Warm-Up: COMP Programming with Iterations 1

Transcription

1 Warm-Up: Suppose I have a method with header: public static boolean foo(boolean a,int b) { if (a) return true; return b > 0; Which of the following are valid ways to call the method and what is the result? int x = foo(true, 3 + 4); System.out.println(foo(!true, -10)); System.out.println(foo(true && false, 1.0 / 2)); System.out.println(foo(foo(false,0), (int)1.0 / 2)); boolean a = foo(foo(false true, 3), -10); COMP Programming with Iterations 1

2 Part 5: Boolean Expressions -- (a.k.a. the things you put in if statements and other things as conditions)

3 Boolean Expressions The year is > true There are 15 months in a year ----> false September is the 9 th month AND it is 2 months before February ---> false The Rangers were stupid to get rid of Jaromir Jagr -----> true Pirates helped stop global warming---> true??? Comp-202 is awesome ---->??????? COMP Programming Basics 3

4 Boolean Expressions Instead of evaluating to a numeric value, boolean expressions evaluate to either true or false mynumber > 0 // can be either true or false You can assign the result of a boolean expression to a variable of type boolean: boolean positive; positive = (mynumber > 0); COMP Programming Basics 4

5 Expressions in general An expression is one of the following A literal value (e.g. 10, 10.0, 10.0f, 'c', foo ) A variable (e.g. x, foo, whatever) A call to a method that returns a value (e.g. Math.pow(3,4)) A combination of other expressions using operators such as +,-,/, etc COMP Conditional Programming 5

6 Boolean Expressions in Java A boolean expression is a specific sort of these expressions. There are several ways to form boolean expressions. A boolean literal value ( true or false) A variable of type boolean (e.g. x, foo, whatever) A call to a method that returns a boolean value A combination of other expressions using operators: Comparison operators (take numbers and return boolean) Boolean operators (take booleans and return boolean) COMP Conditional Programming 6

7 Comparison Operators (1) The result of a comparison is always true or false Used to compare numeric or character values == : equal to!= : not equal to < : less than > : greater than <= : less than or equal to >= : greater than or equal to COMP Conditional Programming 7

8 Comparison Operators (2) int x = 5; x < > true x <= 5; ----> true x > 5 ---> false x >= 3 ---> true x == > true x!= 5 ---> false COMP Conditional Programming 8

9 Comparison Operators (3) Equality (==) and inequality (!=) operators apply to values that have any type The other comparison operators (<, <=, >, >=) only apply to values which have a numeric type (byte, short, int, long, float, double) or that have type char If the operands of a comparison operator have different types, the operand whose type has lower precision gets promoted to the other operand's type COMP Conditional Programming 9

10 Comparing Strings When you want to compare two Strings to each other, you will not use = = Instead you will call a method on each String. String one = a String ; String two = a different String ; boolean areequal = one.equals(two); We will see when we talk about references when you should use.equals() and when you should use = =. For primitive types like int, always use ==, for String it's almost always best to use.equals() COMP Conditional Programming 10

11 Comparing char In Java, each character (like '?' or 'm') is associated with a number. The following expression evaluates to true because the number assigned to the character '+' by the Unicode character set is lower than the number assigned to the character 'J' by the same character set: boolean lessthan = '+' < 'J'; Do not hesitate to use this property of characters in your programs. COMP Conditional Programming 11

12 Unicode Chart symbols Associated numbers Notice that A-Z are 26 codes In a row, as are a-z, and 0-9 are 10 codes in a row. This means to check a char Is uppercase you could check If the code is between 'A' And 'Z' COMP Conditional Programming 12

13 Character Comparisons The unicode number system is well designed. The 26 lowercase letters are all in a row. The 26 uppercase letters are also in a row. Note that there is a gap between the two. This means that 'a' < 'c' ----> true. COMP Conditional Programming 13

14 Floating Point Comparisons You should rarely use the equality operator (==) when comparing two floating point values (float or double) In many situations, you might consider two floating point numbers to be "close enough" even if they aren't exactly equal This is often necessary due to rounding issues. COMP Conditional Programming 14

