Chapter 4: Basic Control Structures Chapter 4 Basic

Chapter 4: Basic Control Structures Chapter 4 Basic

Chapter 4: Basic Control Structures Chapter 4 Basic Control Structures Java Programming FROM THE BEGINNING 1 Copyright 2000 W. W. Norton & Company. Chapter 4: Basic Control Structures 4.1 Performing Comparisons Most programs need the ability to test conditions and make decisions based on the outcomes of those tests. The primary tool for testing conditions is the if statement, which tests whether a boolean expression has the value true or false. Most of the conditions in a program involve comparisons, which are performed using the relational operators and the equality operators. Java Programming FROM THE BEGINNING

2 Copyright 2000 W. W. Norton & Company. Chapter 4: Basic Control Structures Relational Operators The relational operators test the relationship between two numbers, returning a boolean result. < > <= >= Less than Greater than Less than or equal to Greater than or equal to Examples: 5 < 3 false 5 > 3 true 3 > 3 false 5 <= 3 false 5 >= 3 true 3 >= 3 true

Java Programming FROM THE BEGINNING 3 Copyright 2000 W. W. Norton & Company. Chapter 4: Basic Control Structures Relational Operators The relational operators dont require operands to have identical types. If an int value is compared with a double value, the int value will be converted to double before the comparison is performed. The arithmetic operators take precedence over the relational operators, so Java would interpret a - b * c < d + e as (a - b * c) < (d + e) Java Programming FROM THE BEGINNING 4

Copyright 2000 W. W. Norton & Company. Chapter 4: Basic Control Structures Equality Operators Testing whether two values are equal or not equal is done using the equality operators: == Equal to != Not equal to The equality operators have lower precedence than the relational operators. Examples of the equality operators: 6 == 2 6 != 2 2 == 2 2 != 2 false true true false

Java Programming FROM THE BEGINNING 5 Copyright 2000 W. W. Norton & Company. Chapter 4: Basic Control Structures Equality Operators As with the relational operators, the types of the operands dont need to be the same. If an int operand is compared to a double operand, the int value is converted automatically to double type before the comparison is performed: 2 == 2.0 true 2 == 2.1 false Java Programming FROM THE BEGINNING 6 Copyright 2000 W. W. Norton & Company.

Chapter 4: Basic Control Structures Testing Floating-Point Numbers for Equality Because of round-off error, floating-point numbers that seem as though they should be equal may not be. For example, the condition 1.2 - 1.1 == 0.1 is false, because the value of 1.2 - 1.1 is 0.09999999999999987, not 0.1. One way to avoid problems with round-off error is to test whether floating-point numbers are close enough, rather than testing whether theyre equal. Java Programming FROM THE BEGINNING 7 Copyright 2000 W. W. Norton & Company. Chapter 4: Basic Control Structures Testing Objects for Equality If x and y are two object variables of the same type, the expression

x == y tests whether x and y refer to the same object (or both x and y have the value null). The expression x != y tests whether x and y refer to different objects (or just one of x and y has the value null). In either case, the references in x and y are being compared, not the objects that x and y refer to. Java Programming FROM THE BEGINNING 8 Copyright 2000 W. W. Norton & Company. Chapter 4: Basic Control Structures The equals Method The equals method is used to test whether two objects contain matching data. The value of x.equals(y) is true if the objects that x and y represent are equal. Every Java class supports the equals method, although the definition of equals varies from class to

class. For some classes, the value of x.equals(y) is the same as x == y. Java Programming FROM THE BEGINNING 9 Copyright 2000 W. W. Norton & Company. Chapter 4: Basic Control Structures Comparing Strings Strings are objects, so the == operator should not be used to test whether two strings are equal. Instead, use str1.equals(str2) to test whether str1 and str2 contain the same series of characters. The equalsIgnoreCase method is similar to equals but ignores the case of letters. For example, if str1 is "hotjava" and str2 is "HotJava", the value of str1.equalsIgnoreCase(str2) is true. Java Programming FROM THE BEGINNING

10 Copyright 2000 W. W. Norton & Company. Chapter 4: Basic Control Structures Comparing Strings String is one of the few classes in the Java API that supports relational operations. To compare the strings str1 and str2, the compareTo method is used: str1.compareTo(str2) compareTo returns an integer thats less than zero, equal to zero, or greater than zero, depending on whether str1 is less than str2, equal to str2, or greater than str2, respectively. Java Programming FROM THE BEGINNING 11 Copyright 2000 W. W. Norton & Company. Chapter 4: Basic Control Structures

Comparing Strings compareTo looks for the first position in which the strings are different. For example, "aab" is considered to be less than "aba". If the characters in the strings match, then compareTo considers the shorter of the two strings to be smaller. For example, "ab" is less than "aba". Java Programming FROM THE BEGINNING 12 Copyright 2000 W. W. Norton & Company. Chapter 4: Basic Control Structures Comparing Strings To determine whether one character is less than another, the compareTo method examines the Unicode values of the characters. Properties of Unicode characters: Digits are assigned consecutive values; 0 is less than 1, which is less than 2, and so on. Uppercase letters have consecutive values.

Lowercase letters have consecutive values. Uppercase letters are less than lowercase letters. The space character is less than any printing character, including letters and digits. Java Programming FROM THE BEGINNING 13 Copyright 2000 W. W. Norton & Company. Chapter 4: Basic Control Structures 4.2 Logical Operators The logical operators are used to combine the results of comparisons. Example: age >= 18 && age <= 65 There are three logical operators: ! Logical not && Logical and || Logical or ! is a unary operator. && and || are binary operators. All logical operators expect boolean operands and produce boolean results.

Java Programming FROM THE BEGINNING 14 Copyright 2000 W. W. Norton & Company. Chapter 4: Basic Control Structures Performing the And Operation The && operator tests whether two boolean expressions are both true. Behavior of the && operator: Evaluate the left operand. If its false, return false. Otherwise, evaluate the right operand. If its true, return true; if its false, return false. The && operator ignores the right operand if the left operand is false. This behavior is often called short-circuit evaluation. Java Programming FROM THE BEGINNING 15 Copyright 2000 W. W. Norton &

