ('z' - 'a' + 1))
To generalize, a random character between any two characters ch1 and
ch2 with ch1 < ch2 can be generated as follows:
(char)(ch1 + Math.random() * (ch2 – ch1 + 1))
See Appendix B, page 1266, for character set order.

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Class RandomCharacter
// RandomCharacter.java: Generate random characters
public class RandomCharacter {
/** Generate a random character between ch1 and ch2 */
public static char getRandomCharacter(char ch1, char ch2) {
return (char)(ch1 + Math.random() * (ch2 - ch1 + 1)); }
/** Generate a random lowercase letter */
public static char getRandomLowerCaseLetter() {
return getRandomCharacter('a', 'z'); }
/** Generate a random uppercase letter */
public static char getRandomUpperCaseLetter() {
return getRandomCharacter('A', 'Z'); }
/** Generate a random digit character */
public static char getRandomDigitCharacter() {
return getRandomCharacter('0', '9'); }
/** Generate a random character */
public static char getRandomCharacter() {
return getRandomCharacter('u0000', 'uFFFF'); }
}

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Class RandomCharacter
// Test class RandomCharacters
// class RandomCharacters methods are all static
public class TestRandomCharacters
{
public static void main(String[] args)
{
System.out.print("A random character between 'a' and 'z' is: ");
System.out.println(RandomCharacter.getRandomLowerCaseLetter());
System.out.print("A random character between 'A' and 'Z' is: ");
System.out.println(RandomCharacter.getRandomUpperCaseLetter());
System.out.print("A random character between '0' and '9' is: ");
System.out.println(RandomCharacter.getRandomDigitCharacter());
System.out.print("A random character between 'g' and 'm' is: ");
System.out.println(RandomCharacter.getRandomCharacter('g', 'm'));
System.out.print("A random character between '3' and '7' is: ");
System.out.println(RandomCharacter.getRandomCharacter('3', '7'));
System.out.print("A random character between '!' and '*' is: ");
System.out.println(RandomCharacter.getRandomCharacter('!', '*'));
}
}

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Stop and Record…

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A char variable stores a single character.
Character literals are delimited by single quotes:
'a' 'X' '7' '$' ',' 'n' 't'
Example declarations:
char topGrade = 'A';
char terminator = ';', separator = ' ';
Note the distinction between a primitive char variable, which
holds only one character, and a String object, which can
hold multiple characters.

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Character Type - Revisited
char letter = 'A';
char numChar = '4';
char letter = 'u0041'; //Unicode for A
char numChar = 'u0034'; //Unicode for character 4
Four hexadecimal digits.
NOTE: The increment and decrement operators can also be used on char
variables to get the next or preceding Unicode character. For example, the
following statements display character b.
char ch = 'c';
ch = ch + 1;
System.out.println(ch); //prints character d
ch = ch - 2;
System.out.println(ch); //prints character b

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ASCII Code in Decimal
Characters Code Value in Decimal Unicode Value
'0' to '9' 48 to 57 u0030 to u0039
'A' to 'Z' 65 to 90 u0041 to u005A
'a' to 'z' 97 to 122 u0061 to u007A

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Casting char Type
int i = 'a'; //Same as int i = (int)'a'; which is 97
char ch = 97; //Same as char ch = (char)97; which is 'a'

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if (ch >= 'A' && ch <= 'Z')
System.out.println(ch + " is an uppercase letter");
else if (ch >= 'a' && ch <= 'z')
System.out.println(ch + " is a lowercase letter");
else if (ch >= '0' && ch <= '9')
System.out.println(ch + " is a numeric character");
Comparing char Type

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Class Character Methods
Method Description
isDigit(ch) Returns true if the specified character is a digit.
isLetter(ch) Returns true if the specified character is a letter.
isLetterOrDigit(ch) Returns true if the specified character is a letter or digit.
isLowerCase(ch) Returns true if the specified character is a lowercase letter.
isUpperCase(ch) Returns true if the specified character is an uppercase letter.
toLowerCase(ch) Returns the lowercase of the specified character.
toUpperCase(ch) Returns the uppercase of the specified character.

