CSE 21 Introduction to Computing II...How to Write a Recursive Function 9 Step 1 - Write and define the recursive Function Header Your main choices are the Return Type and Parameters

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CSE 21

Intro to Computing II

Functions (continued) and Recursion

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Week of 09/24 - Lecture #4-5 (09/26), Lab #5 Week of 10/01 - Lecture #6 (10/01), Lab #6 Week of 10/08 - Midterm Review (10/10), Lab #7, Project 1 Due Week of 10/15 - Midterm (10/17), NO LAB

Schedule

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Due on Monday October 8th at midnight

Project #1

Wednesday October 17th, in class, 50 minutes long Closed book, no notes, no computers Covers CSE020, anything from the labs, anything from lecture

Up to last lecture (lecture #6) and last lab (Lab #7) Will have a review on October 10th Extended Office Hours from TAs and Lecturer

Midterm

Same concept as name overloading ◦ Use same names, but JAVA knows which is which

Function Overloading ◦ Two or more functions that have Same modifiers (i.e., public static)

Same return type (i.e., void)

Same function name (i.e., print)

Different number of parameters and/or type

Examples ◦ public static void print()

◦ public static void print(String name)

◦ public static void print(String name, int grade)

◦ public static void print(String[] name, int[] grade)

◦ public static void print(String city, String zip)

◦ public static void print(String city, int zip)

◦ public static int print(String city)

Function Overloading

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public static int getAmount(Scanner input, String name) { // 1

System.out.print("Enter the amount of " + name + ": ");

int amount = input.nextInt();

return amount;

}

public static void getAmount(Scanner input, String[] names, int[] amounts) { // 2

for (int i = 0; i < names.length; i++) {

System.out.print("Enter the amount of " + names[i] + " : ");

amounts[i] = input.nextInt();

}

}

public static void main(String[] args) {

Scanner input = new Scanner(System.in);

int sharp = getAmount(input, "Sharp");

int brie = getAmount(input, "Brie");

int swiss = getAmount(input, "Swiss");

getAmount(input, names, amounts);

Function Overloading Example

2 input parameters: Scanner + String

3 input parameters: Scanner + String pointer + int pointer

2 arguments: Scanner + String

3 arguments: Scanner + String[] + int[]

Order of the Types determine the function call 4

getAmount(input, “Random”); ◦ Scanner + String // Match 1

getAmount(“Random”, input); ◦ String + Scanner // Don’t match

getAmount(input, names[0]); ◦ Scanner + String // Match 1

getAmount(input, names); ◦ Scanner + String[] // Don’t match

getAmount(input, names, amounts); ◦ Scanner + String[] + int[] // Match 2

getAmount(input, amounts, names); ◦ Scanner + int[] + String[] // Don’t match

getAmount(input,names[0],amounts[0]); ◦ Scanner + String + int // Don’t match

getAmount(input, names, new int[MAXCHEESE]); ◦ Scanner + String[] + int[] // Match 2

getAmount(input, names, prices); ◦ Scanner + String[] + double[] // Don’t match

Matching Function Calls

public static int getAmount(Scanner input, String name) { // 1

public static void getAmount(Scanner input, String[] names, int[] amounts) { // 2

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Can call a function anywhere in your code ◦ From the main function (as I have shown in class)

◦ From another function

Example ◦ public static void main(){

◦ greet(“Ben”);

◦ }

◦ public static void welcomeMsg() {

◦ System.out.println(“Welcome to CSE021”);

◦ }

◦ public static void greet(String name) {

◦ welcomeMsg();

◦ System.out.println(“Greetings, ” + name + “!”);

◦ }

Calling Functions Outside main

OUTPUT:

Welcome to CSE021

Greetings, Ben!

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Can we have a function that calls itself? ◦ Yes!

What happens in that case?

Let’s try it out… ◦ public static void main(){

◦ greet(“Ben”);

◦ }

◦ public static void welcomeMsg() {

◦ System.out.println(“Welcome to CSE021”);

◦ welcomeMsg();

◦ }

◦ public static void greet(String name) {

◦ welcomeMsg();

◦ System.out.println(“Greetings, ” + name + “!”);

◦ }

This Begs the Question…

OUTPUT:

Welcome to CSE021

Welcome to CSE021

Welcome to CSE021

Welcome to CSE021

…

Infinite “Loop”!