Company. Chapter 4: Basic Control Structures Short-Circuit Evaluation Short-circuit evaluation can save time. More importantly, short-circuit evaluation can avoid potential errors. The following expression tests whether i is not 0 before checking whether j/i is greater than 0: (i != 0) && (j / i > 0) Java Programming FROM THE BEGINNING 16 Copyright 2000 W. W. Norton & Company. Chapter 4: Basic Control Structures Performing the Or Operation The || (or) operator is used to test whether one (or both) of two conditions is true. Behavior of the || operator: Evaluate the left operand. If its true, return true. Otherwise, evaluate the right operand. If its true, return

true; if its false, return false. The || operator also relies on short-circuit evaluation. If the left operand is true, it ignores the right operand. Java Programming FROM THE BEGINNING 17 Copyright 2000 W. W. Norton & Company. Chapter 4: Basic Control Structures Performing the Not Operation When applied to a false value, the ! (not) operator returns true. When applied to a true value, it returns false. The value of 9 < 11 is true, but the value of !(9 < 11) is false. The ! operator is often used to test whether objects (including strings) are not equal: !str1.equals(str2) Java Programming

FROM THE BEGINNING 18 Copyright 2000 W. W. Norton & Company. Chapter 4: Basic Control Structures Precedence and Associativity of And, Or, and Not The ! operator takes precedence over the && operator, which in turn takes precedence over the || operator. The relational and equality operators take precedence over && and ||, but have lower precedence than !. Java would interpret the expression a < b || c >= d && e == f as (a < b) || ((c >= d) && (e == f)) Java Programming FROM THE BEGINNING 19 Copyright 2000 W. W. Norton &

Company. Chapter 4: Basic Control Structures Precedence and Associativity of And, Or, and Not The ! operator is right associative. The && and || operators are left associative. Java would interpret a < b && c >= d && e == f as ((a < b) && (c >= d)) && (e == f) Java Programming FROM THE BEGINNING 20 Copyright 2000 W. W. Norton & Company. Chapter 4: Basic Control Structures Simplifying boolean Expressions boolean expressions that contain the ! operator can often be simplified by applying one of de Morgans Laws:

!(expr1 && expr2) is equivalent to !(expr1) || !(expr2) !(expr1 || expr2) is equivalent to !(expr1) && !(expr2) expr1 and expr2 are arbitrary boolean expressions. Java Programming FROM THE BEGINNING 21 Copyright 2000 W. W. Norton & Company. Chapter 4: Basic Control Structures Simplifying boolean Expressions Using de Morgans Laws, the expression !(i >= 1 && i <= 10) could be rewritten as !(i >= 1) || !(i <= 10) and then simplified to i < 1 || i > 10 This version has fewer operators and avoids using the ! operator, which can make boolean

expressions hard to understand. Java Programming FROM THE BEGINNING 22 Copyright 2000 W. W. Norton & Company. Chapter 4: Basic Control Structures Testing for Leap Years boolean expressions often get complicated, as in the case of testing whether a year is a leap year. A leap year must be a multiple of 4. However, if a year is a multiple of 100, then it must also be a multiple of 400 in order to be a leap year. 2000 is a leap year, but 2100 is not. A boolean expression that tests for a leap year: (year % 4 == 0) && (year % 100 != 0 || year % 400 == 0) Java Programming FROM THE BEGINNING 23 Copyright 2000 W. W. Norton &

Company. Chapter 4: Basic Control Structures 4.3 Simple if Statements The if statement allows a program to test a condition. Form of the if statement: if ( expression ) statement expression must have boolean type. When the if statement is executed, the condition is evaluated. If its true, then statement is executed. If its false, statement is not executed. Java Programming FROM THE BEGINNING 24 Copyright 2000 W. W. Norton & Company. Chapter 4: Basic Control Structures An Example Example of an if statement: if (score > 100)

score = 100; Be careful not to use the = operator in an if statements condition: if (i = 0) Java Programming FROM THE BEGINNING // WRONG 25 Copyright 2000 W. W. Norton & Company. Chapter 4: Basic Control Structures Indentation Each if statement contains an inner statementthe one to be executed if the condition is true. To make it clear that this statement is inside the if statement, programmers normally indent the inner statement. The amount of indentation should be the same as the amount used to indent a method within a class, or a statement within a method.

Java Programming FROM THE BEGINNING 26 Copyright 2000 W. W. Norton & Company. Chapter 4: Basic Control Structures Indentation The appearance of a properly nested program (assuming an indentation of four spaces): Java Programming FROM THE BEGINNING 27 Copyright 2000 W. W. Norton & Company. Chapter 4: Basic Control Structures The Empty Statement Putting a semicolon after the test condition in an if statement is wrong: if (score > 100);

score = 100; // WRONG The compiler treats the extra semicolon as an empty statement, however, so it doesnt detect an error: if (score > 100) ; // Empty statement--does nothing score = 100; Java Programming FROM THE BEGINNING 28 Copyright 2000 W. W. Norton & Company. Chapter 4: Basic Control Structures Blocks An if statement can contain only one inner statement. In order to have an if statement perform more than one action, a block can be used. General form of a block: {

statements } A block is considered to be one statement, even though it may contain any number of statements. Java Programming FROM THE BEGINNING 29 Copyright 2000 W. W. Norton & Company. Chapter 4: Basic Control Structures Blocks Example: if (score > 100) { System.out.println("** Error: Score exceeds 100 **"); score = 100; } Each of the statements inside the block ends with a semicolon, but theres no semicolon after the block itself.

Java Programming FROM THE BEGINNING 30 Copyright 2000 W. W. Norton & Company. Chapter 4: Basic Control Structures Statement Nesting Because of blocks, statements are often deeply nested: Its important to use visual cues to show nesting: Increasing the indentation for each new nesting level. Aligning statements at the same level of nesting. Java Programming FROM THE BEGINNING 31 Copyright 2000 W. W. Norton & Company. Chapter 4: Basic Control Structures Layout of Statements

To avoid indentation creep, its customary to align braces with the statement that encloses them: if (score > 100) { System.out.println("** Error: Score exceeds 100 **"); score = 100; } To conserve vertical space, many programmers put the left curly brace at the end of the previous line: if (score > 100) { System.out.println("** Error: Score exceeds 100 **"); score = 100; } Java Programming FROM THE BEGINNING 32 Copyright 2000 W. W. Norton & Company. Chapter 4: Basic Control Structures 4.4 if Statements with else Clauses The if statement is allowed have an else clause:

if ( expression ) statement else statement There are now two inner statements. The first is executed if the expression is true. The second is executed if the expression is false. Java Programming FROM THE BEGINNING 33 Copyright 2000 W. W. Norton & Company. Chapter 4: Basic Control Structures if Statement Layout An example of an if statement with an else clause: if (a > b) larger = a; else larger = b; Layout conventions:

Align else with if. Put each assignment on a separate line. Indent each assignment. Java Programming FROM THE BEGINNING 34 Copyright 2000 W. W. Norton & Company. Chapter 4: Basic Control Structures if Statement Layout If the statements inside an if statement are very short, programmers will sometimes put them on the same line as the if or else: if (a > b) larger = a; else larger = b; Java Programming FROM THE BEGINNING 35 Copyright 2000 W. W. Norton & Company.