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Class Character Methods
Character ch1 = new Character('b'); //object NOT char type
Character ch2 = new Character(‘9'); //object NOT char type
Character.isLowerCase(ch1) returns true
Character.isLetterOrDigit(ch1) returns true
Character.isDigit(ch1) returns false
Character.isDigit(ch2) returns true
Character.toUpperCase(ch1) returns B

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Class Character Test
// Class Character Test
public class CharacterTest
{
{
Character ch1 = new Character('b'); //object NOT char type
Character ch2 = new Character('9'); //object NOT char type
System.out.println(Character.isLowerCase(ch1)); //returns true
System.out.println(Character.isLetterOrDigit(ch1)); //returns true
System.out.println(Character.isDigit(ch1)); //returns false
System.out.println(Character.isDigit(ch2)); //returns true
System.out.println(Character.toUpperCase(ch1)); //returns B
char ch3 = 'R'; // char type variable
char ch4 = '7'; // char type variable
char ch5 = '*'; // char type variable
System.out.println(Character.isLowerCase(ch3)); //returns false
System.out.println(Character.isLetterOrDigit(ch5)); //returns false
System.out.println(Character.isDigit(ch4)); //returns true
System.out.println(Character.isDigit(ch5)); //returns false
System.out.println(Character.toLowerCase(ch3)); //returns r
}
}

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Escape Sequences
Description Escape Sequence Unicode
Backspace b u0008
Tab t u0009
Linefeed n u000A
Carriage return r u000D
------------------------------------------------------------------------
Backslash u005C
Single Quote ' u0027
Double Quote " u0022

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4. Class String
• To create a String object, we need to declare a variables
of type String:
String title = "Java Software Solutions";
• Each string literal (enclosed in double quotes) represents
a String object
• Once a String object has been created, neither its value
nor its length can be changed. Thus, String objects are
immutable
• The String type is not a primitive type. It is a class type
and known as a object or reference type.

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String Methods
• However, several methods of the String class return
new String objects that are modified versions of the
original string
• A String object is a sequence of characters (known as
Single-Dimensional Array).
String courseName = "CS 2301";
C 1
0
S 3
2
0 6
5
1 4
2 3

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String Index Values
• It is occasionally helpful to refer to a particular character
within a string
• This can be done by specifying the character's numeric
index (position)
• The indexes begin at zero in each string
• In the string "Hello", the character 'H' is at index 0
and the 'o' is at index 4

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Getting Characters from a String
String message = "Welcome to Java";
char ch = message.charAt(0);
System.out.println("The first character in message is “ + ch);
String message = "Welcome to Java";
int messageLength = message.length();
System.out.println("The length of message is " + messageLength);

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String Concatenation
// Three strings are concatenated
String message = "Welcome " + "to " + "Java";
// String Chapter is concatenated with number 2
String s = "Chapter" + 2; // s becomes Chapter2
// String Supplement is concatenated with character B
String s1 = "Supplement" + 'B'; // s1 becomes SupplementB

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Example
public class StringMutation
{
// Prints a string and various mutations of it.
{
String phrase = "Change is inevitable";
String mutation1, mutation2, mutation3, mutation4;
System.out.println ("Original string: "" + phrase + """);
System.out.println ("Length of string: " + phrase.length());
mutation1 = phrase.concat(", except from vending machines.");
mutation2 = mutation1.toUpperCase();
mutation3 = mutation2.replace ('E', 'X');
mutation4 = mutation3.substring (3, 30); //excluding position 30
System.out.println ("Mutation #1: " + mutation1);
System.out.println ("Mutated length: " + mutation4.length());
}
}

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Example
Output:
Original string: "Change is inevitable"
Length of string: 20
Mutation #1: Change is inevitable, except from vending machines.
Mutation #2: CHANGE IS INEVITABLE, EXCEPT FROM VENDING MACHINES.
Mutation #3: CHANGX IS INXVITABLX, XXCXPT FROM VXNDING MACHINXS.
Mutation #4: NGX IS INXVITABLX, XXCXPT F
Mutated length: 27