15 Floating Point Comparisons: Example // Assuming f1 >= f2 difference = f1 - f2; boolean essentiallyequal = difference < ; COMP Conditional Programming 15

16 Creating boolean expressions from other boolean expressions Boolean expressions can also use the following logical operators:! Logical NOT Logical OR && Logical AND All three operators take operands of type boolean and produce results of type boolean That is, the input to the operator is boolean(s) and the output is a boolean. COMP Conditional Programming 16

17 ! operator The! operator refers to not It takes as input one boolean expression and flips the result. So if the boolean expression was true before, then it is false now. COMP Conditional Programming 17

18 ! operator examples! (2 < 3) > false (since 2 < 3)! (3 < 2) -----> true! true > false! false > true! (! (3 > 2)) ---> true!(september comes after August) ---> false!(earth is the 6 th planet from the sun) ---> true!(the Rangers are stupid for getting rid of Jagr) ---> false COMP Conditional Programming 18

19 && operator The && operator refers to and It takes as input two boolean expressions. The result of this operator is true if both operands are true and false if at least one of the operands is false. COMP Conditional Programming 19

20 && operator 1 < 2 && 2 < > true 1 < 1 && 2 < > false! (1 < 1) && 2 < > true (Television starts with a T) && (Java can also be coffee) --> true COMP Conditional Programming 20

21 operator The operator refers to or It takes as input two boolean expressions. The result of this operator is true if at least one of the operands is true and false if at both of the operands are false. Note that the or is NOT exclusive. This means if both operands are true the result will be true. COMP Conditional Programming 21

22 operator examples 1 < 1 2 < > true! (3 < > 1000 ) ---> false (Vegetables are healthy) (Fruit is healthy) ---> true COMP Conditional Programming 22

23 How The Java Compiler Evaluates && and If left operand of a && expression evaluates to false, the remaining operands are not evaluated In p1 && p2, if p1 is false, p2 is never looked at. If left operand of a expression evaluates to true, the remaining operands are not evaluated In p1 p2, if p1 is true, p2 is never looked at. This is called short-circuit evaluation. COMP Conditional Programming 23

24 Aside: How The Java Compiler Evaluates && and This is useful in the following case. Suppose you have an int variable x and you aren't sure if x is equal to zero or not. if ( x!= 0 && 1 / x < 5 ) COMP Conditional Programming 24

25 A bit on clean code using boolean expessions boolean tall = height > 6.0; if(tall == true) x = 5; The above is not needed. Remember that the if statement always checks if the condition is true. So if (tall) tests is tall true if (tall == true) tests is it true that tall is equal to true, which is the same thing. COMP Conditional Programming 25

26 Careful... boolean tall = height > 6.0; if(tall = true) x = 5; This sets tall to true, so x = 5 always executes, regardless of the value of height. This is a logical error: compiler will not detect it! COMP Conditional Programming 26

27 Exercise: Complete the main() method of the MinOfThree class by adding code which determines which of the three numbers entered by the user is the smallest number, and displays that number COMP Conditional Programming 27

28 MinOfThree.java import java.util.scanner; public class MinOfThree { public static void main(string[] args) { Scanner keyboard = new Scanner(System.in); int num1, num2, num3, min; System.out.print("Enter a number: "); num1 = keyboard.nextint(); System.out.print("Enter another number: "); num2 = keyboard.nextint(); System.out.print("Enter a third number: "); num3 = keyboard.nextint(); // Add your code here COMP Conditional Programming 28

29 Advanced Conditional Statements (not examinable) 1) The switch statement 2) The conditional operator

30 The Conditional Operator condition? expression1 : expression2 If condition evaluates to true, then expression1 is evaluated; if it evaluates to false, then expression2 is evaluated COMP Conditional Programming 30

31 Conditional Operator Examples larger = (num1 > num2)? num1 : num2; If num1 is greater that num2, then num1 is assigned to larger; otherwise, num2 is assigned to larger COMP Conditional Programming 31

32 Conditional operator vs. if-else The conditional operator is like an if-else statement, except that instead of executing one of two possible branches, it evaluates to one of two possible values. larger = (num1 > num2)? num1 : num2;...is the same as: if (num1 > num2) larger = num1; else larger = num2; COMP Conditional Programming 32