Chapter 4: Basic Control Structures if Statement Layout Recommended layout when the inner statements are blocks: if () { } else { } Other layouts are also common. For example: if () { } else { } Java Programming FROM THE BEGINNING 36 Copyright 2000 W. W. Norton & Company. Chapter 4: Basic Control Structures

Nested if Statements The statements nested inside an if statement can be other if statements. An if statement that converts an hour expressed on a 24-hour scale (023) to a 12-hour scale: if (hour <= 11) if (hour == 0) System.out.println("12 midnight"); else System.out.println(hour + " a.m."); else if (hour == 12) System.out.println("12 noon"); else System.out.println((hour - 12) + " p.m."); Java Programming FROM THE BEGINNING 37 Copyright 2000 W. W. Norton & Company. Chapter 4: Basic Control Structures Nested if Statements For clarity, its probably a good idea to put braces around the inner if statements:

if (hour <= 11) { if (hour == 0) System.out.println("12 midnight"); else System.out.println(hour + " a.m."); } else { if (hour == 12) System.out.println("12 noon"); else System.out.println((hour - 12) + " p.m."); } Java Programming FROM THE BEGINNING 38 Copyright 2000 W. W. Norton & Company. Chapter 4: Basic Control Structures Cascaded if Statements Many programs need to test a series of conditions, one after the other, until finding one thats true. This situation is best handled by nesting a series of if statements in such a way that the else clause of each is another if statement.

This is called a cascaded if statement. Java Programming FROM THE BEGINNING 39 Copyright 2000 W. W. Norton & Company. Chapter 4: Basic Control Structures Cascaded if Statements A cascaded if statement that prints a letter grade: if (score >= 90) System.out.println("A"); else if (score >= 80 && score <= 89) System.out.println("B"); else if (score >= 70 && score <= 79) System.out.println("C"); else if (score >= 60 && score <= 69) System.out.println("D"); else System.out.println("F"); Java Programming

FROM THE BEGINNING 40 Copyright 2000 W. W. Norton & Company. Chapter 4: Basic Control Structures Cascaded if Statements To avoid indentation creep, programmers customarily put each else underneath the original if: if (score >= 90) System.out.println("A"); else if (score >= 80 && score <= 89) System.out.println("B"); else if (score >= 70 && score <= 79) System.out.println("C"); else if (score >= 60 && score <= 69) System.out.println("D"); else System.out.println("F"); Java Programming FROM THE BEGINNING 41

Copyright 2000 W. W. Norton & Company. Chapter 4: Basic Control Structures Cascaded if Statements General form of a cascaded if statement: if ( expression ) statement else if ( expression ) statement else if ( expression ) statement else statement The else clause at the end may not be present. Java Programming FROM THE BEGINNING 42 Copyright 2000 W. W. Norton & Company. Chapter 4: Basic Control Structures

Simplifying Cascaded if Statements A cascaded if statement can often be simplified by removing conditions that are guaranteed (because of previous tests) to be true. The letter grade example has three such tests: if (score >= 90) System.out.println("A"); else if (score >= 80 && score <= 89) System.out.println("B"); else if (score >= 70 && score <= 79) System.out.println("C"); else if (score >= 60 && score <= 69) System.out.println("D"); else System.out.println("F"); Java Programming FROM THE BEGINNING 43 Copyright 2000 W. W. Norton & Company. Chapter 4: Basic Control Structures Simplifying Cascaded if Statements A simplified version of the letter grade if statement:

if (score >= 90) System.out.println("A"); else if (score >= 80) System.out.println("B"); else if (score >= 70) System.out.println("C"); else if (score >= 60) System.out.println("D"); else System.out.println("F"); Java Programming FROM THE BEGINNING 44 Copyright 2000 W. W. Norton & Company. Chapter 4: Basic Control Structures Program: Flipping a Coin Using if statements, its easy to write a program that asks the user to guess the outcome of a simulated coin flip. The program will indicate whether or not the user guessed correctly: Enter heads or tails: tails Sorry, you lose.

If the users input isnt heads or tails (ignoring case), the program will print an error message and terminate. Java Programming FROM THE BEGINNING 45 Copyright 2000 W. W. Norton & Company. Chapter 4: Basic Control Structures The Math.random Method Simulating a coin flip can be done using the Math.random method. This method returns a random number (technically, a pseudorandom number) thats greater than or equal to 0.0 and less than 1.0. If Math.random returns a number less than 0.5, the program will consider the outcome of the coin flip to be heads. Java Programming FROM THE BEGINNING 46

Copyright 2000 W. W. Norton & Company. Chapter 4: Basic Control Structures CoinFlip.java // Asks the user to guess a coin flip import jpb.*; public class CoinFlip { public static void main(String[] args) { // Prompt user to guess heads or tails SimpleIO.prompt("Enter heads or tails: "); String userInput = SimpleIO.readLine(); if (!userInput.equalsIgnoreCase("heads") && !userInput.equalsIgnoreCase("tails")) { System.out.println("Sorry, you didn't enter heads " + "or tails; please try again."); return; } Java Programming FROM THE BEGINNING 47 Copyright 2000 W. W. Norton & Company.

Chapter 4: Basic Control Structures // Choose a random number double randomNumber = Math.random(); // Determine whether user guessed correctly if (userInput.equalsIgnoreCase("heads") && randomNumber < 0.5) System.out.println("You win!"); else if (userInput.equalsIgnoreCase("tails") && randomNumber >= 0.5) System.out.println("You win!"); else System.out.println("Sorry, you lose."); } } After reading the users input, the program validates it, to make sure that it meets the requirements of the program. Java Programming FROM THE BEGINNING 48 Copyright 2000 W. W. Norton & Company. Chapter 4: Basic Control Structures

The Dangling else Problem When one if statement contains another, the dangling else problem can sometimes occur. Example: if (n <= max) if (n > 0) sum += n; else sum += max; When this statement is executed, the sum variable doesnt change if n is larger than max, an unexpected outcome. Java Programming FROM THE BEGINNING 49 Copyright 2000 W. W. Norton & Company. Chapter 4: Basic Control Structures The Dangling else Problem The problem is ambiguity. There are two ways to read the if statement:

Interpretation 1 Interpretation 2 if (n <= max) { if (n <= max) { if (n > 0) if (n > 0) sum += n; sum += n; } else else sum += max; sum += max; } When if statements are nested, Java matches each else clause with the nearest unmatched if, leading to Interpretation 2. Java Programming FROM THE BEGINNING 50 Copyright 2000 W. W. Norton & Company. Chapter 4: Basic Control Structures The Dangling else Problem To force Interpretation 1, the inner statement will

need to be made into a block by adding curly braces: if (n <= max) { if (n > 0) sum += n; } else sum += max; Always using braces in if statements will avoid the dangling else problem. Java Programming FROM THE BEGINNING 51 Copyright 2000 W. W. Norton & Company. Chapter 4: Basic Control Structures Ambiguity Ambiguity is common in programming languages. An expression such as a + b * c could mean either (a + b) * c or a + (b * c). Java resolves ambiguity in expressions by adopting rules for precedence and associativity. Ambiguity in expressions can be avoided by using parentheses, just as ambiguity in if statements

can be avoided by using braces. Java Programming FROM THE BEGINNING 52 Copyright 2000 W. W. Norton & Company. Chapter 4: Basic Control Structures 4.5 The boolean Type boolean expressions are used in if statements, but the boolean type has other uses. Variables and parameters can have boolean type, and methods can return boolean values. Java Programming FROM THE BEGINNING 53 Copyright 2000 W. W. Norton & Company. Chapter 4: Basic Control Structures

Declaring boolean Variables boolean variables are ideal for representing data items that have only two possible values. In the CoinFlip program, the users choice (heads or tails) could be recorded in a boolean variable: boolean headsWasSelected; Good names for boolean variables often contain a verb such as is, was, or has. Java Programming FROM THE BEGINNING 54 Copyright 2000 W. W. Norton & Company. Chapter 4: Basic Control Structures Assigning to a boolean Variable boolean variables can be assigned either true or false: headsWasSelected = true; The value assigned to a boolean variable often depends on the outcome of a test:

if (userInput.equalsIgnoreCase("heads")) headsWasSelected = true; else headsWasSelected = false; Theres a better way to get the same effect: headsWasSelected = userInput.equalsIgnoreCase("heads"); Java Programming FROM THE BEGINNING 55 Copyright 2000 W. W. Norton & Company. Chapter 4: Basic Control Structures Testing a boolean Variable An if statement can be used to test whether a boolean variable is true: if (headsWasSelected) Comparing the variable with true is unnecessary: if (headsWasSelected == true) To test whether headsWasSelected is false, the best technique is to write

if (!headsWasSelected) rather than if (headsWasSelected == false) Java Programming FROM THE BEGINNING 56 Copyright 2000 W. W. Norton & Company. Chapter 4: Basic Control Structures Displaying the Value of a boolean Variable Both the System.out.print and the System.out.println methods are capable of displaying a boolean value: System.out.println(headsWasSelected); Either the word true or the word false will be displayed. Java Programming FROM THE BEGINNING 57

Copyright 2000 W. W. Norton & Company. Chapter 4: Basic Control Structures Program: Flipping a Coin (Revisited) CoinFlip2.java // Asks the user to guess a coin flip import jpb.*; public class CoinFlip2 { public static void main(String[] args) { boolean headsWasSelected = false; // Prompt user to guess heads or tails SimpleIO.prompt("Enter heads or tails: "); String userInput = SimpleIO.readLine(); if (userInput.equalsIgnoreCase("heads")) headsWasSelected = true; else if (!userInput.equalsIgnoreCase("tails")) { System.out.println("Sorry, you didn't enter heads " + "or tails; please try again."); return; } Java Programming FROM THE BEGINNING 58

Copyright 2000 W. W. Norton & Company. Chapter 4: Basic Control Structures Program: Flipping a Coin (Revisited) // Choose a random number double randomNumber = Math.random(); // Determine whether user guessed correctly if (headsWasSelected && randomNumber < 0.5) System.out.println("You win!"); else if (!headsWasSelected && randomNumber >= 0.5) System.out.println("You win!"); else System.out.println("Sorry, you lose."); } } Java Programming FROM THE BEGINNING 59 Copyright 2000 W. W. Norton & Company. Chapter 4: Basic Control Structures

4.6 Loops Most algorithms contain steps that require an action to be repeated more than once. The recipe for Hollandaise sauce in Chapter 1 contained the following step: 5. Beat the yolks with a wire whisk until they begin to thicken. Add: 1 tablespoon boiling water. The first sentence consists of an action to be repeated (beat the yolks with a wire whisk) and a condition to be checked ([the yolks] begin to thicken). Java Programming FROM THE BEGINNING 60 Copyright 2000 W. W. Norton & Company. Chapter 4: Basic Control Structures Loop Terminology A language construct that repeatedly performs an action is called a loop. In Java, every loop has a statement to be repeated (the loop body) and a condition to be checked (the

controlling expression). Each time the loop body is executed, the controlling expression is checked. If the expression is true, the loop continues to execute. If its false, the loop terminates. A single cycle of the loop is called an iteration. Java Programming FROM THE BEGINNING 61 Copyright 2000 W. W. Norton & Company. Chapter 4: Basic Control Structures Types of Loops Java has three loop statements: while do for All three use a boolean expression to determine whether or not to continue looping. All three require a single statement as the loop body. This statement can be a block, however. Java Programming

FROM THE BEGINNING 62 Copyright 2000 W. W. Norton & Company. Chapter 4: Basic Control Structures Types of Loops Which type of loop to use is mostly a matter of convenience. The while statement tests its condition before executing the loop body. The do statement tests its condition after executing the loop body. The for statement is most convenient if the loop is controlled by a variable whose value needs to be updated each time the loop body is executed. Java Programming FROM THE BEGINNING 63 Copyright 2000 W. W. Norton & Company.

Chapter 4: Basic Control Structures The while Statement The while statement is the simplest of Javas loop statements. Form of the while statement: while ( expression ) statement The controlling expression must have boolean type. The loop body can be any statement. Example: while (i < n) i *= 2; Java Programming FROM THE BEGINNING // Controlling expression // Loop body 64 Copyright 2000 W. W. Norton & Company. Chapter 4: Basic Control Structures The while Statement When a while statement is executed, the

controlling expression is evaluated first. If it has the value true, the loop body is executed and the expression is tested again. Flow of control within a while statement: Java Programming FROM THE BEGINNING 65 Copyright 2000 W. W. Norton & Company. Chapter 4: Basic Control Structures The while Statement When a while statement terminates, the controlling expression is guaranteed to be false. (In other words, the logical negation of the controlling expression must be true.) The body of a while statement is not executed at all if the controlling expression is false to begin with. Java Programming FROM THE BEGINNING 66

