INTRO TO OOP FOR FUNCTIONS DATA SCIENCE PROF. JOHN GAUCH OVERVIEW - - PDF document

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INTRO TO OOP FOR DATA SCIENCE

• PROF. JOHN GAUCH

FUNCTIONS

OVERVIEW

OVERVIEW

§ In real life, we often find ourselves doing the same task

• ver and over

§ Example: make toast and jam for breakfast in the morning § Example: drive our car from home to work and back § Once we have decided on our favorite way to do these tasks, we can write down the steps we normally take § Make a recipe card for making breakfast items § Write down series of turns to travel from A to B § This written descriptions will let others reuse our work

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OVERVIEW

§ Functions in Java allow us to reuse code § When we declare a function we write down the code we want to reuse in our program § We can call a function to execute this code anywhere we want in our program § We can customize a function by providing input parameters and calculate results using this input § Functions provide a fast/simple way to reuse code which saves a lot of programmer time/effort

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OVERVIEW

§ Functions play an important role in software development § Break a big problem down into a sequence of smaller problems that we know how to solve § Implement and test solutions to each of the smaller problems using functions § Use the functions we created above to create an effective solution to the big problem § Functions in the same category are often packaged together to create function libraries § Java has created function libraries for input/output, string manipulation, mathematics, random numbers, etc.

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OVERVIEW

§ Lesson objectives: § Learn the syntax for declaring functions in Java § Learn how to call and trace the execution of functions § Learn how to define and use function parameters § Study example programs showing their use § Complete online labs on functions § Complete programming project using functions

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FUNCTIONS

PART 1 CREATING AND USING FUNCTIONS

DECLARING FUNCTIONS

§ In order to declare a function in Java we need to provide the following information: § The name of the function § List of operations to be performed § Type of data value to be returned § Types and names of parameters (if any) § Declaration of local variables (if any) § Value to be returned to the main program (if any)

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DECLARING FUNCTIONS

§ Function return values § The return( ) statement exits the function, and returns a value back to the program where the function was called § You can use the return( ) statement anywhere in function, but the bottom of the function is preferred § The type of the return value depends on the application § Typical mathematical functions return float values § Typical I/O functions return input data or status flags § Some functions perform calculations but return no value (we use the special data type "void" in this case)

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DECLARING FUNCTIONS

§ Consider the following programming task: § Prompt the user to input a value between 1..9 § Read the integer value from the user § Loop until a valid input value is entered § Prompt the user to input a value between 1..9 § Read the integer value from the user § We can declare a Java function to package this code together so it can be reused in different programs

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DECLARING FUNCTIONS

// Function declaration example static int ReadNum() { int Number = 0; while ((Number < 1) || (Number > 9)) { System.out.print("Enter a number between 1..9: "); Number = scanner.nextInt(); } return( Number ); }

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Name of the function we are declaring

DECLARING FUNCTIONS

// Function declaration example static int ReadNum() { int Number = 0; while ((Number < 1) || (Number > 9)) { System.out.print("Enter a number between 1..9: "); Number = scanner.nextInt(); } return( Number ); }

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Operations to be performed by the function

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DECLARING FUNCTIONS

// Function declaration example static int ReadNum() { int Number = 0; while ((Number < 1) || (Number > 9)) { System.out.print("Enter a number between 1..9: "); Number = scanner.nextInt(); } return( Number ); }

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Data type of the function return value

DECLARING FUNCTIONS

// Function declaration example static int ReadNum() { int Number = 0; while ((Number < 1) || (Number > 9)) { System.out.print("Enter a number between 1..9: "); Number = scanner.nextInt(); } return( Number ); }

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This local variable can only be used within this function

DECLARING FUNCTIONS

// Function declaration example static int ReadNum() { int Number = 0; while ((Number < 1) || (Number > 9)) { System.out.print("Enter a number between 1..9: "); Number = scanner.nextInt(); } return( Number ); }

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Value returned by the function to the main program

CALLING FUNCTIONS

§ Now that we have declared the function ReadNum how can we use this function in the main program? § We need to specify the following in a function call § The name of the function we wish to execute § Variables passed in as parameters (if any) § Operations to be performed with return value (if any) § The main program will jump to function code, execute it, and return with the value that was calculated § Return values can be used to assign variables or they can be output (we should not ignore them)