33 Conditional Operator Examples System.out.println ("Your change is " + count + " dime" + ((count == 1)? "" : "s")); If count evaluates to 1, then "dime" is printed If count evaluates to any value other than 1, then an "s" is added at the end of "dime" COMP Conditional Programming 33

34 Usefulness: Variable scope if (x < 0) { int absolutevalue = -x; else { int absolutevalue = x; //We can't use variable absolutevalue //here because we finished the { // it was declared in. COMP Conditional Programming 34

35 Usefulness: Variable scope int absolutevalue; if (x < 0) { absolutevalue = -x; else { absolutevalue = x; //Now we can use absolutevalue but //it's less clean To make sure //it got set, we need to remember both if/else COMP Conditional Programming 35

36 Solution 1: Use/write a method int absolutevalue = Math.abs(x); //Great when the method already exists! COMP Conditional Programming 36

37 Solution 2: Use conditional operator int absolutevalue = x < 0? -x : x; Another example: public static double myabsolutevalue(double x) { return x < 0? -x : x; COMP Conditional Programming 37

38 COMP-202 Unit 4: Programming with Iterations Doing the same thing again and again and again and again and again and again and again and again and again... CONTENTS: While loops Class (static) variables and constants Top Down Programming For loops Nested Loops

39 Repetition Statements Repetition statements allow us to execute a block of code or (set of) statement(s) multiple times; -These statements are normally called loops COMP Programming with Iterations 39

40 Repetition Statements in Java -Java has two main kinds of repetition statements: the while loop and the for loop - While and for loops are equivalent However, in certain circumstances, choosing one of these statements over the other results in a program that is easier to understand. COMP Programming with Iterations 40

41 Part 1: While loops

42 Recall : If statement if (condition) { //some code here... //code here happens regardless COMP Programming with Iterations 42

43 Recall : If statement if (condition) { //some code here... //code here happens regardless An if statement defines a block of code. COMP Programming with Iterations 43

44 Recall : If statement if (condition) { //some code here... //code here happens regardless We test a condition which can be any boolean expression. COMP Programming with Iterations 44

45 Recall : If statement if (condition) { //some code here... //code here happens regardless If the condition evaluates to true then we execute the block of code once. Otherwise we do not. COMP Programming with Iterations 45

46 Benefits of If Statements We can perform actions or commands some of the time but not all. Forces us to organize things : Certain events will only happen in one case. This creates a clear division. COMP Programming with Iterations 46

47 Doing the same thing many times Sometimes, we will want to execute the same block of code many times. How can we do that? COMP Programming with Iterations 47

48 Copy / Paste The naïve thing to do is copy paste your code. What are some problems with this? COMP Programming with Iterations 48

49 Copy / Paste 1)Annoying : Who wants to copy / paste that much 2)Error prone : Easy to make a mistake 3)Difficult to maintain : Hard to edit or fix mistakes (you have to edit the same code many times which can lead to more errors) 4)What if you don't know ahead of time how many steps you need? COMP Programming with Iterations 49

50 while loops In Java, we can create a while loop. A while loop is a statement that defines a block of code that continues to execute until a condition is false. COMP Programming with Iterations 50

51 if statement vs while loop if (condition) { //block of code //Go here //no matter what while (condition) { //block of code //Go here //only after //condition is false COMP Programming with Iterations 51

52 Syntax difference Syntactically, the only difference between a while loop and an if statement is the word while instead of if. The effect of this change is that the block of code continues to be repeated as long as condition is evaluated to be true. COMP Programming with Iterations 52

53 Example of a while loop int x = 0; while (x < 4) { System.out.println( I have to write + this over and over. ); x++; COMP Programming with Iterations 53

54 Example of a while loop int x = 0; while (x < 4) { System.out.println( I have to write + this over and over. ); x++; The purpose of the variable x here is to act as a loop counter It keeps track of how many times the loop has executed COMP Programming with Iterations 54

55 Example of a while loop int x = 0; while (x < 4) { System.out.println( I have to write + this over and over. ); x++; Initially, we set the variable x equal to 0. This means the first time we check the condition x < 4, the condition is true, so we execute the loop body. COMP Programming with Iterations 55