Copyright 2000 W. W. Norton & Company. Chapter 4: Basic Control Structures Blocks as Loop Bodies Most loops will need more than one statement within the loop body, so the body will have to be a block. Consider the problem of finding the greatest common divisor (GCD). The GCD of two integers is the largest integer that divides both numbers evenly, with no remainder. For example, the GCD of 15 and 35 is 5. Java Programming FROM THE BEGINNING 67 Copyright 2000 W. W. Norton & Company. Chapter 4: Basic Control Structures Blocks as Loop Bodies Euclids algorithm for computing the GCD:

1. Let m and n be variables containing the two numbers. 2. If n is 0, then stop: m contains the GCD. 3. Divide m by n. Save the divisor in m, and save the remainder in n. 4. Repeat the process, starting at step 2. The algorithm will need a loop of the form while (n != 0) { } Java Programming FROM THE BEGINNING 68 Copyright 2000 W. W. Norton & Company. Chapter 4: Basic Control Structures Blocks as Loop Bodies A possible (but incorrect) body for the loop: m = n; n = m % n; // Save divisor in m // Save remainder in n

Writing the loop body correctly requires the use of a temporary variable: a variable that stores a value only briefly. while r = m = n = } (n != 0) { m % n; // Store remainder in r n; // Save divisor in m r; // Save remainder in n Java Programming FROM THE BEGINNING 69 Copyright 2000 W. W. Norton & Company. Chapter 4: Basic Control Structures Blocks as Loop Bodies Be careful to use braces if the body of a loop

contains more than one statement. Neglecting to do so may accidentally create an infinite loop: while r = m = n = (n != 0) m % n; n; r; // WRONG; braces needed An infinite loop occurs when a loops controlling expression is always true, so the loop can never terminate. Java Programming FROM THE BEGINNING 70 Copyright 2000 W. W. Norton & Company. Chapter 4: Basic Control Structures

Blocks as Loop Bodies A table can be used to show how the variables change during the execution of the GCD loop: Initial After After After After value iteration 1 iteration 2 iteration 3 iteration 4 r ? 30 12 6 0 m 30 72 30 12 6 n 72 30 12 6 0 The GCD of 30 and 72 is 6, the final value of m. Java Programming FROM THE BEGINNING 71 Copyright 2000 W. W. Norton & Company. Chapter 4: Basic Control Structures Declaring Variables in Blocks A temporary variable can be declared inside a block: while int m = n =

} (n != 0) { r = m % n; // Store remainder in r n; // Save divisor in m r; // Save remainder in n Any block may contain variable declarations, not just a block used as a loop body. Java Programming FROM THE BEGINNING 72 Copyright 2000 W. W. Norton & Company. Chapter 4: Basic Control Structures Declaring Variables in Blocks Java prohibits a variable declared inside a block from having the same name as a variable (or parameter) declared in the enclosing method. Declaring a variable inside a block isnt always a good idea.

The variable can be used only within the block. A variable declared in a block is created each time the block is entered and destroyed at the end of the block, causing its value to be lost. Java Programming FROM THE BEGINNING 73 Copyright 2000 W. W. Norton & Company. Chapter 4: Basic Control Structures Example: Improving the Fraction Constructor (skip, revisit after Ch3) The original version of the Fraction class provides the following constructor: public Fraction(int num, int denom) { numerator = num; denominator = denom; }

This constructor doesnt reduce fractions to lowest terms. Executing the statements Fraction f = new Fraction(4, 8); System.out.println(f); will produce 4/8 as the output instead of 1/2. Java Programming FROM THE BEGINNING 74 Copyright 2000 W. W. Norton & Company. Chapter 4: Basic Control Structures Example: Improving the Fraction Constructor (skip, revisit at Ch3) An improved constructor should compute the GCD of the fractions numerator and denominator and then divide both the numerator and the denominator by the GCD. The constructor should also adjust the fraction so that the denominator is never negative. Java Programming

FROM THE BEGINNING 75 Copyright 2000 W. W. Norton & Company. Chapter 4: Basic Control Structures Example: Improving the Fraction Constructor (skip, revisit at Ch3) An improved version of the Fraction constructor: public Fraction(int num, int denom) { // Compute GCD of num and denom int m = num, n = denom; while (n != 0) { int r = m % n; m = n; n = r; } // Divide num and denom by GCD; store results in instance // variables if (m != 0) { numerator = num / m; denominator = denom / m; }

Java Programming FROM THE BEGINNING 76 Copyright 2000 W. W. Norton & Company. Chapter 4: Basic Control Structures Example: Improving the Fraction Constructor (skip, at Ch3)is never Adjust fraction so revisit that denominator // if (denominator < 0) { numerator = -numerator; denominator = -denominator; } negative }

If the GCD of num and denom is 0, the constructor doesnt assign values to numerator and denominator. Java automatically initializes these variables to 0 anyway, so there is no problem. Java Programming FROM THE BEGINNING 77 Copyright 2000 W. W. Norton & Company. Chapter 4: Basic Control Structures 4.7 Counting Loops Many loops require a counter: a variable whose value increases or decreases systematically each time through the loop. A loop that reads 10 numbers entered by the user and sums them would need a variable that keeps track of how many numbers the user has entered so far. Java Programming FROM THE BEGINNING

78 Copyright 2000 W. W. Norton & Company. Chapter 4: Basic Control Structures A Countdown Loop Consider the problem of writing a loop that displays a countdown: T T T T T T T T T T minus minus minus minus minus minus minus

minus minus minus 10 and counting 9 and counting 8 and counting 7 and counting 6 and counting 5 and counting 4 and counting 3 and counting 2 and counting 1 and counting Java Programming FROM THE BEGINNING 79 Copyright 2000 W. W. Norton & Company. Chapter 4: Basic Control Structures A Countdown Loop The countdown loop will need a counter that's assigned the values 10, 9, , 1:

int i = 10; while (i > 0) { System.out.println("T minus " + i + " and counting"); i -= 1; } i != 0 could be used instead of i > 0 as the controlling expression. However, i > 0 is more descriptive, since it suggests that i is decreasing. Java Programming FROM THE BEGINNING 80 Copyright 2000 W. W. Norton & Company. Chapter 4: Basic Control Structures Counting Up A loop that displays the numbers from 1 to n along with their squares: int i = 1; while (i <= n) { System.out.println(i + " " + i * i); i += 1; }

Output of the loop if n is 5: 1 2 3 4 5 1 4 9 16 25 Java Programming FROM THE BEGINNING 81 Copyright 2000 W. W. Norton & Company. Chapter 4: Basic Control Structures Counter Variables Variables used as counters should be integers, not floating-point numbers. Counters often have names like i, j, or k (but not

l). Using short names for counters is a tradition. Also, theres often no more meaningful name for a counter than i. Java Programming FROM THE BEGINNING 82 Copyright 2000 W. W. Norton & Company. Chapter 4: Basic Control Structures Increment and Decrement Operators Most loops that have a counter variable will either increment the variable (add 1 to it) or decrement the variable (subtract 1 from it). One way to increment or decrement a variable is to use the + or - operator in conjunction with assignment: i = i + 1; i = i - 1; // Increment i // Decrement i

Another way is to use the += and -= operators: i += 1; i -= 1; // Increment i // Decrement i Java Programming FROM THE BEGINNING 83 Copyright 2000 W. W. Norton & Company. Chapter 4: Basic Control Structures Increment and Decrement Operators Java has a special operator for incrementing a variable: ++, the increment operator. There are two ways to use ++ to increment a variable: ++i; i++; When placed before the variable to be incremented, ++ is a prefix operator. When placed after the variable, ++ is a postfix operator.

