1. Recursion Pepper

2. Recursion Definition English –procedure that can repeat a version of itself indefinitely – such as mirrors looking at each other. Math –defining an object in terms of itself Factorials: Fibonacci:

3. Recursion in Nature Snowflakes http://en.wikipedia.org/wiki/Recursive_defi nition

4. Java Recursion Definition A method calls itself Another way to repeat code

5. Add Up Example Call yourself repeatedly until you say to stop. Example: add up 4 numbers using addUp. -- Input – number to count -- Ouput – total of all those numbers added up Logic: If the number I am counting is 0, just return 0. If the number I am counting is anything else, return the number I have + the total of all the rest (the number I have – 1) Requires: Trust the function will do its job A stopper A way to reach the stopper (decrement or increment) Code the addUp method and call it to addUp(4)

6. Start by trusting it will work Create a method that assumes it will do the job it says it will: Return the number you have + everything else that needed to be done public static int addUp(int numberToCount) { // something that is NOT numberToCount will have to be put here return __________________; }

7. Then, write the stopping code When should it stop calling itself? What should it do in that last case? public static int addUp(int numberToCount) { if (numberToCount == 1) // stop when you are down to #1 { // last called case work return __________________;} else { // normal work return numberToCount + addUp(numberToCount-1); }

8. addUp Solution public class AddUp { public static void main() { System.out.println(addUp(4); } public static int addUp(int numberToCount) { if (numberToCount == 1) { return numberToCount;} else { return numberToCount + addUp(numberToCount-1); } *This can be acted and traced in class.

9. Alternative: For public static int addUp(int numberToCount) { int sum = 0; for (int count =1; count <= numberToCount;count++) { sum = sum + count; } return sum; }

10. Create a string of stars YOU TRY: starString routine -- Input – number of stars needed -- Ouput – String of that many stars Logic: If the number I am counting is 1, just return 1 star. If the number I am counting is anything else, return one star + all the rest of the stars (the number I have – 1) Requires: Trust the function will do its job A stopper A way to reach the stopper (decrement or increment) Code the starString method and call it to create starString(10)

11. String of Stars public static String starString (int numberStars) { if (numberStars == 0) { return(""); } else { return "*" + starString(numberStars-1); }

12. Using Pictures Book uses Drawing Panel, We can use PictureIt Libraries: –javalib.worldimages.* –java.awt.Color; Classes: –WorldImage show() method place(WorldImage, x, y) – x,y is center –AImage makeRectangle(length, width, mode)

13. Work with shapes Make a Rectangle keep getting smaller until it is size 5 wide. The goal is:

14. Work with shapes First code without recursion: –create a method that takes in the size of the square. Code it to return 1 slightly smaller square outline on a square. –Call that method from your main method to see one square on your canvas.

15. Code of just the one square import javalib.worldimages.*; import java.awt.Color; public class Test7 { public static void main() { WorldImage myWorld = printInsideSquares ( 600); myWorld.show(); } public static WorldImage printInsideSquares( int size) { WorldImage mainSquare = AImage.makeRectangle(size,size,Mode.OUTLINED); WorldImage littleSquare = AImage.makeRectangle(size/10*9,size/10*9, Color.RED, Mode.OUTLINED); mainSquare = mainSquare.place( littleSquare, size/2, size/2); return mainSquare; }

16. Work with shapes Code the base case: –Add an if statement to return just one square of the given size when the size is < 5. Code the recursion: Instead of placing the slightly smaller square on the big square, place a call to your method with that slighly smaller size.

17. Work with shapes import javalib.worldimages.*; import java.awt.Color; public class Test6 { public static void main() { WorldImage myWorld = printInsideSquares ( 600); myWorld.show(); } public static WorldImage printInsideSquares( int size) { if (size <= 5) { return AImage.makeRectangle(size,size,Mode.OUTLINED); } else { WorldImage mainSquare = AImage.makeRectangle(size,size,Mode.OUTLINED); // WorldImage littleSquare = AImage.makeRectangle(size/2,size/2,Color.RED, Mode.OUTLINED); mainSquare = mainSquare.place( printInsideSquares( size/10*9), size/2, size/2 ); return mainSquare; }