56 Example of a while loop int x = 0; while (x < 4) { System.out.println( I have to write + this over and over. ); x++; Next, we execute the loop body, which first involves printing to the screen. COMP Programming with Iterations 56

57 Example of a while loop int x = 0; while (x < 4) { System.out.println( I have to write + this over and over. ); x++; The next command of the loop body is increment x. This gives x the value of 1. COMP Programming with Iterations 57

58 Example of a while loop int x = 0; while (x < 4) { System.out.println( I have to write + this over and over. ); x++; Once the loop body finishes at the, the condition is then rechecked. Since x = 1 and 1 < 4, the block of code happens again. COMP Programming with Iterations 58

59 Example of a while loop int x = 0; while (x < 4) { System.out.println( I have to write + this over and over. ); x++; This procedure happens 2 more times. On the 4 th step, we test the condition and x = 3. Then after printing and adding 1 to x, x is now 4. COMP Programming with Iterations 59

60 Example of a while loop int x = 0; while (x < 4) { System.out.println( I have to write + this over and over. ); x++; If x == 4, then the condition is false, so we exit the loop and resume the code after the loop block has finished. COMP Programming with Iterations 60

61 Definition: iteration An iteration is a single execution of the instructions in the loop body. The previous loop had 4 iterations. One each for x=0, x=1, x=2, x=3

62 Important Clarification The condition of the while loop is only evaluated 1 time per step or iteration of the loop right before the block of code executes. The significance of this is if the condition changes inside the loop, the loop will keep going. COMP Programming with Iterations 62

63 Important Clarification int x = 0; while (x < 4) { x = x + 10; System.out.println( x is now 10 ); x = x - 10; x++; COMP Programming with Iterations 63

64 Important Clarification int x = 0; while (x < 4) { x = x + 10; System.out.println( x is now 10 ); x = x - 10; x++; Although x = 10 at this point, the loop condition is not tested until later, when x=1 again COMP Programming with Iterations 64

65 Practice Exercise: Figure out what the following loop does. int i = 0; while (i < 100) { if ( i % 3 == 0) { System.out.println(i); i++; COMP Programming with Iterations 65

66 What will this loop do? int x = 0; while (x < 4) { System.out.println(x); COMP Programming with Iterations 66

67 It goes on forever! The above is what is known as an infinite loop It will go on forever because we never change the value of x, which will always be less than 4 We will keep printing 0 to the screen. This is known as an infinite loop COMP Programming with Iterations 67

68 Tangent: Halting Problem (1) Alan Turing investigated the problem of: Given a computer program, can you detect if there is an infinite loop in it. He proved that you can not write a computer program to test definitively whether any computer program has an infinite loop. You'll know if the program ends, but not if it has an infinite loop COMP Programming with Iterations 68

69 Tangent: Halting Problem (2) This seems like a useless thing to prove, but it has consequences: 1)Philosophically, computers can't solve everything 2)Sometimes, we can take a more useful problem and prove that we can't solve it either, because if we could, then we'd be able to solve the Halting Problem COMP Programming with Iterations 69

70 One command while loops Like if statements, if you put a command following the while loop without a {, it will only include 1 line in your loop. -A very bad thing to do: int x = 0; while (x < 4); { // this is an infinite loop now! x++ COMP Conditional Programming 70

71 How many iterations does the following loop consist of? int x = 4; while (x > 4) { System.out.println( I have to write + this over and over. ); x++;

72 How many iterations does the following loop consist of? int x = 4; while (x > 4) { System.out.println( I have to write + this over and over. ); x++; 0 iterations because x is not > 4 at the beginning

73 How many iterations does the following int x = 6; loop consist of? while (x > 4) { System.out.println( I have to write + this over and over. ); x--;

74 How many iterations does the following int x = 6; loop consist of? while (x > 4) { System.out.println( I have to write + this over and over. ); x--; 2 iterations : 1 for x = 6, 1 for x = 5

75 How many iterations does the following int x = 6; loop consist of? while (x > 4) { System.out.println( I have to write + this over and over. ); x++;

76 How many iterations does the following int x = 6; loop consist of? while (x > 4) { System.out.println( I have to write + this over and over. ); x++; Infinite! x starts out equal to 6, we check if it is less than

77 How many iterations does the following int x = 3; loop consist of? while (x < 11) { System.out.println( I have to write + this over and over. ); x += 2;

78 How many iterations does the following int x = 3; while (x < 11) { System.out.println( I have to write + this over and over. ); x += 2; 4 iterations: x=3, x=5, x=7, x=9 loop consist of?