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We introduce a new term, Recursive Function ◦ A function that calls itself

Difficult concept to grasp ◦ Function behaves exactly the same when it is calling itself

◦ Recursion is similar to loops

◦ Function parameters are used to stop the recursion

Easy to get infinite loop

◦ Study and Practice are both necessary

Understanding/Exploiting Recursion ◦ Follow a series of steps

◦ Trace the code and function calls

Recursive Function

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Divide the problem into smaller sub-problems ◦ Divide and conquer

◦ Same concept as using functions

The solved small problems together solve the big problem

Theoretical Example ◦ Problem: print the elements of an array

◦ Sub-problem: print one element of an array

◦ Solving the sub-problem “array.length” times will print the array

◦ The sub-problem is what goes inside the function, which calls itself

◦ Needs to make sure we have a stopping condition

Without one, we get an infinite loop

Practical Example ◦ public static void print(int[] arr, int indexToPrint) {

◦ if(indexToPrint==arr.length) return;

◦ System.out.println(arr[indexToPrint]);

◦ print(arr, indexToPrint+1);

◦ }

How to Write a Recursive Function

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Step 1 - Write and define the recursive Function Header ◦ Your main choices are the Return Type and Parameters

Step 2 – Write out a sample/example Function Call ◦ Make sure that the call will do what you want “in theory”

◦ You might realize that your Function Header is incorrect

Step 3 – Think when you want to stop the recursion ◦ This is similar to the condition in of a loop and is called Stopping Condition

◦ You will use it to stop the function from calling itself

◦ Without a Stopping Condition we will have an infinite loop

Step 4 – Write the function body ◦ This is what the function does

Step 5 – Make the function call itself ◦ The function call will solve a smaller problem than the current one

◦ This is done by changing one or more parameters

◦ Similar to a for or a while loop

Writing Recursive Functions

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Problem Statement: print an entire array

Sub-problem: print an element in the array

Step 1 - Write and define the recursive Function Header ◦ public static void print(int[] arr, int indexToPrint)

Step 2 – Write out a sample/example Function Call ◦ int[] arr={1,5,9,6,7}; print(arr, 0);

Step 3 – Think when you want to stop the recursion ◦ if(indexToPrint==arr.length) return;

Step 4 – Write the function body ◦ System.out.println(arr[indexToPrint]);

Step 5 – Make the function call itself ◦ print(arr, indexToPrint+1);

Final Function ◦ public static void print(int[] arr, int indexToPrint) {




◦ }

Example #1 of the Process

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To make sure our recursive function works, we must trace it





◦ }

Call from main ◦ int[] arr={1,5,9,6,7}; print(arr, 0);

Trace Output

print(arr, 0) 1

print(arr, 1) 5

print(arr, 2) 9

print(arr, 3) 6

print(arr, 4) 7

print(arr, 5)

Tracing Example #1

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Problem Statement: print an entire array in reverse order

Sub-problem: print an element in the array

Step 1 - Write and define the recursive Function Header ◦ public static void print(int[] arr, int indexToPrint)

Step 2 – Write out a sample/example Function Call ◦ int[] arr={1,5,9,6,7}; print(arr, arr.length-1);

Step 3 – Think when you want to stop the recursion ◦ if(indexToPrint==-1) return;

Step 4 – Write the function body ◦ System.out.println(arr[indexToPrint]);

Step 5 – Make the function call itself ◦ print(arr, indexToPrint-1);


◦ if(indexToPrint==-1) return;


◦ print(arr, indexToPrint-1);

◦ }


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To make sure our recursive function works, we must trace it


◦ if(indexToPrint==-1) return;


◦ print(arr, indexToPrint-1);

◦ }

Call from main ◦ int[] arr={1,5,9,6,7}; print(arr, arr.length-1);

Trace Output

print(arr, 4) 7

print(arr, 3) 6

print(arr, 2) 9

print(arr, 1) 5

print(arr, 0) 1

print(arr, -1)

Tracing Example #2

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◦ public static void print(int[] arr, int indexToPrint) {




◦ }

◦ public static void print(int[] arr, int indexToPrint) {




◦ }

◦ Call from main: int[] arr={1,5,9,6,7}; print(arr, 0);

Trace Output

print(arr, 0) 7

print(arr, 1) 6

print(arr, 2) 9

print(arr, 3) 5

print(arr, 4) 1

print(arr, 5)

The Order Matters…

Prints in Order

Prints in

Reverse Order!

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Problem Statement: sum all integers between 1 and max

Sub-problem: sum one integer with the rest of the numbers

Step 1 - Write and define the recursive Function Header ◦ public static int sumAll(int max)

Step 2 – Write out a sample/example Function Call ◦ int sum = sumAll(5); // sum should be set to 5+4+3+2+1=15

Step 3 – Think when you want to stop the recursion ◦ if(max==0) return 0; // You have to return 0, because your return type is int!

