Functions in Java

Functions in Java Functions are very important ways to “package” or encase (encapsulate) actions. Functions are methods that return a value of a given type, so are called typed methods. Within the definition there is a result, of a given type, which must be returned. Functions are parts of other expressions; they do not stand alone. Max2 is shown below in a general form, with an external and internal view. Graphic View of function max2 Data flow view (external) a 3 p 5 max2 b 5 c The max2 function can be used and reUsed In various ways was shown; The max2 is part of a larger expression such as q Use: c = max2 (a,b); Data space view (internal) a 3.0 p b 5.0 q max 5.0 local LargestOf2 = max2 (a, b); largestOf3 = max2 ( max2 (a,b), c); largestOf4 = max2 ( max2(a,b), Max2(c,d) ); biggestOf4 = max2 ( max2(a, max2(b, max2(c,d))); 5.0 result 1 Syntax of a type method is similar to that of a void method as shown below. This kind of method has a type, that is returned, which is placed right before its name. Also, the typed method involves a box called result, which is declared initially, is assigned some value, and it is finally returned. And the type method can have no JJS.start command; that is only in a routine. void name ( slotList ) type // Does nameList { ; description type name ( slotList ) type result ; type nameList // Does JJS.start(); //one main { ; description actions result = expression actions return result ; }//end void method name }//end Note: similarities and differences type method name 2 Max2 is shown defined below next to the syntax diagram. The definition of max2 consists mainly of filling in the boxes of the general syntax. General Syntax definition of Function type name ( slotList ) type result ; type nameList // Does ; actions expression return result ; }//end int max2 ( int p, int q ) int description result = { Definition of the max2 Function type method name int // Does { result; max ; maximum of 2 ints if (p > q) { max = p; }else{ max = q; }//end if result = max; return result; }//end type method max2 3 Maximum of Two is done again as follows. It shows a main method which calls max2, and it shows the function max2 defined in a different layout (with the header spread over many linesrather than one), and with a different structure (having no temporary box named max) and involving a different type (double rather than int). // Name An Onymous void mainA() { double first, second, max; // Does Maximum of 2 reals, another way JJS.start(); JJS.outputlnString ("Enter 2 reals: "); first = JJS.inputDouble (); second = JJS.inputDouble (); max = max2 (first, second); JJS.outputlnString ("The maximum is "); JJS.outputlnDouble (max); }//end void main // Function max2 (p,q) of reals double max2 ( double p, double q) { double result; // Does return max of 2 reals if (p > q) { result = p; }else{ result = q; }// end if return result; }//end real function max2 4 Maximum of Three is done by using max3 which call max2 twice. // Name An Onymous void mainB(); int first, second, third, max; // Does Max3: functions calling functions JJS.start(); JJS.outputlnString ("Enter 3 values : "); first = JJS.inputInt (); // do also second = JJS.inputInt (); // an echo third = JJS.inputInt (); // of these max = max3 (first, second, third); JJS.outputlnString ("The maximum is "); JJS.outputlnDouble (max); }//end void mainB f s t x y z max2 t max2 Enter 3 values : 3 6 5 The maximum is 6 // Function max2 (p,q) of ints int max2 (int p, int q) { int result; // Does return max of 2 ints if (p > q) { result = p; }else{ result = q; }// end if return result; }//end int function max2 // Function max3 (x,y,z) int max3 (int x, int y, int z) { int result; int temp; // Does return max of 3 ints temp = max2 (x,y); result = max2 (temp, z); return result; }//end int function max3 max3 5 Some convenient typed methods int round (double x) { int result; // Does round a real to nearest int result = JJS.doubleToInt (x + 0.5); return result; }//end integer method round double degreesToRadians (double d) { double result; // Does do angle conversion result = d * Math.PI / 180.0); return result; }//end real method degrees2radians int abs (int x) { int result; // Does return positive value if (x < 0) { result = 0 - x; }else{ result = x; }//end if return result }//end int method abs double celsiusToFahrenheit (double c) { double result; // Does convert tempertures result = (9.0/5.0)*c + 32.0; return result; }//end double method c2f Do define some other convenient typed methods such as: radiansToDegrees, fahrenheitToCelsius, sine (degrees), log10(x). 