79 Off-By-One Errors It is a common logical error or bug to write loop conditions that result in the loop body being executed one time too few, or one time too many You should always test your code to check that your loops conditions do not cause such errors. COMP Programming with Iterations 79

80 Off-By-One Errors Example //this code is supposed to print all positive //values of x up until 5: int x = 1; while (x < 5) { System.out.println(x); x++; COMP Programming with Iterations 80

81 Off-By-One Errors Example The problem is the last iteration is x = 4. We should change the condition to: (x <= 5) OR (x < 6) COMP Programming with Iterations 81

82 Off-By-One Errors Tips To avoid off by one errors, you should always manually confirm the first step of a loop as well as the last step of a loop. Make sure the numbers are what you are expecting. COMP Programming with Iterations 82

83 General loop tips Try to think of exactly what it is that you want to do over and over again Figure out the range of values you want to try again and again. Is the loop counter also used in the computation? Make sure that your loop starts or initializes with the right result Make sure that your loop terminates with the correct result COMP Programming with Iterations 83

84 xample: Print every integer from 1 to n int i = 1; while (i <= n) { System.out.println(i); i++; COMP Programming with Iterations 84

85 Example: Performing the same code n times If you have code that you want to perform a fixed number of times, one way to do that is with a while loop and a counter: int counter = 0; while (counter < n) { //whatever you want done counter++; COMP Programming with Iterations 85

86 Exercise: While loop In unit 3, we looked at an example where we wanted to read 10 numbers and convert all of them from Fahrenheit to Celcius. Write a program using a while loop that reads 10 numbers from the keyboard, converts them one at a time to Fahrenheit, and prints the result to the screen. (Answers on next slide: no peaking!) COMP Programming with Iterations 86

87 import java.util.scanner; public class FahrenheitConverter { public static final double NUM_CONVERSIONS = 10; public static void main(string[] args) { int i = 0; Scanner reader = new Scanner(System.in); while (i < NUM_CONVERSIONS) { System.out.println(convertToCelcius(reader.nextInt())); i++; public static double converttocelcius(double fahrenheit){ return (fahrenheit 32.0) * 5.0 / 9.0; COMP Programming with Iterations 87

88 art 2: Class Variables and Constants

89 Class Constants (final) Very often, you will have a constant that you want to use throughout your entire class in many different methods. -Improves readability -Avoid errors -Easier to maintain Remember that we can declare a constant the same way as a variable, except we add the word final before the type. COMP Programming with Iterations 89

90 Class Constants (final) Sometimes, you'll declare a constant inside a method as normal, but you can also declare a final static constant outside of any method, but inside of a class: public class ConstantExample { public static final int NUM_STATES = 50; public static final int NUM_PROVINCES = 10; public static void main(string[] args) {... COMP Programming with Iterations 90

91 Class Constants (final) Now, throughout you code you won't have mysterious magic numbers like 50 and 10 throughout your code. It's easier to say for sure which 50's refer to the number of states and which 50's refer to something entirely different. Also will be much easier if the constant changes over time for whatever reason. COMP Programming with Iterations 91

92 Scope of variables and constants Remember, that any time you create a variable or constant, it's scope is only within the block of code it was declared in. This means that anywhere inside that block of code, the variable or constant is available and outside the block it is not. COMP Programming with Iterations 92

93 Scope of variables and constants public class CustomerService { public static final String COMPANY_NAME = Videotron ; public static void answercall() { System.out.print( Your call is very important to us. +Please stay on the line and a ); System.out.println( COMPANY_NAME + representative will be with your shortly ); public static void humanpicksup() { System.out.print( You owe + COMPANY_NAME + money for random ); System.out.println( surcharges. We hope you'll continue to enjoy our service. ); waitforswearing(); //The identifier COMPANY_NAME is now available throughout your entire class // CustomerService COMP Programming with Iterations 93