Step 4 – Write the function body ◦ The function body will be empty for this one, the sum is in the return statement

Step 5 – Make the function call itself ◦ return sumAll(max-1) + max;

Final Function ◦ public static int sumAll(int max) {

◦ if(max==0) return 0;

◦ return sumAll(max-1) + max;

◦ }


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Declaration and Invocation

public static long sumAll(int max) { // Declaration System.out.println("sumAll " + n);

if (max == 0) return 0; else return sumAll(max - 1) + n; }


System.out.println("sumAll output for 5 is " + sumAll(5)); System.out.println("sumAll output for 10 is " + sumAll(10)); System.out.println("sumAll output for 20 is " + sumAll(20)); System.out.println("sumAll output for 15 is " + sumAll(15)); System.out.println();

}

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Tracing sumAll(2) public static long sumAll(2) { System.out.println("sumAll " + 2);

if (2 == 0) return 0; else return 2 + sumAll(2 - 1); }

OUTPUT: sumAll 2

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OUTPUT: sumAll 2 sumAll 1

public static long sumAll(1) { System.out.println("sumAll " + 1);


Invoke

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OUTPUT: sumAll 2 sumAll 1 sumAll 0



Invoke


if (0 == 0) return 0;

Invoke

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Tracing sumAll(2) public static long sumAll(int 2) { System.out.println("sumAll " + 2);


OUTPUT: sumAll 2 sumAll 1 sumAll 0

public static long sumAll(int 1) { System.out.println("sumAll " + 1);

if (1 == 0) return 0; else return 1 + 0; }

Invoke

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Tracing sumAll(2) public static long sumAll(int 2) { System.out.println("sumAll " + 2);

if (2 == 0) return 0; else return 2 + 1; }

OUTPUT: sumAll 2 sumAll 1 sumAll 0 sumAll of 2 is 3


System.out.println("sumAll of 2 is " +sumAll(2)); }

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Any iterative solution can be converted to a recursive solution

Any recursive solution can be converted to an iterative solution

Iterative

◦ subTotal = 0;

◦ for (int i = 1; i <= max ; i++) {

◦ subTotal += i;

◦ }

Recursive

◦ public static int sumAll(int n) {

◦ if (n == 0)

◦ return 0;

◦ else

◦ return sumAll(n-1) + n;

Iterative vs Recursive

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Missing the stopping condition ◦ public static int sumAll(int max) {


◦ }

◦ Infinite Loop!

Wrong Function Call - no guarantee that the function will exit ◦ public static int sumAll(int max) {

◦ if(max==0) return 0;


◦ }

◦ Calling the function with sumAll(-1) will result in an Infinite Loop!

Too many function calls ◦ Your computer has limited memory

◦ You will run out of space when calling sumAll(50000)

◦ Should not happen in this class!

Takes too much time to compute ◦ Should not happen in this class!

Common Recursion Mistakes

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Problem Statement: compute the factorial of a number

Sub-problem: multiply one integer with the rest of the numbers

Step 1 - Write and define the recursive Function Header ◦ public static int Fact(int number)

Step 2 – Write out a sample/example Function Call ◦ int factorial = Fact(5); // factorial should be set to 5*4*3*2*1=120

Step 3 – Think when you want to stop the recursion ◦ if(number==1) return 1; // You have to return 1, your return type is int!

Step 4 – Write the function body ◦ The function body is empty; the multiplication is in the return statement

Step 5 – Make the function call itself ◦ return Fact(number-1) * number;

Final Function ◦ public static int Fact(int number) {

◦ if(number==1) return 1;

◦ return Fact(number-1) * number;

◦ }


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Tracing Fact(5)

Fact(5)

Fact(4)

Fact(3)

Fact(2)

Fact(1)

Fact(1)

Return 1

Fact (2)

Return 1*2

Fact (3)

Return 2*3

Fact (4)

Return 6*4

Fact (5)

Return 24*5

public static int Fact(int number)

{

if(number==1) return 1;

return Fact(number-1) * number;

}

Call from main: Fact(5)

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Problem Statement: compute the fibonacci of a number

Sub-problem: add the previous two numbers together

Step 1 - Write and define the recursive Function Header ◦ public static int Fib(int number)

Step 2 – Write out a sample/example Function Call ◦ int fibonacci = Fib(5); // fibonacci should be set to 2+3=5

Step 3 – Think when you want to stop the recursion ◦ if(number==0) return 0;

◦ If(number==1) return 1;

Step 4 – Write the function body

Step 5 – Make the function call itself ◦ return Fib(number-1) + Fib(number-2);

Final Function ◦ public static int Fib(int number) {

◦ if(number==1) return 1;

◦ return Fib(number-1) * number;

◦ }


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Fib(5)

Fib(4)1

Fib(3)1

Fib(2)1 Fib(1)1

Fib(2)2

Fib(3)2

Fib(2)3 Fib(1)2

Tracing Fib(5)

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CSE 21 Introduction to Computing II...How to Write a Recursive Function 9 Step 1 - Write and define the recursive Function Header Your main choices are the Return Type and Parameters

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