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CALLING FUNCTIONS

public static void main (String[] args) { … // Function usage example int Num = 0; Num = ReadNum(); cout << "Your Lucky number is " << Num << endl; … }

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This function call will cause the main program to jump to the ReadNum function, execute that code and store the return value in variable Num

CALLING FUNCTIONS

§ We can trace the executions functions in a program using the "black box" method § Draw a box for the main program § Draw a second box for the function being called § Draw an arrow from the function call in the main program to the top of the function being called § Draw a second arrow from the bottom of the function back to the main program labeled with the return value § Using this black box diagram we can visualize the execution of the program by following the arrows

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CALLING FUNCTIONS

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public static int main() { Num = ReadNum(); } static int ReadNum() { return(…); } We leave the main program and jump to the ReadNum function

CALLING FUNCTIONS

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public static int main() { Num = ReadNum(); } static int ReadNum() { return(…); } We then execute the code inside the ReadNum function

CALLING FUNCTIONS

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public static int main() { … Num = ReadNum(); … } static int ReadNum() { return(…); } When we reach the bottom of the ReadNum function we return a value to the main program. If the user enters the number 6 the return value would be 6 6

CALLING FUNCTIONS

public static int main() { … // Function usage example int Num = 0; Num = ReadNum(); cout << "Your Lucky number is " << Num << endl; … }

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ReadNum returned the value 6, which is now stored in Num variable

CALLING FUNCTIONS

public static int main() { … // Function usage example int Num = 0; Num = ReadNum(); cout << "Your lucky number is << Num << endl; Num = ReadNum(); cout << "Your second lucky number is " << Num << endl; … }

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Each time we call ReadNum the code in the function will be executed and a new value will be returned

FUNCTIONS WITHOUT RETURN VALUES

§ What happens if a function does not have a return value? § In some cases, we just want a function to print out something like a help message or a command menu § In this case, the function return type is void § Since the function does not need to return anything to the main program, we can omit the return statement § When the code reaches the bottom of the function, it will automatically return to the location the function was called in the main program

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FUNCTIONS WITHOUT RETURN VALUES

// Function declaration example static void PrintMenu() { cout << "Welcome to ACME bank:\n"; cout << "Please enter one of the commands below:\n"; cout << " 0 – Quit this banking program\n"; cout << " 1 – Deposit money into your account\n"; cout << " 2 – Withdraw money from your account\n"; cout << " 3 – Transfer money between accounts\n"; }

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FUNCTIONS WITHOUT RETURN VALUES

int main() { … // Function usage example PrintMenu(); int Command = scanner.nextInt(); cout << "Command:" << Command << ":\n"; … }

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When we call PrintMenu, the program will jump to the function, print the messages, and then return to this location

CODE DEMO

Draw.java

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SUMMARY

§ In this section we have shown how a function can be declared in in Java § We have also shown how a function can be called from within the main program § Finally, we have shown how the "box method" can be used to trace the execution of functions in a program

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FUNCTIONS

PART 2 PARAMETERS

PARAMETERS

§ A function often needs data to perform desired task § We can pass data into function using parameters § When defining a function, we need to specify the data types and the names of all parameters § When calling the function, we need to provide the values of all parameters in the same order they were defined § Example § To calculate the square of a number in a function, we need to pass in the number to square as a value parameter

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PARAMETERS

// Function with value parameter static float Square( float Number ) { float Result = Number * Number; return( Result ); }

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Number is a float parameter We can use Number in

• ur function to calculate

desired return value

PARAMETERS

public static int main() … // Calling the Square function cout << Square(3.0) << endl; float Num = 5.0; cout << Square(Num) << endl; … }

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Call function with value 3.0 Call function with value 5.0

PARAMETERS

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public static int main() { … cout << Square(3.0); … } static float Square(Number=3.0) { … float Result = Number * Number; return(Result); } When we call Square(3.0) we initialize the parameter Number with a value of 3.0

PARAMETERS

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public static int main() { … cout << Square(3.0); … } static float Square(Number=3.0) { … float Result = Number * Number; return(Result); } The function calculates and returns a value of 9.0 to the main program 9.0

