2 1 Functions Functions in Mathematics x y

2. 1 Functions

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

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

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

Writing Functions in Java functions. Easy to write your own. 2. 0 input f(x) = x output 1. 414213… Numerically Computing a Square-Root: Newton-Raphson Method 5

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

Function to calculate Square Root using Newton-Raphson Method 2. 0 input f(x) = x output 1. 414213… 7

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

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

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: Control transfers to the function code. Argument variables are assigned the values given in the call. Function code is executed. Return value is assigned in place of the function name in calling code. Control transfers back to the calling code. n n n Note. This is known as “pass/call by value. ” 10

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

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. two different variables with the same name i public class Newton { public static double sqrt(double c) { double epsilon = 1 e-15; if (c < 0) return Double. Na. N; double t = c; while (Math. abs(t - c/t) > epsilon * t) t = (c/t + t) / 2. 0; return t; } scope of c scope of epsilon scope of t public static void main(String[] args) { double[] a = new double[args. length]; for (int i = 0; i < args. length; i++) a[i] = Double. parse. Double(args[i]); for (int i = 0; i < a. length; i++) { double x = sqrt(a[i]); Std. Out. println(x); } } } Best practice: declare variables to limit their scope. 12

Why Are Functions An Important Concept / Technique? Good Software Design. Problem-solving: from large problems to smaller sub-problems. Easier to understand solutions to smaller sub-problems. Easier to test smaller sub-problems. We can re-use sub-problem solutions (functions). 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 n n n // Two functions for getting random values // between 0 and N-1 public static int random. Val (int N) { return (int) (Math. random() * N); } // between a and b, i. e. in range [a, b) public static double random. Val(double a, double b) { return a + Math. random() * (b-a); } 13

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

Function Challenge 1 b Q. What happens when you compile and run the following code? public class Cubes 2 { public static int cube(int i) { int i = i * i; return i; } public static void main(String[] args) { int N = Integer. parse. Int(args[0]); for (int i = 1; i <= N; i++) Std. Out. println(i + " " + cube(i)); } } Compiler error: i is already defined 15

Function Challenge 1 c Q. What happens when you compile and run the following code? public class Cubes 3 { public static int cube(int i) { i = i * i; } public static void main(String[] args) { int N = Integer. parse. Int(args[0]); for (int i = 1; i <= N; i++) Std. Out. println(i + " " + cube(i)); } } Compiler error: missing return statement 16

Function Challenge 1 d Q. What happens when you compile and run the following code? public class Cubes 4 { public static int cube(int i) { i = i * i; return i; } public static void main(String[] args) { int N = Integer. parse. Int(args[0]); for (int i = 1; i <= N; i++) Std. Out. println(i + " " + cube(i)); } } Correct: the i in cube() and the i in main() are different 17

Function Challenge 1 e Q. What happens when you compile and run the following code? public class Cubes 5 { public static int cube(int i) { return i * i; } public static void main(String[] args) { int N = Integer. parse. Int(args[0]); for (int i = 1; i <= N; i++) Std. Out. println(i + " " + cube(i)); } } Correct and preferred style 18

Dr. Java Demo Printing An Array + Debugging 19