6 // Name An Onymous void mainC() { double first, second, third, area; // Does area of a triangle JJS.start() { JJS.outputlnString ("Enter 3 sides : "); first = JJS.inputDouble (); //do also second = JJS.inputDouble (); //an echo third = JJS.inputDouble (); //of these area = triArea (first, second, third); JJS.outputlnString ("The area is "); JJS.outputlnDouble (area); }//end void mainC double triArea (double a, double b, double c ) { double result; double s, t; // Does area of a triangle // Need positive lengths of sides a,b,c // using Hero's formula s = (a + b + c) / 2.0; t = s*(s-a)*(s-b)*(s-c); result = Math.sqrt (t); return result; }//end double function triArea Enter 3 sides : 3.0 4.0 5.0 The area is 6.0 Enter 3 sides : 3.0 4.0 7.0 The area is 0.0 Enter 3 sides : 3.0 3.0 3.0 The area is 3.89711 7 // Name An Onymous void mainD() { double pay, hours, rate; // Does First Weekly Gross Pay: uses Choices JJS.start() { JJS.outputlnString ("Enter hours : "); hours = JJS.inputDouble (); JJS.outputlnString ("Enter rate = JJS.inputDouble (); pay rate : "); Enter hours : 50.0 Enter rate : 10.00 The gross pay is 550 = grossPay (hours, rate); JJS.outputString ("The gross pay is "); JJS.outputDouble ( pay); }//end void mainD double grossPay (double hrs, double rate) { double result; // Does return real gross pay // Need real positive (hrs < 7*24) & rate if (hrs < 40.0) { result = hrs * rate; }else{ result = rate * 40.0 + rate * 1.50 * (hrs - 40.0); }// end if return result; }//end function grossPay 8 A “Monolithic” program (at the left) broken into “Sub” programs (at the right) // Name An Onymous void mainE() { int fact, num; // Does compute factorial: uses While JJS.start() { JJS.outputlnString ("Enter an int "); num = JJS.inputInt (); JJS.outputlnInt (num); fact = 1; while (num > 0) { fact = fact * num; num = num - 1; }//end while JJS.outputString ("Factorial is JJS.outputlnInt (fact); }//end void mainE Enter an int 10 Factorial is 3628800 "); // Name An Onymous void mainF() { int fact, num; // Does call factorial JJS.start(); JJS.outputlnString ("Enter an int "); num = JJS.inputInt (); JJS.outputlnInt (num); JJS.outputlnInt ( factorial (num) ); //end void mainF int factorial (int num) { int result; int fact; // Does factorial with decreasing index // Need an integer (num >= 0) fact = 1; while (num > 0) { fact = fact * num; num = num - 1; }//end while result = fact; return result; }//end int function factorial 9 Combinations computes the number of ways that m things can be chosen n at a time. For example 10 things can be arranged 2 at a time in 45 ways given by the formula: c = n!/((n - r)!/r!) The following main code shows how factorial is reused 3 times. void myMain () { int c,n,r; // Does compute combinations // Shows reUse of factorial function JJS.start(); n = 10; r = 2; c = factorial (n) / (factorial(n-r)*factorial(r)); JJS.outputString ("Combinations = "); JJS.outputlnInt ( c ); JJS.outputString ("\n"); // gap }//end void method myMain int factorial (int num) { int result; int fact, i; // Does factorial of num // Need positive integer num fact = 1; i = 1; while (i <= num) { fact = fact * i; i = i + 1; }//end while result = fact; return result; }//end int function factorial Combinations = 45 10 Many more ways (3) to do sub-programs: Factorial again // Name An Onymous void mainG() { int fact, num; // Does compute factorial JJS.start(); JJS.outputlnString ("Enter an int "); num = JJS.inputInt (); JJS.outputlnInt ( factorial (num) ); }//end void mainG Enter an int 10 Factorial is 3628800 int factorial (int num) { int result; // Does factorial without temp fact box // Need (num >= 0) result = 1; while (num > 0) { result = result * num; num = num - 1; }//end while return result; }//end int function factorial int factorial (int num) { int result; int fact; // Does factorial: the original way // Need (num >= 0) fact = 1; while (num > 0) { fact = fact * num; num = num - 1; }//end while result = fact; return result; }//end int function factorial int factorial (int num) { int result; int i; // Does factorial: using a for loop // Need (num >= 0) result = 1; for (i=1; i= 0) if (num > 0) { result = num * factorial (num - 1); }else{ result = 1; }//end if return result; }//end int function factorial = 5*4*3*2*1 = 120 Enter an int 10 Factorial is 3628800 Enter an int 16 Factorial is 2004189184 12 // Name An Onymous void mainI() { int first, second, num, sum, rolls, odds; double prob, percent; // Does Count Odd Dice sums JJS.start(); JJS.outputlnString ("Enter rolls :"); rolls = JJS.inputInt (); int roll () { int result; double prob, side; // Does roll one die prob = Math.random (); side = 6.0 * prob; result = JJS.doubleToInt(side) + 1; return result; }//end int function roll odds = 0; // Reset number of odd sums num = 0; while (num < rolls) { int sum2 () { int result; int first, second; sum = sum2(); if ( (sum % 2) == 1) { odds = odds + 1; }//end if num = num + 1; }//end while // Does return sum 2 to 12 of 2 rolls first = roll(); second = roll(); result = first + second; return result; }//end int function sum2 percent = 100.0 * JJS.intToDouble (odds) / JJS.intToDouble (rolls); JJS.outputString ("Percent odds = "); JJS.outputlnDouble (percent); }//end void mainI Enter rolls : 1000 Percent odds = 50.1 13 Some type functions involving Strings String firstChar (String str) { String result; // Does give first char result = str.substring (1,1); return result; }//end String method firstChar boolean isChar (String str) { boolean result; // Does tell if str is short result = (str.length() == 1); return result; }//end String method is a Char String joined (String str1, String