PARAMETERS

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public static int main() { … float Num = 5.0; cout << Square(Num); … } static float Square(Number=5.0) { … float Result = Number * Number; return(Result); } When we call Square(3.0) we initialize the parameter Number with a value of 3.0

PARAMETERS

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public static int main() { … float Num = 5.0; cout << Square(Num); … } static float Square(Number=5.0) { … float Result = Number * Number; return(Result); } The function calculates and returns a value of 25.0 to the main program 25.0

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SQUARE ROOT EXAMPLE

§ How can we calculate the square root R of a number N? § Use the ancient Babylonian method § Make initial guess of square root value R = N / 2 § Calculate N / R § The correct answer is somewhere between R and N / R § Make new guess R = (R + N / R) / 2 § Keep iterating until the value of R converges (or we get tired of doing this process)

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SQUARE ROOT EXAMPLE

§ Example: Calculating square root of 49 § Initial guess R = 49 / 2 = 24.5 § Calculate N/R = 49 / 24.5 = 2 § New guess R = (24.5 + 2) / 2 = 13.25 § Calculate N/R = 49 / 13.25 = 3.69 § New guess R = (13.25 + 3.69) / 2 = 8.47 § Calculate N/R = 49 / 8.47 = 5.78 § New guess R = (8.47 + 5.78) / 2 = 7.125 § Calculate N/R = 49 / 7.125 = 6.877 § New Guess R = (7.125 + 6.877) / 2 = 7.001

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SQUARE ROOT EXAMPLE

// Function to calculate square root static double my_sqrt(double number) { double root = number / 2; for (int count = 0; count < 10; count++) root = (root + number / root) / 2; return (root); }

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With a bottom up approach we implement this function first before completing the main program

SQUARE ROOT EXAMPLE

// Function to calculate square root static double my_sqrt(double number) { double root = number / 2; for (int count = 0; count < 10; count++) root = (root + number / root) / 2; return (root); }

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Notice that we are looping a fixed number of times

SQUARE ROOT EXAMPLE

// Main body of program public static int main() { double Number = 49; double Root = my_sqrt(Number); System.out.println("Number = " + Number); System.out.println("Root = " + Root); return 0 ; }

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With a bottom up approach we use a simple main program to debug the my_sqrt function

SQUARE ROOT EXAMPLE

// Main body of program public static int main() { System.out.print("Enter a positive number: "); double Input = scanner.nextDouble(); if ((Input > 0) System.out.println("Root = " + my_sqrt(Number)); return 0 ; }

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In the final version we add a user interface in main and call the my_sqrt function

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SUM DIGITS EXAMPLE

§ How can we calculate the sum of the digits in an integer between 0..99999? § Find each of the 5 digits in the number § Add them up to get the sum of digits § How can we implement this using functions? § We can implement a SumDigits function to extract the individual digits of the number and calculate their sum § We can write a main program that prompts the user for input, does error checking, and calls SumDigits to calculate the final answer

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SUM DIGITS EXAMPLE

§ Should we implement the function or main program first? § There is no right way or wrong way to do this § If we implement and test the main program before SumDigits, this is called a top down approach § In this case, we need to implement a "dummy" version of SumDigits to test the main program § If we implement and test SumDigits before the main program, this is called a bottom up approach § In this case, we need a "simple" version of the main program to test the SumDigits function

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SUM DIGITS EXAMPLE

// Function to calculate sum of digits static int SumDigits(int Number) { // Return answer return (42); }

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With a top down approach we create a dummy version of this function that has the correct parameters but does not do any real work

SUM DIGITS EXAMPLE

// Main body of program public static int main() { System.out.print("Enter number in [0..99999] range: "); int Input = scanner.nextInt(); if ((Input < 0) || (Input > 99999)) System.out.print("Number must be in [0..99999]"); else System.out.print("Sum digits = " + SumDigits(Input)); return 0 ; }

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With a top down approach we write a main program that calls the dummy function

SUM DIGITS EXAMPLE

Top down program output: Enter number in [0..99999] range: 123 Sum digits = 42 Enter number in [0..99999] range: 23456 Sum digits = 42 Enter number in [0..99999] range: 222222 Number must be in [0..99999]

