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Mathematical Functions, Characters, and Strings

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Motivations Suppose you need to estimate the area enclosed by four cities, given the GPS locations (latitude and longitude) of these cities, as shown in the following diagram. How would you write a program to solve this problem? You will be able to write such a program after completing this chapter.

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Objectives To solve mathematics problems by using the methods in the Math class (§4.2). To represent characters using the char type (§4.3). To encode characters using ASCII and Unicode (§4.3.1). To represent special characters using the escape sequences (§4.4.2). To cast a numeric value to a character and cast a character to an integer (§4.3.3). To compare and test characters using the static methods in the Character class (§4.3.4). To introduce objects and instance methods (§4.4). To represent strings using the String objects (§4.4). To return the string length using the length() method (§4.4.1). To return a character in the string using the charAt(i) method (§4.4.2). To use the + operator to concatenate strings (§4.4.3). To read strings from the console (§4.4.4). To read a character from the console (§4.4.5). To compare strings using the equals method and the compareTo methods (§4.4.6). To obtain substrings (§4.4.7). To find a character or a substring in a string using the indexOf method (§4.4.8). To program using characters and strings (GuessBirthday) (§4.5.1). To convert a hexadecimal character to a decimal value (HexDigit2Dec) (§4.5.2). To revise the lottery program using strings (LotteryUsingStrings) (§4.5.3). To format output using the System.out.printf method (§4.6).

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Mathematical Functions Java provides many useful methods in the Math class for performing common mathematical functions.

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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. 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.

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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(x+0.5). long round(double x) Return (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 Math.rint(-2.5) returns -2.0 Math.round(2.6f) returns 3 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. random() Returns a random double value in the range [0.0, 1.0).

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The random Method Generates a random double value greater than or equal to 0.0 and less than 1.0 (0

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Case Study: Computing Angles of a Triangle Write a program that prompts the user to enter the x- and y-coordinates of the three corner points in a triangle and then displays the triangle’s angles.

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$Character Data Type char letter = 'A'; (ASCII) char numChar = '4'; (ASCII) char letter = '\u0041'; (Unicode) char numChar = '\u0034'; (Unicode)$

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Character Data Type char letter = 'A'; (ASCII) char numChar = '4'; (ASCII) char letter = '\u0041'; (Unicode) char numChar = '\u0034'; (Unicode)

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Unicode Format

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ASCII Code for Commonly Used Characters

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Escape Sequences for Special Characters

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Appendix B: ASCII Character Set

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ASCII Character Set, cont.

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Casting between char and Numeric Types

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Comparing and Testing Characters

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Methods in the Character Class

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The String Type The char type only represents one character. To represent a string of characters, use the data type called String. For example, String message = "Welcome to Java"; String is actually a predefined class in the Java library just like the System class and Scanner class. The String type is not a primitive type. It is known as a reference type. Any Java class can be used as a reference type for a variable. Reference data types will be thoroughly discussed in Chapter 9, “Objects and Classes.” For the time being, you just need to know how to declare a String variable, how to assign a string to the variable, how to concatenate strings, and to perform simple operations for strings.

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Simple Methods for String Objects

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Simple Methods for String Objects

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Getting String Length

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Getting Characters from a String

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Converting Strings "Welcome".toLowerCase() returns a new string, welcome. "Welcome".toUpperCase() returns a new string, WELCOME. " Welcome ".trim() returns a new string, Welcome.

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String Concatenation String s3 = s1.concat(s2); or String s3 = s1 + s2; // 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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Reading a String from the Console Scanner input = new Scanner(System.in); System.out.print("Enter three words separated by spaces: "); String s1 = input.next(); String s2 = input.next(); String s3 = input.next(); System.out.println("s1 is " + s1); System.out.println("s2 is " + s2); System.out.println("s3 is " + s3);

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Reading a Character from the Console Scanner input = new Scanner(System.in); System.out.print("Enter a character: "); String s = input.nextLine(); char ch = s.charAt(0); System.out.println("The character entered is " + ch);

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Comparing Strings

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Obtaining Substrings

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Finding a Character or a Substring in a String

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Finding a Character or a Substring in a String

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Conversion between Strings and Numbers

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Problem: Guessing Birthday The program can guess your birth date. Run to see how it works.

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Mathematics Basis for the Game 19 is 10011 in binary. 7 is 111 in binary. 23 is 11101 in binary

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Case Study: Converting a Hexadecimal Digit to a Decimal Value Write a program that converts a hexadecimal digit into a decimal value.

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Case Study: Revising the Lottery Program Using Strings A problem can be solved using many different approaches. This section rewrites the lottery program in Listing 3.7 using strings. Using strings simplifies this program.