Java Programming FROM THE BEGINNING 84 Copyright 2000 W. W. Norton & Company. Chapter 4: Basic Control Structures Increment and Decrement Operators Java also has an operator for decrementing a variable: --, the decrement operator. The -- operator can go in front of the variable or after the variable: --i; i--; Java Programming FROM THE BEGINNING 85 Copyright 2000 W. W. Norton & Company. Chapter 4: Basic Control Structures

Increment and Decrement Operators When ++ and -- are used in isolation, it doesnt matter whether the operator goes before or after the variable. When ++ and -- are used within some other type of statement, it usually does make a difference: System.out.println(++i); // Increments i and then prints the new // value of i System.out.println(i++); // Prints the old value of i and then // increments i Java Programming FROM THE BEGINNING 86 Copyright 2000 W. W. Norton & Company. Chapter 4: Basic Control Structures Increment and Decrement Operators ++ and -- can be used in conjunction with other operators: i = 1; j = ++i + 1;

i is now 2 and j is now 3. The outcome is different if the ++ operator is placed after i: i = 1; j = i++ + 1; Both i and j are now 2. Java Programming FROM THE BEGINNING 87 Copyright 2000 W. W. Norton & Company. Chapter 4: Basic Control Structures Side Effects The ++ and -- operators dont behave like normal arithmetic operators. Evaluating the expression i + j doesnt change i or j. Evaluating ++i causes a permanent change to i, however. The ++ and -- operators are said to have a side effect, because these operators do more than simply produce a result. Java Programming

FROM THE BEGINNING 88 Copyright 2000 W. W. Norton & Company. Chapter 4: Basic Control Structures Using the Increment and Decrement Operators in Loops The increment and decrement operators are used primarily to update loop counters. A modified version of the countdown loop: while (i > 0) { System.out.println("T minus " + i + " and counting"); i--; } Using --i instead of i-- would give the same result. Java Programming FROM THE BEGINNING 89 Copyright 2000 W. W. Norton &

Company. Chapter 4: Basic Control Structures Using the Increment and Decrement Operators in Loops A modified version of the squares example: while (i <= n) { System.out.println(i + " " + i * i); i++; } ++ and -- can sometimes be used to simplify loops, including the countdown loop: while (i > 0) { System.out.println("T minus " + i-- + " and counting"); } The braces are no longer necessary. Java Programming FROM THE BEGINNING 90 Copyright 2000 W. W. Norton & Company.

Chapter 4: Basic Control Structures Using the Increment and Decrement Operators in Loops The CourseAverage program of Section 2.11 would benefit greatly from counting loops. In particular, a loop could be used to read the eight program scores and compute their total: String userInput; double programTotal = 0.0; int i = 1; while (i <= 8) { SimpleIO.prompt("Enter Program " + i + " score: "); userInput = SimpleIO.readLine(); programTotal += Convert.toDouble(userInput); i++; } Java Programming FROM THE BEGINNING 91 Copyright 2000 W. W. Norton & Company. Chapter 4: Basic Control Structures

Program: Counting Coin Flips The CountFlips program will flip an imaginary coin any number of times. After the user enters the number of flips desired, CountFlips will print the number of heads and the number of tails: Enter number of flips: 10 Number of heads: 6 Number of tails: 4 Java Programming FROM THE BEGINNING 92 Copyright 2000 W. W. Norton & Company. Chapter 4: Basic Control Structures A Coin-Flipping Loop There are several ways to write a loop that flips a coin n times. Two possibilities: Technique 1 Technique 2 int i = 1; while (i <= n) { while (n > 0) {

i++; n--; } } The first technique preserves the value of n. The second avoids using an additional variable. Java Programming FROM THE BEGINNING 93 Copyright 2000 W. W. Norton & Company. Chapter 4: Basic Control Structures CountFlips.java // Counts the number of heads and tails in a series of coin // flips import jpb.*; public class CountFlips { public static void main(String[] args) { // Prompt user to enter number of flips SimpleIO.prompt("Enter number of flips: "); String userInput = SimpleIO.readLine(); int flips = Integer.parseInt(userInput);

Java Programming FROM THE BEGINNING 94 Copyright 2000 W. W. Norton & Company. Chapter 4: Basic Control Structures // Flip coin for specified number of times int heads = 0, tails = 0; while (flips > 0) { if (Math.random() < 0.5) heads++; else tails++; flips--; } // Display number of heads and tails System.out.println("Number of heads: " + heads); System.out.println("Number of tails: " + tails); } } Java Programming FROM THE BEGINNING

95 Copyright 2000 W. W. Norton & Company. Chapter 4: Basic Control Structures A Possible Modification An alternate version of the while loop: while (flips-- > 0) if (Math.random() < 0.5) heads++; else tails++; Java Programming FROM THE BEGINNING 96 Copyright 2000 W. W. Norton & Company. Chapter 4: Basic Control Structures 4.8 Exiting from a Loop: The break Statement Javas break statement allows a loop to

terminate at any point, not just at the beginning. Form of the break statement: break; Executing a break statement inside the body of a loop causes the loop to terminate immediately. Each break statement is usually nested inside an if statement, so that the enclosing loop will terminate only when a certain condition has been satisfied. Java Programming FROM THE BEGINNING 97 Copyright 2000 W. W. Norton & Company. Chapter 4: Basic Control Structures Uses of the break Statement The break statement has several potential uses: Premature exit from a loop Exit from the middle of a loop Multiple exit points within a loop Java Programming FROM THE BEGINNING

98 Copyright 2000 W. W. Norton & Company. Chapter 4: Basic Control Structures Premature Exit from a Loop The problem of testing whether a number is prime illustrates the need for premature exit from a loop. The following loop divides n by the numbers from 2 to n 1, breaking out when a divisor is found: int d = 2; while (d < n) { if (n % d == 0) break; // Terminate loop; n is not a prime d++; } if (d < n) System.out.println(n + " is divisible by " + d); else System.out.println(n + " is prime"); Java Programming FROM THE BEGINNING 99