94 Scope of class variables public class Scope { public static String companyname = Videotron ;... Variables work the same way. This means that one thing you can do to share a variable between methods is create a variable outside of any method. In this case, you'll still want to write static. This is not generally good practice unless you know what you are doing! COMP Programming with Iterations 94

95 Class Variables These sorts of variables (or constants) are known as class variables (or class constants). They are called this because they belong to the entire class as opposed to one method. COMP Programming with Iterations 95

96 Example of bad use of class variables import java.util.scanner; public class BadFahrenheitConversion { public static double degrees = 0.0; public static Scanner reader = new Scanner(System.in); public static void main(string[] args) { degrees = reader.nextdouble(); converttocelcius(); System.out.println(degrees); public static void converttocelcius() { degrees = (degrees 32.0) * 5.0 / 9.0; COMP Programming with Iterations 96

97 Problems with this: Leads to bugs! 1)The variable degrees is used for different purposes (first it is fahrenheit then it is degrees) Confusing! 2)The method converttocelcius() has a side effect which is unexpected. 3)The code is not reusable. What if you copied this into a different program that already had a variable degrees defined? 4)Because you are doing 2 things with 1 variable, the print statement could be separated from when the value is set. 5)reader can be used by a different method and the main() method wouldn't know. COMP Programming with Iterations 97

98 Better (no class variables) import java.util.scanner; public class BadFahrenheitConversion { public static void main(string[] args) { Scanner reader = new Scanner(System.in); double fahrenheitdegrees = reader.nextdouble(); double celciusdegrees = converttocelcius(fahrenheitdegrees); System.out.println(celciusDegrees); public static double converttocelcius(double degrees) { return (degrees 32.0) * 5.0 / 9.0; COMP Programming with Iterations 98

99 Static constants Static constants do not normally have this problem since their values don't change. There are still cases where it is better to pass a constant to a method rather than use it. We will see later on that there are indeed times to create static variables, but for starters we should not use static variables and should only use static constants with simple types (i.e. int, double, float, boolean, etc. String is OK too despite the capital S) COMP Programming with Iterations 99

100 Part 3: Top Down Programming

101 Example A prime number is a positive integer >= 2 whose only divisors are 1 and itself. Write a method that calculates whether a number is prime or not using a while loop. The method should take as input an int and return a boolean value of true if the number is prime and false otherwise. COMP Programming with Iterations 101

102 Steps to solve this: First, you should figure out the input and the output of the method. This is normally given in this course, sometimes in words, sometimes in Java terminology With this knowledge, you can write the method header. If this step is not easy, then you need to think about the problem more to understand what it is you are trying to solve! COMP Programming with Iterations 102

103 Steps to solve this: public static boolean isprime(int n) { COMP Programming with Iterations 103

104 Steps to solve this: The next thing to figure out is an algorithm to solve the problem. This is not always easy. In the case of prime numbers, how can we figure out if a number n is prime (if we were doing it by hand)? COMP Programming with Iterations 104

105 Steps to solve this: 1)Check every number from 2 up until n 1. 2)If any of these numbers evenly divide n (i.e. are factors of n), then n is not prime 3)If none of them divide n, then n is prime COMP Programming with Iterations 105

106 Steps to solve this: 1)Check every number from 2 up until n 1. 2)If any of these numbers evenly divide n (i.e. are factors), then n is not prime 3)If none of them divide n, then n is prime The word every strongly implies you'll need some sort of loop. COMP Programming with Iterations 106

107 Steps to solve this: 1)Check every number from 2 up until n 1. 2)If any of these numbers evenly divide n (i.e. are factors), then n is not prime 3)If none of them divide n, then n is prime The if means we'll need some sort of if statement. n not equals prime is our conclusion and in Java will translate to a return statement with the value false COMP Programming with Iterations 107

108 Steps to solve this: 1)Check every number from 2 up until n 1. 2)If any of these numbers evenly divide n (i.e. are factors), then n is not prime 3)If none of them divide n, then n is prime One thing to be very careful of is that none means we have to check ALL of the numbers to make the conclusion. COMP Programming with Iterations 108