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This shows the dummy

• utput from the function

This shows error checking is working correctly in main program

SUM DIGITS EXAMPLE

§ How can we find the individual digits of the number so we can calculate their sum? § The first digit is easy, just divide by 10000 to trim off the last four digits of the number int Digit1 = Number / 10000; § The last digit is also easy, just use the modulo 10

• peration to trim off the first four digits of the number

int Digit5 = Number % 10;

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SUM DIGITS EXAMPLE

§ The other digits require a careful combination of modulo and division operations to trim off digits from the front and the back of the number int Digit2 = (Number % 10000) / 1000; int Digit3 = (Number % 1000) / 100; int Digit4 = (Number % 100) / 10; § Notice there is a very nice symmetry to these calculations, which is often a sign that you have the correct logic

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SUM DIGITS EXAMPLE

// Function to calculate sum of digits static int SumDigits(int Number) { // Get digits and calculate their sum int Digit1 = Number / 10000; int Digit2 = (Number % 10000) / 1000; int Digit3 = (Number % 1000) / 100; int Digit4 = (Number % 100) / 10; int Digit5 = Number % 10; return (Digit1+Digit2+Digit3+Digit4+Digit5); }

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With a bottom up approach we implement SumDigits function first

SUM DIGITS EXAMPLE

// Main body of program public static int main() { int Input = 12345; int Sum = SumDigits(Input); System.out.println("Input = " + Input); System.out.println("Sum = " + Sum); return 0 ; }

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With a bottom up approach we write a very simple main program to call SumDigits and edit this main program to debug the SumDigits code

SUM DIGITS EXAMPLE

Bottom up program output: Input = 12345 Sum = 15

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This shows the correct

• utput from the SumDigits

function but there is no user interface in the main program

SUM DIGITS EXAMPLE

Final program output: Enter number in [0..99999] range: 123 Sum digits = 6 Enter number in [0..99999] range: 23456 Sum digits = 20 Enter number in [0..99999] range: 222222 Number must be in [0..99999]

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The final version shows the proper user interface and the correct output from SumDigits

GRADE EXAMPLE

§ Functions are not required to return results at the end of a function, they can also return in the middle of a function § We can demonstrate this with two functions to convert test scores from [0..100] into letter grades [A..F] § Option 1: Use if-else statements to calculate and save letter grade and the return result at the end § Option 2: Use if-else to calculate letter grade and return the result as soon as it is found

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GRADE EXAMPLE

// Function to calculate letter grades static char GetGrade( float Average ) { if (Average >= 90) Grade = 'A'; else if (Average >= 80) Grade = 'B'; else if (Average >= 70) Grade = 'C'; else if (Average >= 60) Grade = 'D'; else Grade = 'F'; return Grade; }

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Option 1 The function calculates letter grade and returns the result at the end

GRADE EXAMPLE

// Function to calculate letter grades static char GetGrade( float Average ) { if (Average >= 90) return 'A'; if (Average >= 80) return 'B'; if (Average >= 70) return 'C'; if (Average >= 60) return 'D'; return 'F’; }

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Option 2 The function calculates letter grade and returns result immediately

GRADE EXAMPLE

public static int main() { … // Calling function to calculate grade float NewScore = 86.4; char NewGrade = GetGrade(NewScore); System.out.println("Your final grade is " + NewGrade); … }

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We call the GetGrade function with NewScore as a parameter

GRADE EXAMPLE

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public static int main() { … float NewScore = 86.4; char NewGrade = GetGrade(NewScore); … } static char GetGrade( Average=86.4) { … return Grade; } We call GetGrade with Average of 86.4

GRADE EXAMPLE

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public static int main() { … float NewScore = 86.4; char NewGrade = GetGrade(NewScore); … } static char GetGrade( Average=86.4) { … Grade = ‘B’; … return Grade; } We calculate value of Grade to be ‘B’

GRADE EXAMPLE

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public static int main() { … float NewScore = 86.4; char NewGrade = GetGrade(NewScore); … } static char GetGrade( Average=86.4) { … Grade = ‘B’; … return Grade; } The return value is stored in NewGrade variable in main ‘B’