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Other String Methods
String S1 = "Welcome";
String S2 = new String(char[]);
S2 = " Hello! ";
char ch = S1.charAt(index);
int length = S1.length();
int index = S1.indexOf(ch);
int index = S1.lastIndexOf(ch);
boolean b = S1.equals(S2);
boolean b = S1.equalsIgnoreCase(S2);
boolean b = S1.startsWith(S2);
Boolean b = S1.endsWith(S2);
String S = S1.toUpperCase();
String S = S2.toLowerCase();
String S = S2.substring(i); //from position i to last position
String S = S2.substring(i,j); //excluding j position
String S = S2.replace(ch1,ch2);
String S = S2.trim(); //returns "Hello!", no spaces

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Reading Strings
Scanner input = new Scanner(System.in);
System.out.print("Enter three words separated by spaces: ");
String s1 = input.next();
System.out.println(“First word is " + s1);
System.out.println(“Second word is " + s2);
System.out.println(“Third word is " + s3);
Note: If we use
String s1 = input.nextLine();
s1 contains all typed characters until we press the "Enter" key.

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Reading Characters
//Characters are read as strings
Scanner input = new Scanner(System.in);
System.out.print("Enter a character: ");
String s = input.nextLine(); //must press the Enter key
char ch = s.charAt(0);
System.out.println("The entered character is " + ch);

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Comparing Strings
Method Description
Returns true if this string is equal to string s1.
Returns true if this string is equal to string s1; it is case insensitive.
Returns an integer greater than 0, equal to 0, or less than 0 to indicate whether
this string is greater than, equal to, or less than s1.
Same as compareTo except that the comparison is case insensitive.
Returns true if this string starts with the specified prefix.
Returns true if this string ends with the specified suffix.
equals(s1)
equalsIgnoreCase(s1)
compareTo(s1)
compareToIgnoreCase(s1)
startsWith(prefix)
endsWith(suffix)

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Obtaining Substrings
Method Description
Returns this string’s substring that begins with the character at the specified
beginIndex and extends to the end of the string, as shown in Figure 4.2.
Returns this string’s substring that begins at the specified beginIndex and
extends to the character at index endIndex – 1, as shown in Figure 9.6.
Note that the character at endIndex is not part of the substring.
substring(beginIndex)
substring(beginIndex,
endIndex)

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Method Description
Returns the index of the first occurrence of ch in the string. Returns -1 if not
matched.
Returns the index of the first occurrence of ch after fromIndex in the string.
Returns -1 if not matched.
Returns the index of the first occurrence of string s in this string. Returns -1 if
not matched.
Returns the index of the first occurrence of string s in this string after
fromIndex. Returns -1 if not matched.
Returns the index of the last occurrence of ch in the string. Returns -1 if not
matched.
Returns the index of the last occurrence of ch before fromIndex in this
string. Returns -1 if not matched.
Returns the index of the last occurrence of string s. Returns -1 if not matched.
Returns the index of the last occurrence of string s before fromIndex.
Returns -1 if not matched.
indexOf(ch)
indexOf(ch, fromIndex)
indexOf(s)
indexOf(s, fromIndex)
lastIndexOf(ch)
lastIndexOf(ch,
fromIndex)
lastIndexOf(s)
lastIndexOf(s,
fromIndex)
indexOf() method

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Conversion of Strings/Numbers
You can convert strings of digits to numbers:
String intString = “123”;
int intValue = Integer.parseInt(intString);
String doubleString = “123.456”;
double doubleValue = Double.parseDouble(doubleString);
You can convert numbers to strings:
int number = 123456;
String s = "" + number; //gives "123456"

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5. printf() Statement
Use the printf statement.
System.out.printf(format, items);
Where format is a string that may consist of substrings and
format specifiers.
A format specifier specifies how an item should be displayed.
An item may be a numeric value, character, boolean value, or a
string.
Each specifier begins with a percent (%) sign.

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Frequently-Used Specifiers
Specifier Output Example .
%b a boolean value true or
false
%c a character 'a'
%d a decimal integer 200
%f a floating-point number 45.4600000
%e a standard scientific notation 4.556000e+01
%s a string "Java is cool"
int count = 5;
double amount = 45.56;
System.out.printf("count is %d and amount is %f", count, amount);
Output: count is 5 and amount is 45.5600000
items
Homework: Type and run program FormatDemo, listing 4.6, page 148. It shows
how to display tabulated outputs using printf() statement.

04-Math_Functions.pptx data structure and algo

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