Copyright 2000 W. W. Norton & Company. Chapter 4: Basic Control Structures Loops with an Exit in the Middle Loops in which the exit point is in the middle of the body are fairly common. A loop that reads user input, terminating when a particular value is entered: while (true) { SimpleIO.prompt("Enter a number (enter 0 to stop): "); String userInput = SimpleIO.readLine(); int n = Integer.parseInt(userInput); if (n == 0) break; System.out.println(n + " cubed is " + n * n * n); } Using true as the controlling expression forces the loop to repeat until the break statement is executed. Copyright 2000 W. W. Norton & Java Programming FROM THE BEGINNING

100 Company. Chapter 4: Basic Control Structures 4.9 Case Study: Decoding Social Security Numbers The first three digits of a Social Security Number (SSN) form the area number, which indicates the state or U.S. territory in which the number was originally assigned. The SSNInfo program will ask the user to enter an SSN and then indicate where the number was issued: Enter a Social Security number: 078-05-1120 Number was issued in New York Java Programming FROM THE BEGINNING 101 Copyright 2000 W. W. Norton & Company. Chapter 4: Basic Control Structures

Input Validation SSNInfo will partially validate the users input: The input must be 11 characters long (not counting any spaces at the beginning or end). The input must contain dashes in the proper places. There will be no check that the other characters are digits. Java Programming FROM THE BEGINNING 102 Copyright 2000 W. W. Norton & Company. Chapter 4: Basic Control Structures Input Validation If an input is invalid, the program will ask the user to re-enter the input: Enter a Social Security number: 078051120 Error: Number must have 11 characters Please re-enter number: 07805112000 Error: Number must have the form ddd-dd-dddd Please re-enter number: 078-05-1120 Number was issued in New York

Java Programming FROM THE BEGINNING 103 Copyright 2000 W. W. Norton & Company. Chapter 4: Basic Control Structures Design of the SSNInfo Program An overall design for the program: 1. Prompt the user to enter an SSN and trim spaces from the input. 2. If the input isnt 11 characters long, or lacks dashes in the proper places, prompt the user to re-enter the SSN; repeat until the input is valid. 3. Compute the area number from the first three digits of the SSN. 4. Determine the location corresponding to the area number. 5. Print the location, or print an error message if the area number isnt legal. Java Programming FROM THE BEGINNING 104

Copyright 2000 W. W. Norton & Company. Chapter 4: Basic Control Structures Design of the SSNInfo Program A pseudocode version of the loop in step 2: while (true) { if (user input is not 11 characters long) { print error message; else if (dashes are not in the right places) { print error message; else break; prompt user to re-enter input; read input; } Java Programming FROM THE BEGINNING 105 Copyright 2000 W. W. Norton & Company. Chapter 4: Basic Control Structures

Design of the SSNInfo Program The input will be a single string, which can be trimmed by calling the trim method. The first three digits of this string can be extracted by calling substring and then converted to an integer by calling Integer.parseInt. This integer can then be tested by a cascaded if statement to see which location it corresponds to. Java Programming FROM THE BEGINNING 106 Copyright 2000 W. W. Norton & Company. Chapter 4: Basic Control Structures SSNInfo.java // // // // // // //

// // // Program name: SSNInfo Author: K. N. King Written: 1999-06-18 Prompts the user to enter a Social Security number and then displays the location (state or territory) where the number was issued. The input is checked for length (should be 11 characters) and for dashes in the proper places. If the input is not valid, the user is asked to re-enter the Social Security number. import jpb.*; public class SSNInfo { public static void main(String[] args) { // Prompt the user to enter an SSN and trim the input SimpleIO.prompt("Enter a Social Security number: "); String ssn = SimpleIO.readLine().trim(); Java Programming FROM THE BEGINNING 107 Copyright 2000 W. W. Norton & Company.

Chapter 4: Basic Control Structures // If the input isn't 11 characters long, or lacks dashes // in the proper places, prompt the user to re-enter // the SSN; repeat until the input is valid. while (true) { if (ssn.length() != 11) { System.out.println("Error: Number must have 11 " + "characters"); } else if (ssn.charAt(3) != '-' || ssn.charAt(6) != '-') { System.out.println( "Error: Number must have the form ddd-dd-dddd"); } else break; SimpleIO.prompt("\nPlease re-enter number: "); ssn = SimpleIO.readLine().trim(); } // Get the area number (the first 3 digits of the SSN) int area = Integer.parseInt(ssn.substring(0, 3)); Java Programming FROM THE BEGINNING 108 Copyright 2000 W. W. Norton & Company.

Chapter 4: Basic Control Structures // Determine the String location; if (area == else if (area <= else if (area <= else if (area <= else if (area <= else if (area <= else if (area <= else if (area <= else if (area <= else if (area <= else if (area <= else if (area <= else if (area <= else if (area <= else if (area <= else if (area <= else if (area <= else if (area <= location corresponding to the area number 0) 3) 7)

9) 34) 39) 49) 134) 158) 211) 220) 222) 231) 236) 246) 251) 260) 267) Java Programming FROM THE BEGINNING location location location location location location location location location

location location location location location location location location location 109 = = = = = = = = = = = = = = = = =

= null; "New Hampshire"; "Maine"; "Vermont"; "Massachusetts"; "Rhode Island"; "Connecticut"; "New York"; "New Jersey"; "Pennsylvania"; "Maryland"; "Delaware"; "Virginia"; "West Virginia"; "North Carolina"; "South Carolina"; "Georgia"; "Florida"; Copyright 2000 W. W. Norton & Company. Chapter 4: Basic Control Structures else else else else

else else else else else else else else else else else else else else else else if if if if if if if if if if if

if if if if if if if if if (area (area (area (area (area (area (area (area (area (area (area (area (area (area (area (area (area (area

(area (area <= <= <= <= <= <= <= <= <= <= <= <= <= <= <= <= <= <= <= <= 302) 317) 361) 386)

399) 407) 415) 424) 428) 432) 439) 448) 467) 477) 485) 500) 502) 504) 508) 515) Java Programming FROM THE BEGINNING location location location location location location location location

location location location location location location location location location location location location 110 = = = = = = = = = = = = = =

= = = = = = "Ohio"; "Indiana"; "Illinois"; "Michigan"; "Wisconsin"; "Kentucky"; "Tennessee"; "Alabama"; "Mississippi"; "Arkansas"; "Louisiana"; "Oklahoma"; "Texas"; "Minnesota"; "Iowa"; "Missouri"; "North Dakota"; "South Dakota"; "Nebraska"; "Kansas"; Copyright 2000 W. W. Norton &

