1. 2.1 Functions

2. Functions in Mathematics f x y z f (x, y, z) Domain Range

3. Functions in Computer Science f x y z f (x, y, z) Input Output Algorithm Allows you to clearly separate the tasks in a program. Enables reuse of code

4. 4 Functions (Static Methods) Java function. n Takes zero or more input arguments. n Returns zero or one output value. n public static void main(String args[]) Applications. n Scientists use mathematical functions to calculate formulas. n Programmers use functions to build modular programs. n You use functions for both. Examples. Built-in functions: Math.random(), Math.abs(), Integer.parseInt(). Princeton I/O libraries: StdIn.readInt(), StdDraw.line(), StdAudio.play(). User-defined functions: main().

5. 5 Writing Functions in Java Java functions. Easy to write your own. f(x) =  x input 2.0 1.414213… output Numerically Computing a Square-Root: Newton-Raphson Method

6. The Newton-Raphson Algorithm To Compute Square Root of Positive Number c: { t = c; //initial estimate of square-root while(square-root of c is not found) { if(t == c/t) found square-root of x; else t = Average of t and c/t; } 6

7. 7 Function to calculate Square Root using Newton-Raphson Method f(x) =  x input 2.0 1.414213… output

8. 8 Functions overloading multiple arguments Overloading: Different argument types Different number of arguments Different return value is NOT overloading

9. 9 Flow of Control Key point. Functions provide a new way to control the flow of execution.

10. 10 Flow of Control Key point. Functions provide a new way to control the flow of execution. Summary of what happens when a function is called: n Control transfers to the function code. n Argument variables are assigned the values given in the call. n Function code is executed. n Return value is assigned in place of the function name in calling code. n Control transfers back to the calling code. Note. This is known as “pass/call by value.”

11. Can a Function Alter Its Arguments? The short answer for Java: Only if the argument is an array! n (Later we’ll see that objects are like arrays in this way.) Call by Value. n The argument-variable defined in the function signature is like a local variable inside the function. n A copy of the value of the actual argument is copied into the argument-variable when its called n Changes made to the argument-variable inside the function do not update anything back in the “caller”. Call by Reference. n The argument-variable defined in the function signature refers to the same data variable that’s passed when the function is called. n Changes made to the argument-variable inside the function do update the variable in the “caller”. 11

12. 12 Scope Scope (of a name). The code that can refer to that name. Ex. A variable's scope is code following the declaration in the block. Best practice: declare variables to limit their scope. public class Newton { public static double sqrt(double c) { double epsilon = 1e-15; if (c < 0) return Double.NaN; double t = c; while (Math.abs(t - c/t) > epsilon * t) t = (c/t + t) / 2.0; return t; } public static void main(String[] args) { double[] a = new double[args.length]; for (int i = 0; i < args.length; i++) a[i] = Double.parseDouble(args[i]); for (int i = 0; i < a.length; i++) { double x = sqrt(a[i]); StdOut.println(x); } two different variables with the same name i scope of c scope of epsilon scope of t

13. 13 Why Are Functions An Important Concept / Technique? Good Software Design. n Problem-solving: from large problems to smaller sub-problems. n Easier to understand solutions to smaller sub-problems. n Easier to test smaller sub-problems. n We can re-use sub-problem solutions (functions). n Hide details from rest of design. (Example: sqrt. Do we care how it’s done inside function?) Abstraction. Reducing or factoring out details so that one can focus on a few important concepts // Two functions for getting random values // between 0 and N-1 public static int randomVal (int N) { return (int) (Math.random() * N); } // between a and b, i.e. in range [a,b) public static double randomVal(double a, double b) { return a + Math.random() * (b-a); }

14. 14 Function Challenge 1a Q. What happens when you compile and run the following code? public class Cubes1 { public static int cube(int i) { int j = i * i * i; return j; } public static void main(String[] args) { int N = Integer.parseInt(args[0]); for (int i = 1; i <= N; i++) StdOut.println(i + " " + cube(i)); } % javac Cubes1.java % java Cubes1 6 1 2 8 3 27 4 64 5 125 6 216

15. 15 Function Challenge 1b Q. What happens when you compile and run the following code? public class Cubes2 { public static int cube(int i) { int i = i * i * i; return i; } public static void main(String[] args) { int N = Integer.parseInt(args[0]); for (int i = 1; i <= N; i++) StdOut.println(i + " " + cube(i)); } Compiler error: i is already defined

16. 16 Function Challenge 1c Q. What happens when you compile and run the following code? public class Cubes3 { public static int cube(int i) { i = i * i * i; } public static void main(String[] args) { int N = Integer.parseInt(args[0]); for (int i = 1; i <= N; i++) StdOut.println(i + " " + cube(i)); } Compiler error: missing return statement

17. 17 Function Challenge 1d Q. What happens when you compile and run the following code? public class Cubes4 { public static int cube(int i) { i = i * i * i; return i; } public static void main(String[] args) { int N = Integer.parseInt(args[0]); for (int i = 1; i <= N; i++) StdOut.println(i + " " + cube(i)); } Correct: the i in cube() and the i in main() are different

18. 18 Function Challenge 1e Q. What happens when you compile and run the following code? public class Cubes5 { public static int cube(int i) { return i * i * i; } public static void main(String[] args) { int N = Integer.parseInt(args[0]); for (int i = 1; i <= N; i++) StdOut.println(i + " " + cube(i)); } Correct and preferred style

19. Dr. Java Demo Printing An Array + Debugging 19