str2) { String result; // Does join 2 strs with space result = str1 + “ “ + sdtr2; return result; }//end String join Strings Void mainString() { String first, mid, last; String initial, fullName; // Does manipulate names JJS.Start(); first = “John”; mid = “Michael”; last = “Gates”; initial = firstChar (mid); fullname = joined (first, initial); fullname = joined (fullname, last); JJS.outputlnString (fullname); //end void method mainString John M Gates 14 Boolean type methods: many ways to get even boolean isEven (int n) { boolean result; // Needs (n >= 0) // Does tell if n is even if ( (n % 2) == 0) { result = true; }else{ result = false; }//end if return result; }//end boolean method isEven boolean isEven (int n) { boolean result; // Needs (n >= 0) // Does tell if n is even result = n; while (result > 1) { result -= 2; }//end while return (result == 0); }//end boolean method isEven boolean isEven (int n) { boolean result; // Does tell if n is even result = false; if ( (n % 2) == 0) { result = true; }//end if 2 divides n return result; }//end boolean method isEven boolean isEven (int n) { boolean result; // Does tell if n is even result = ( (n%2) == 0); return result; }//end boolean method isEven boolean isEven (int n) { return ( (n%2) == 0); }//end boolean method isEven 15 Some Logical type methods: Or, Not, Nor boolean not (boolean p) { boolean result; // Does logical Not result = ! p ; return result; }//end boolean method Not boolean or (boolean p, boolean q) { boolean result; // Does logical Or in result = p || q; return result; }//end boolean method Or boolean nor (boolean p, boolean q) { boolean result; // Does operate as a Nor result = not( or(p,q) ); return result; }//end boolean method Nor void NorTest() { boolean a, b, c; //Does show Nor operator JJS.start(); JJS.outputlnString (“Enter truths”); a= JJS.inputBoolean(); JJS.outputlnBoolean (a); b= JJS.inputBoolean(); JJS.outputlnBoolean (b); // c = nor(a,b); JJS.outputlnString (“The Nor is “); JJS.outputlnBoolean (nor(a,b)); }// end void method logicTest Enter truths true false The Nor is false play = (tied or early) and not rain = and ( or(tied,early), not(rain) ) 16 Fallacies, are improper arguments that are not true. For example consider the following truth, which may look like a proper form of argument: (p -> q) ! P --------! q ----- if p implies q and not p then (therefore) q is not true Using the following example for symbols p, q shows the wrong reasoning: If the fire is lit then there is light And the fire is not lit Therefore there is no light But the light need not come only from the fire (perhaps from a bulb, sun, etc) This fallacy can be written as a single expression: ( (p -> q) && ! p ) -> ! q It can be disproved by a truth table. Actually the entire table is not required; only one case is sufficient, and this is the second case (when p is false and q is true). p F F T T 1 q F T F T 2 ((p -> q) T T 3 && T T ! p ) -> ! q T T T T F F 5 4 7 6 17 More Boolean type methods: disproving a fallacy ( (p --> q) && !p) --> !q boolean not (boolean p) { boolean result; // Does logical Not in prefix form result = ! p ; return result; }//end boolean method Not boolean or (boolean p, boolean q) { boolean result; // Does logical Or in prefix form result = p || q; return result; }//end boolean method Or boolean and (boolean p, boolean q) { boolean result; // Does logical And in prefix form result = p && q; return result; }//end boolean method And boolean implies (boolean p, boolean q) { boolean result; // Does “if p then q” = ! p | q result = or (not(p), q); return result; }//end boolean method implies void logicTest() { boolean a,b,c,d, p, q; //Does show a fallacy p = false; q = true; a b c d e = = = = = implies(p,q); not(p); not(q); a && b; implies (d,c); // // // // // premise premise conclude both falacy JJS.outputlnBoolean(e); //false! }// end void method logicTest 18 Problems on typed methods Trunc(r) which returns the truncated value of real value r kilometersToMiles (km) converts metric distances milesToKilometers (mi) converts distances Mean3(a,b,c) returns the average of 3 values areaRectangle (wid, length) computer the area of a rectangle Hypot (x, y) returns the hypotenuse given sides of a right triangle withinBounds (val, lo ,hi) returns truth of value val being within a given lower bound and a higher one. sizeInt(i) returns the number of decimals in integer i lsd(i) returns the least significant digit of an int i. msd(i) returns the most significantr digit of an int i. Mod(num, den) returns the remainder of num / den Div (num, den) returns the quotient of num / den Finally, you provide one. 19 More Problems on typed methods Define the following arithmetic methods acting on ints: Sum(a,b) adding the given two integers. Dif (a,b) subtracting these ints Prod(a,b) multiplying the ints Quot(a,b) dividing the ints Pow(a,b) taking a to power b Rem (a,b) remainder when a is divided by b lsd (n) msd (n) least significant digit of n (rightmost) most significant digit of n (leftmost) Some boolean methods: evenlyDivides(a,b) isMultipleOf(a,b) isTwiceSize(a,b) isfactorOf(a,b) isHalfOf(a,b) 20