109 Now lets analyze each step in detai 1)Check every number from 2 up until n 1. 2)If any of these numbers evenly divide n (i.e. are factors), then n is not prime 3)If none of them divide n, then n is prime We know how to do something for every number. We know the code for printing every number from 1 to n. We just have to modify it to go from 2 until n-1 and to do other stuff instead of print! COMP Programming with Iterations 109

110 Steps to solve this: 1)Check every number from 2 up until n 1. 2)If any of these numbers evenly divide n (i.e. are factors), then n is not prime 3)If none of them divide n, then n is prime How can we check if a number x evenly divides n? COMP Programming with Iterations 110

111 Steps to solve this: How can we check if a number x evenly divides n? 1)Use int division. If x / n * n is equal to x, then x must be a multiple of n. Otherwise, we'd have lost information on the division. ex: 6 / 3 * 3 = 6 (6 is a multiple of 3) 5 / 3 * 3 = 3 (since 5 / 3 = 1 in integer division) 2)Use modulo % operator. x % n == 0 if x is a multiple of n. (ex: 48 hours after midnight is 0:00, since 48 is a multiple of 24) COMP Programming with Iterations 111

112 Solution public static boolean isprime(int n) { int x = 2; while (x < n) { if (n % x == 0) { return false; x++; return true; COMP Programming with Iterations 112

113 Even better solution public static boolean isprime(int n) { if (n < 2) { return false; int x = 2; while (x < n) { if (n % x == 0) { return false; x++; return true; COMP Programming with Iterations 113

114 Careful not to make this mistake! public static boolean isprime(int n) { if (n < 2) { return false; int x = 2; while (x < n) { if (n % x == 0) { return false; else { return true; x++; COMP Programming with Iterations 114

115 Careful not to make this mistake! public static boolean isprime(int n) { if (n < 2) { return false; int x = 2; while (x < n) { if (n % x == 0) { return false; else { return true; /* This code returns true if the first number for x (2) isn't a factor of n*/ x++; COMP Programming with Iterations 115

116 Top Down Programming The way we solved this problem is using a technique called topdown programming. We started out with a big goal (determine if a number is prime) Then we looked at the various steps we needed to solve that. (loop through all numbers, check conditions, return statement) We then examined how to solve those various steps (counter + while loop, % operator) COMP Programming with Iterations 116

117 Exercise Now that you have a method isprime, write another method printprimes. Your method should take as input an int n and return void. Your method should then print the first n prime numbers. When you write this method, for practice with taking an exam, try to write it on a piece of paper (or without seeing what the computer does). When you do this, call the method isprime(). But try not to think about how the method isprime() works. Focus only on what it does. COMP Programming with Iterations 117

118 Part 4: The for Statement

119 Common loop theme Very often in loops, one will do 3 things: 1)Perform some initialization before the loop starts. 2)Check a condition before an iteration of the loop starts. 3)Perform some finalization at the end of each iteration. COMP Programming with Iterations 119

120 Example loop int x = 0; //initialization while (x < 4) //condition { System.out.println(x); x++; //finalization at the end of each step COMP Programming with Iterations 120

121 for loop As this theme was so commonly used, Java added a for loop. A for loop is mostly the same as a while loop, but it adds as part of the for loop syntax an initialization and finalization step. for (initialization; condition; finalization) { //loop body COMP Programming with Iterations 121

122 for loop for (initialization; condition; finalization) { //loop body The initialization step happens once per loop. It happens right before the first step of the for loop COMP Programming with Iterations 122

123 for loop for (initialization; condition; finalization) { //loop body The condition is checked before each iteration of the loop. This is the same as in a while loop. COMP Programming with Iterations 123

124 for loop for (initialization; condition; finalization) { //loop body The finalization happens at the very end of every iteration of the loop. COMP Programming with Iterations 124

125 for loop for (int i = 0; i < 4; i++) { System.out.println(i); This does the same as the while loop prior. It prints the numbers 0,1,2,3 COMP Programming with Iterations 125