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PRIME FACTORS EXAMPLE

§ How can we calculate and print the prime factors of an integer that is between 1..100? § We need to check to see if the input value can be divided evenly by prime factors less than 100 § We also need to modify the input value by repeatedly dividing it by this prime factor until it is no longer a factor input = 50 2 is a factor, input = 50/2 = 25 5 is a factor, input = 25/5 = 5 5 is a factor, input = 5/5 = 1

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PRIME FACTORS EXAMPLE

§ How can we use functions to solve this problem? § We can create a CheckFactors function that takes the input number and the factor we want to test as inputs § We must call this function several times in the main program with different prime factors § Since our input will be [1..100] we only need to check prime factors up to the square root of 100 (i.e. 2,3,5,7)

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PRIME FACTORS EXAMPLE

// Function to check one prime factor static int CheckFactor(int number, int factor) { // Loop dividing number by factors while (number % factor == 0) { System.out.println(factor + " is a factor"); number = number / factor; } return number; }

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Here we test if factor divides evenly into number

PRIME FACTORS EXAMPLE

// Function to check one prime factor static int CheckFactor(int number, int factor) { // Loop dividing number by factors while (number % factor == 0) { System.out.println(factor + " is a factor"); number = number / factor; } return number; }

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Here we divide input number by factor and return the final value

PRIME FACTORS EXAMPLE

// Main body of program public static void main(String[] args) { // Read input value Scanner scnr = new Scanner(System.in); System.out.print("Enter an integer: "); int number = scnr.nextInt(); // Check input value if ((Num < 1) || (Num > 100)) System.out.println("Number must be in [1..100]");

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PRIME FACTORS EXAMPLE

… // Calculate prime factors else { Num = CheckFactors(Num, 2); Num = CheckFactors(Num, 3); Num = CheckFactors(Num, 5); Num = CheckFactors(Num, 7); if (Num > 1) System.out.println(Num << " is a factor"); }

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We call the CheckFactors function four times to check if Num is divisible by 2,3,5,7 and print a message if it is a factor

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PRIME FACTORS EXAMPLE

… // Calculate prime factors else { Num = CheckFactors(Num, 2); Num = CheckFactors(Num, 3); Num = CheckFactors(Num, 5); Num = CheckFactors(Num, 7); if (Num > 1) System.out.println(Num << " is a factor"); }

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The remainder after division is also a prime factor

PRIME FACTORS EXAMPLE

Sample program output: Enter number in [1..100] range: 42 2 is a factor 3 is a factor 7 is a factor Enter number in [1..100] range: 65 5 is a factor 13 is a factor

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PRIME FACTORS EXAMPLE

§ How can we extend this program to handle input values greater than 100? § We can add a loop in the main program that calls the CheckFactors function with every value between 2 and the square root of Num to see if they are factors for (int Factor=2; Factor<sqrt(Num); Factor++) CheckFactors(Num, Factor); § This code is shorter but is actually slower because we are also checking non-prime factors (i.e. 4, 6, 8, 9, etc.)

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CODE DEMO

Factors.java Prime3.java Prime4.java

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SUMMARY

§ In this section we have described how functions with parameters can be used to get data into functions § We have also shown how return values from functions can be used in the main program (or other functions) § Finally, we have discussed several programs that use functions with parameters to solve problems § Square root § Sum of digits § Grade calculation § Prime factors

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FUNCTIONS

PART 3 RECURSION

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RECURSION

§ Recursion is a very powerful problem solving method § Recursive functions call themselves to solve problems § We reduce "size" of problem each recursive function call § Need to have a terminating condition to stop recursion § Visualize using black box method with inputs and returns § Recursive solutions can also be implemented via iteration § Sometimes the recursive function is smaller § Sometimes the iterative function is faster

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RECURSION

§ Example: calculating N factorial § Recursive solution solves problem in terms of itself § Factorial(N) = N * Factorial(N-1) § This is the recurrence relationship § We must stop at some point § Factorial(1) = 1 § This is the terminating condition

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FACTORIAL EXAMPLE

// Recursive Factorial function static int Factorial(int Num) { if (Num <= 1) return(1); else return( Num * Factorial(Num-1) ); }

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This is the terminating condition of for the recursive function Notice that we are recursively calling the Factorial function with a smaller parameter value