Company. Chapter 4: Basic Control Structures else else else else else else else else else else else else else else else else else else else else if if if if

if if if if if if if if if if if if if if if if (area (area (area (area (area (area (area (area (area (area (area

(area (area (area (area (area (area (area (area (area <= <= <= <= <= <= <= <= <= <= <= <= <= <= <= <= <= <=

<= <= 517) 519) 520) 524) 525) 527) 529) 530) 539) 544) 573) 574) 576) 579) 580) 584) 585) 586) 588) 595) Java Programming FROM THE BEGINNING location

location location location location location location location location location location location location location location location location location location location 111 = = = = = = =

= = = = = = = = = = = = = "Montana"; "Idaho"; "Wyoming"; "Colorado"; "New Mexico"; "Arizona"; "Utah"; "Nevada"; "Washington"; "Oregon"; "California"; "Alaska"; "Hawaii"; "District of Columbia";

"Virgin Islands"; "Puerto Rico"; "New Mexico"; "Pacific Islands"; "Mississippi"; "Florida"; Copyright 2000 W. W. Norton & Company. Chapter 4: Basic Control Structures else else else else else else else else else else else else else } }

if if if if if if if if if if if if (area (area (area (area (area (area (area (area (area (area (area (area <= <=

<= <= <= <= <= <= <= <= <= <= 599) 601) 626) 645) 647) 649) 653) 658) 665) 675) 679) 680) location location location location

location location location location location location location location location = = = = = = = = = = = = = "Puerto Rico"; "Arizona"; "California"; "Texas";

"Utah"; "New Mexico"; "Colorado"; "South Carolina"; "Louisiana"; "Georgia"; "Arkansas"; "Nevada"; null; // Print the location, or print an error message if the // area number isn't legal if (location != null) System.out.println("Number was issued in " + location); else System.out.println("Number is invalid"); Java Programming FROM THE BEGINNING 112 Copyright 2000 W. W. Norton & Company. Chapter 4: Basic Control Structures 4.10 Debugging

When a program contains control structures such as the if and while statements, debugging becomes more challenging. It will be necessary to run the program more than once, with different input data each time. Each set of input data is called a test case. Java Programming FROM THE BEGINNING 113 Copyright 2000 W. W. Norton & Company. Chapter 4: Basic Control Structures Statement Coverage Make sure that each statement in the program is executed by at least one test case. (This testing technique is called statement coverage.) Check that the controlling expression in each if statement is true in some tests and false in others. Try to test each while loop with data that forces the controlling expression to be false initially, as well as data that forces the controlling expression to be true initially. Java Programming

FROM THE BEGINNING 114 Copyright 2000 W. W. Norton & Company. Chapter 4: Basic Control Structures Debugging Loops Common types of loop bugs: Off-by-one errors. Possible cause: Using the wrong relational operator in the loops controlling expression (such as i < n instead of i <= n). Infinite loops. Possible causes: Failing to increment (or decrement) a counter inside the body of the loop. Accidentally creating an empty loop body by putting a semicolon in the wrong place. Never-executed loops. Possible causes: Inverting the relational operator in the loops controlling expression (i > n instead of i < n, for example). Using the == operator in a controlling expression. Java Programming FROM THE BEGINNING 115 Copyright 2000 W. W. Norton &

Company. Chapter 4: Basic Control Structures Debugging Loops A debugger is a great help in locating loop-related bugs. By stepping through the statements in a loop body, its easy to locate an off-by-one error, an infinite loop, or a never-executed loop. Another approach: Use System.out.println to print the value of the counter variable (if the loop has one), plus any other important variables that change during the execution of the loop. Java Programming FROM THE BEGINNING 116 Copyright 2000 W. W. Norton & Company.

Recently Viewed Presentations

  • Formal Languages Alphabet: a finite set of symbols

    Formal Languages Alphabet: a finite set of symbols

    Theorem: The recognizable langs are closed under Kleene star. Hint: guess-factor string and simulate. Reducibilities. Def: A language A is reducible to a language B if . computable function/map ƒ:å*®å* where "wwÎAÛ ƒ(w)ÎB.
  • Complex Numbers - mdcollege.edu.in

    Complex Numbers - mdcollege.edu.in

    Complex Numbers Definition A complex number z is a number of the form where x is the real part and y the imaginary part, written as x = Re z, y = Im z. j is called the imaginary unit...
  • Chapte 19  2015 Cengage Learning. All Rights Reserved.

    Chapte 19 2015 Cengage Learning. All Rights Reserved.

    The Equal-Means Test(slide 1 of 4) Set up the first question as a hypothesis test. The null hypothesis is that there are no differences in population means across treatment levels: The alternative is the opposite: that at least one pair...
  • Getting Started with EPICS Lecture Series

    Getting Started with EPICS Lecture Series

    Mclennan models PM304 and PM600. Intelligent Motion Systems, Inc. (IMS) models IM483 and MDrive. MX device driver. Physik Instrumente (PI) GmbH & Co. model C-844. MicroMo model MVP 2001 B02. Micos model MoCo dc controller. Delta Tau PMAC2-VME controller. Feature...
  • doi:10.1016/S0092-8674(02)01087-5 Copyright  2002 Cell Press. Whole-Genome Analysis of

    doi:10.1016/S0092-8674(02)01087-5 Copyright 2002 Cell Press. Whole-Genome Analysis of

    Hedgehog/Patched signaling maintains Wg expression in neighboring cells. Maintainence of Expression. Wg secreted . binds to frizzled on engrailed expressing cells. continues expression of engrailed and hedgehog. ... PowerPoint Presentation Last modified by:
  • Homework problems

    Homework problems

    Arial Calibri Office Theme Homework problems PowerPoint Presentation PowerPoint Presentation PowerPoint Presentation 20c: C7H14O2 20c: C7H14O2 PowerPoint Presentation PowerPoint Presentation PowerPoint Presentation PowerPoint Presentation PowerPoint Presentation PowerPoint Presentation PowerPoint Presentation Ketones PowerPoint Presentation ...
  • Identifying and Classifying Game Animals

    Identifying and Classifying Game Animals

    Class is the third level. Mammalia, Reptilia, and Aves are examples of classes within the chordataphylum. Each class is further broken into orders, which are based on feeding characteristics. ... ticks, mites, and scorpions are arachnids. They four pairs of...
  • Définitions

    Définitions

    Evacuation utérine sous contrôle échographique. Faible niveau de preuve ne permet pas de recommander: prostaglandines . utilisation d'utéro-tonique en per et post opératoire