126 for loop vs while loop for (int i = 0; i < 4; i++) { System.out.println(i); int i = 0; while (i < 4) { System.out.println(i); i++; COMP Programming with Iterations 126

127 Benefit of for loop for loops are more readable than while loops in some cases. For example, in the previous case, it is obvious when looking at the statement int i = 0; that the statement is part of the loop. In the case of the while loop it isn't as obvious. COMP Programming with Iterations 127

128 Accidental error in while loop int x = 0; while (x < 4) { System.out.println(x); x++; Here it is not quite as obvious that int x = 0; is related to the loop. This means you or someone else could carelessly separate the 2 parts and cause a mistake (for example while copying and pasting) COMP Programming with Iterations 128

129 Benefit of while loop Typically, one chooses a while loop over a for loop if there is an indefinite number of iterations one wants to execute. For example, if you wanted to continue to do something until a certain event occurs. This translates better with a while loop because you don't have a loop counter anyway. COMP Programming with Iterations 129

130 Benefit of while loop int lastleafcupchampionship = 1967; while (lastleafcupchampionship == 1967) { System.out.println( Wow, even the Rangers are better. ); COMP Programming with Iterations 130

131 Infinite loop? int lastleafcupchampionship = 1967; while (lastleafcupchampionship == 1967) { System.out.println( Wow, even the Rangers are better. ); COMP Programming with Iterations 131

132 Treating a for loop like a while loop The statements in a for loop header can be anything including the empty statement: int x = 0; for (; x < 4; ) { System.out.println(x); x++; COMP Programming with Iterations 132

133 COMP Programming with Iterations 133

134 Exercise: Rewrite the isprime() method that we wrote to use a for loop instead of a while loop. Rewrite the printprimes() method as well. COMP Programming with Iterations 134

135 Part 5: Nested Loops

136 Nested Loops Sometimes, we will put a loop inside of a loop. When this happens...sometimes our brain is tied in a bit of a knot (buda-dum-dum-chi) COMP Programming with Iterations 136

137 Example : Print coordinate table Suppose we want to print all non-negative combinations of x and y in a grid. We can use 1 for loop inside another to do this. COMP Programming with Iterations 137

138 Example : Print coordinate table First, think about y being fixed. For any given y, if I want to print a range of x's, I can do this using a for loop. int y = 1; for (int x = 0; x < 10; x++) { System.out.print( ( + y +, + x + ), ); System.out.print( \n ); COMP Programming with Iterations 138

139 Example : Print coordinate table int y = 1; for (int x = 0; x < 10; x++) { System.out.print( ( + y +, + x + ), ); System.out.print( \n ); We know that this code will loop over x from 0 up until and including 9, and print: (1,0), (1,1), (1,2), (1,3), (1,4), (1,5), (1,6), (1,7), (1,8), (1,9) COMP Programming with Iterations 139

140 Example : Print coordinate table Now, I want to do this for every y from 0 to 10 as well. So we need to replace the y = 1 part with a loop that changes the value of y. COMP Programming with Iterations 140

141 Example : Print coordinate table for (int y = 0; y < 10; y++) { for (int x = 0; x < 10; x++) { System.out.print( ( + y +, + x + ), ); System.out.print( \n ); COMP Programming with Iterations 141

142 Using constants for (int y = 0; y < 10; y++) { for (int x = 0; x < 10; x++) { System.out.print( ( + y +, + x + ), ); System.out.print( \n ); It's better to replace the number 10 with a constant describing why we are using the number 10. It may be as simple as NUM_Y_COORDS, but it should be something COMP Programming with Iterations 142

143 Using constants final int VERTICAL_SIZE = 10; //could also be class constants? final int HORIZONTAL_SIZE = 10; for (int y = 0; y < VERTICAL_SIZE; y++) { for (int x = 0; x < HORIZONTAL_SIZE; x++) { System.out.print( ( + y +, + x + ), ); System.out.print( \n ); COMP Programming with Iterations 143

144 Exercise: Rewrite the above code using: 1)a while loop on the outside and a for loop on the inside 2)a for loop on the outside and a while loop on the inside 3)2 while loops COMP Programming with Iterations 144