FACTORIAL EXAMPLE

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main() { … Factorial(3); … } Factorial(3) { … return 3*Factorial(2); … }

• First, the main program calls Factorial(3)

FACTORIAL EXAMPLE

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main() { … Factorial(3); … } Factorial(3) { … return 3*Factorial(2); … } Factorial(2) { … return 2*Factorial(1); … }

• First, the main program calls Factorial(3)
• Then, Factorial(3) calls Factorial(2)

FACTORIAL EXAMPLE

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main() { … Factorial(3); … } Factorial(3) { … return 3*Factorial(2); … } Factorial(2) { … return 2*Factorial(1); … } Factorial(1) { … return 1; … }

• First, the main program calls Factorial(3)
• Then, Factorial(3) calls Factorial(2)
• Then, Factorial(2) calls Factorial(1)

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FACTORIAL EXAMPLE

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main() { … Factorial(3); … } Factorial(3) { … return 3*Factorial(2); … } Factorial(2) { … return 2*Factorial(1); … } Factorial(1) { … return 1; … }

1

• First, the main program calls Factorial(3)
• Then, Factorial(3) calls Factorial(2)
• Then, Factorial(2) calls Factorial(1)
• Then, Factorial(1) returns 1

FACTORIAL EXAMPLE

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main() { … Factorial(3); … } Factorial(3) { … return 3*Factorial(2); … } Factorial(2) { … return 2*Factorial(1); … } Factorial(1) { … return 1; … }

2 1

• First, the main program calls Factorial(3)
• Then, Factorial(3) calls Factorial(2)
• Then, Factorial(2) calls Factorial(1)
• Then, Factorial(1) returns 1
• Then, Factorial(2) returns 2*1=2

FACTORIAL EXAMPLE

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main() { … Factorial(3) … } Factorial(3) { … return 3*Factorial(2); … }

6

Factorial(2) { … return 2*Factorial(1); … } Factorial(1) { … return 1; … }

2 1

• First, the main program calls Factorial(3)
• Then, Factorial(3) calls Factorial(2)
• Then, Factorial(2) calls Factorial(1)
• Then, Factorial(1) returns 1
• Then, Factorial(2) returns 2*1=2
• Then, Factorial(3) returns 3*2=6
• Finally, the main program prints 6

FACTORIAL EXAMPLE

§ In this case, the iterative solution is the same size and will run slightly faster than the recursive solution // Iterative Factorial function static int Factorial(int Num) { int Product = 1; for (int Count = 1; Count <= Num; Count++) Product = Product * Count; return( Product ); }

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SUM EXAMPLE

§ Example: calculating sum of all numbers from 1..N § Recursive solution solves problem in terms of itself § Sum(N) = N + Sum(N-1) § This is called the recurrence relationship § We must stop at some point § Sum(1) = 1 § This is called the terminating condition

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SUM EXAMPLE

// Recursive summation function static int Sum(int Num) { if (Num <= 1) return(1); else return( Num + Sum(Num-1) ); }

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This is the terminating condition of for the recursive function Notice that we are recursively calling the Sum function with a smaller parameter value

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SUM EXAMPLE

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main() { … Sum(3) … } Sum(3) { … Sum(2) … }

6

Sum(2) { … Sum(1) … } Sum(1) { … … }

3 1

• First, the main program calls Sum(3)
• Then, Sum(3) calls Sum (2)
• Then, Sum(2) calls Sum (1)
• Then, Sum(1) returns 1
• Then, Sum(2) returns 2+1=3
• Finally, Sum(3) returns 3+3=6

SUM EXAMPLE

§ In this case the iterative solution is the same size and will run slightly faster than the recursive solution // Iterative summation function static int Sum(int Num) { int Total = 0; for (int Count = 0; Count <= Num; Count++) Total = Total + Count; return(Total); }

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FIBONACCI EXAMPLE

§ Example: calculating the Nth Fibonacci number from the sequence 1,1,2,3,5,8,13,21,34,55… § Recursive solution solves problem in terms of itself § Fibonacci(N) = Fibonacci(N-1) + Fibonacci(N-2) § This is the recurrence relationship § We must stop at some point § Fibonacci(1) = 1 § Fibonacci(2) = 1 § These are the terminating conditions

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FIBONACCI EXAMPLE

§ This recursive function calls itself twice each time it is called so there are a lot of function calls to calculate the answer // Recursive Fibonacci function static int Fibonacci(int Num) { if (Num <= 2) return(1); else return( Fibonacci(Num-1) + Fibonacci(Num-2) ); }

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FIBONACCI EXAMPLE

// Iterative Fibonacci function int Fibonacci(int Num) { int Num1 = 1; int Num2 = 1; for (int Count = 1; Count < Num; Count++) { int Num3 = Num1 + Num2; Num1 = Num2; Num2 = Num3; } return (Num1); }

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§ This iterative function is slightly longer than the recursive solution but it is much faster at run time

INFINITE RECURSION

§ What happens if we make a mistake implementing the recurrence relationship? § If the recursive function call has the same parameter value the function will call itself forever § This programming bug is called infinite recursion § Your program will crash with a message like "stack

• verflow" because it ran out of memory

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INFINITE RECURSION

// Infinite recursion function static int Forever(int Num) { if (Num < 0) return(0); else return( Forever(Num) + 1 ); }

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We are recursively calling the Forever function with the same parameter value

INFINITE RECURSION

§ The corresponding iterative program will not crash, but it will run forever adding one to the Total variable // Infinite iteration function static int Forever(int Num) { int Total = 0; while (Num < 0) Total = Total + 1; return( Total ); }

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POWER EXAMPLE

§ Example: calculating N raised to integer power P § Recursive solution solves problem in terms of itself § Pow(N, P) = N * Pow(N, P-1) § This is the recurrence relationship § We must stop at some point § Pow(N, 0) = 1 § Pow(N, 1) = N § These are the terminating conditions

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POWER EXAMPLE

// Recursive Pow function int Pow(int N, int P) { System.out.print;n("calling pow " + N + " " + P); if (P == 0) return 1; else if (P == 1) return N; else return N * Pow(N,P-1) }

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We are calling the Pow function with a smaller parameter value

POWER EXAMPLE

// Main program int main() { System.out.print("Enter number: "); int Number = scanner.nextInt(); System.out.print("Enter power: "); int Power= scanner.nextInt(); System.out.println("Result = " + Pow(Number, Power)); return(0); }

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POWER EXAMPLE

Sample program output when number=2, power=8: calling pow 2 8 calling pow 2 7 calling pow 2 6 calling pow 2 5 calling pow 2 4 calling pow 2 3 calling pow 2 2 calling pow 2 1 Result = 256

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Notice that the power is decreasing by one with each recursive function call and eventually reaches the terminating condition

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POWER EXAMPLE

§ Can we come up with a faster solution? § Divide the exponent in half instead of subtracting one § Recurrence relationships § Pow(N, P) = Pow(N, P/2) * Pow(N, P/2) when P is even § Pow(N, P) = Pow(N, P/2) * Pow(N, P/2) * N when P is odd § Terminating conditions § Pow(N, 0) = 1 § Pow(N, 1) = N

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POWER EXAMPLE

int pow2(int N, int P) { System.out.println("calling pow2 " + N + " " + P); if (P == 0) return 1; else if (P == 1) return N;

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POWER EXAMPLE

else if (P % 2 == 0) { int temp = pow2(N, P/2); return temp * temp; } else // if (P % 2 == 1) { int temp = pow2(N, P/2); return temp * temp * N; } }

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Notice that the power is decreasing by half with each recursive function call to pow2

POWER EXAMPLE

Sample program output when number=2, power=25: calling pow2 2 25 calling pow2 2 12 calling pow2 2 6 calling pow2 2 3 calling pow2 2 1 Result = 33554432

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We obtain the same solution after only 5 function calls instead of 25 function calls for the previous implementation

SUMMARY

§ In this section we have focused on recursive functions § We need to implement the recurrence relationship § We need to implement the terminating conditions § Recursion has several pros and cons § Sometimes the recursive solution is smaller and easier to understand than the iterative solution § Recursion can be much slower when there are a large number of "redundant" function calls § Recursion can be much faster when a "divide and conquer" approach is used

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FUNCTIONS

PART 4 FUNCTION LIBRARIES

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FUNCTION LIBRARIES

§ Function libraries are collections of similar functions grouped together in one file for ease of use § By using built in Java libraries we can increase code reuse and decrease development and debugging time § To use the functions in a Java library we need to add import commands at the top of our program § This tells the Java compiler what functions are available for use in your program § You can read online Java documentation to find out what different functions do and what parameters are needed

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FUNCTION LIBRARIES

§ In this section, we will discuss some of the most common and powerful function libraries § java.lang.Math - this library contains all of the common math functions you are used to using § Basic math functions § Exponential and logarithmic functions § Trigonometric functions

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MATH LIBRARY

§ Basic Math functions include: § Math.abs(param) – returns the absolute value of of an integer or float param § Math.ceil(param) – rounds a float param value up to the next larger integer § Math.floor(param) – rounds a float param value down to the next smaller integer § Math.round(param) – rounds a float param to the nearest integer (up or down)

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MATH LIBRARY

§ Basic Math functions include: § Math.min(param1, param2) – returns the minimum value of the two params § Math.max(param1, param2) – returns the maximum value

• f the two params

§ Math.random() – returns a pseudo random number in the range [0..1]

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MATH LIBRARY

§ Exponential and logarithmic functions include: § Math.E – the most accurate represention of E that can be stored in a double (2.71828…) § Math.exp(param) – returns E raised to the power param § Math.log(param) – returns the natural logarithm of param § Math.log10(param) – returns base10 logarithm of param

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MATH LIBRARY

§ Exponential and logarithmic functions include: § Math.pow(param1, param2) – returns param1 raised to the power param2 § Math.sqrt(param) – returns the square root of param, which is the same as Math.pow(param, 0.5) § Math.cbrt(param) – returns the cube root of param, which is the same as Math.pow(param, 1.0/3.0)

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MATH LIBRARY

§ Trigonometric functions include: § Math.PI – the most accurate representation of PI that can be stored in a double (3.14159…) § Math.toDegrees(param) – converts an angle in radians into an angle in degrees (same as multiplying by 180/PI) § Math.toRadians(param) – converts an angle in degrees into an angle in radians (same as multiplying by PI/180)

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MATH LIBRARY

§ Trigonometric functions include: § Math.sin(param) – returns the sine of angle param (where the angle is in radians) § Math.cos(param) – returns the cosine of angle param (where the angle is in radians) § Math.tan(param) – returns the tangent of angle param (where the angle is in radians)

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MATH LIBRARY

§ Trigonometric functions include: § Math.asin(param) – returns the arc sine of a param value between [-1..1], which is the inverse of sin § Math.cos(param) – returns the arc cosine of a param value between [-1..1], which is the inverse of cos § Math.tan(param) – returns the arc tangent of a param value between [-1..1], which is the inverse of tan

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MATH LIBRARY

§ See the official Java documentation here

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MATH LIBRARY

public static void main(String[] args) { // Calculate and print sin and cos table System.out.printf("%5s %12s %12s\n", "angle", "cos(angle)", "sin(angle)"); for (int Degrees = 0; Degrees <= 360; Degrees += 10) { double Radians = Math.toRadians(Degrees); System.out.printf("%5d %12.5f %12.5f\n", Degrees, Math.cos(Radians), Math.sin(Radians)); } }

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CODE DEMO

Random.java

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SOFTWARE ENGINEERING TIPS

§ Start your program with "empty" function bodies § Helps debug the main program and parameter passing § Implement and test bodies of functions one at a time § This way you are never far from a running program § Print debugging messages inside each function § To see which function is being called and its parameters § Give functions and parameters meaningful names § Make your code easier to read and understand

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SOFTWARE ENGINEERING TIPS

§ Common mistakes when creating functions § Poor choice of the return type of a function § Poor choice of data types for parameters § Common mistakes when calling functions: § Incorrect number of parameters § Incorrect data type of parameters § Incorrect ordering of parameters § Function return value not used properly

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SUMMARY

§ In this section we have introduced Java function libraries and some example programs that use these libraries § Learning how to use the the built in Java libraries is an important skill for all programmers to develop § You do not want to waste your time to reinvent a function that has already been written and debugged § We have also discussed several software engineering tips for creating and debugging programs using functions

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