TA office hours are over after this week, but Dan and Maja will still be around for the next month

Transcription

1 TA office hours are over after this week, but Dan and Maja will still be around for the next month Feel free to me to request an appointment. My schedule is flexible. We will have more office hours before the exam, too. These will be announced on WebCT. 1

2 Recursion: solve a problem of size n by solving smaller instances of that same problem using them to build the solution for n

3 Example Write a recursive method m() that computes the partial sum of the following series: 1/3 + 2/5 + 3/7 + 4/ i / (2i + 1) In other words, m(2) should return result of 1/3 + 2/5 m(3) should return result of 1/3 + 2/5 + 3/7 m(0), m(-1) are undefined 3

4 Example Write a recursive method that computes the partial sum of the following series: 1/3 + 2/5 + 3/7 + 4/ i / (2i + 1) Idea: to compute m(n), assume I know how to compute m(n-1): m(n) = n/(2n + 1) + m(n-1) 4

5 Example Write a recursive method that computes the partial sum of the following series: 1/3 + 2/5 + 3/7 + 4/ i / (2i + 1) Idea: to compute m(n), assume I know how to compute m(n-1): m(n) = n/(2n + 1) + m(n-1) Base case (simplest case, no recursive call) m(1) = 1.0/3 5

6 Example Write a recursive method that computes the partial sum of the following series: 1/3 + 2/5 + 3/7 + 4/ i / (2i + 1) How it works for m(4): m(4) = 4/(2*4 + 1) + m(3) m(3) = 3/(2*3 + 1) + m(2) m(2) = 2/(2*2 + 1) + m(1) m(1) = base case = 1/3 6

7 Recursive program + try-catch blocks + command-line parameters Write a class with two methods: catalan() and main() catalan() is a recursive method that computes the n th Catalan number: C(0) = 1 C(n) = (4*n -2)/(n+1)*C(n-1) The main() method reads a String from the command-line, converts it to an integer with Integer.parseInt(), calls the catalan() method on it and prints the result. If the number of arguments is not 1, if the given argument is < 1 or if parseint() throws an exception print something like Usage: java RecursiveCatalan <positive-integer> Solution: See RecursiveCatalan.java 7

8 Another recursive program + arrays Write a recursive program that, given an array of integers (the integers can be negative, 0, positive), returns the largest number in the array. For solution, see Exercise 20_13.java 8

9 2D arrays 9

10 Common midterm error: jagged arrays int[][] a = new int[2][1]; int[] a0 = {1,2,3; int[] a1 = {4; a[0] = a0; a[1] = a1; The above example is legal: it compiles and runs fine. (But on the midterm, lots of students stated that this kind of operation is not allowed.) a[0] contains an address pointing to an array of size 1. We can't change the size of the array a[0] points to, but we can change the content of a[0] so that it points to another array (of any size). This is what's happening on the second-to-last line of the example above. 10

11 exercise: 2D arrays Write a method that accepts an int[][] called img as parameter and returns a new int[][] that is the transpose of img {{ 1, 2, 3, { 4, 5, 6 produces { { 1, 4, {2, 5, {3, 6 11

12 Solution public static int[][] transpose(int[][] img){ int width = img.length; int height = img[0].length; int[][] newimg = new int[height][width]; for(int y = 0; y < height; y++) for(int x = 0; x < width; x++) newimg[y][x] = img[x][y]; return newimg;

13 exercise: more 2D arrays [no solution provided (compile and test your code to see whether it's doing the right thing. having trouble? drop by during office hours)] Write a method that (given a 2D int array called img, (x,y) coordinates, a vertical distance and a horizontal distance), returns a new array that is a cropped version of img You may assume that all the parameters are within the bounds of the array e.g. given coordinates 2,2 and v distance 1 and h distance 0 { { 0, 0, 0, 0, produces { 0, 0, 0, 0, { 0, 0, 0, 0, { 0, 0, 0, 0 { {0, {0, {0 13

14 Extra exercises 14

15 a longer exercise for ArrayLists in picture-collection.pdf This exercise is adapted from an old assignment, and the solutions to that assignment are provided in w13-thursday.zip. You will not be able to compile or run this code, unfortunately. (Since some files are missing.) The solutions do not match the instructions in picture-collection.pdf exactly, but they're close. For good practice with file i/o, try to write code to match the specification found in picture-collection/docs/simplecollectionloader.html and picturecollection/docs/simplecollectionwriter.html 15

16 What will this print? public class MyInteger { private int x; public MyInteger(int myx) { x = myx; public double add(int y, int z) { System.out.println("add(i,i): " + x + " + " + y + " + " + z); return x + y + z; public double add(double y, double z) { System.out.println("add(d,d): " + x + " + " + y + " + " + z); return x + y + z; public static void main(string[] args) { MyInteger n1 = new MyInteger(1); MyInteger n2 = new MyInteger(2); double r1, r3; r1 = n1.add(3, 4); r3 = n1.add(5, 6.0); System.out.println("n1.add(3, 4) == " + r1); System.out.println("n2.add(3, 4) == " + n2.add(3, 4)); System.out.println("n3.add(5, 6.0) == " + r3);

17 Solution add(i,i): add(d,d): n1.add(3, 4) == 8.0 add(i,i): n2.add(3, 4) == 9.0 n3.add(5, 6.0) == 12.0

18 Command-line parameters What is displayed by the following program if we run it like this: java Cat java Cat 4 5 java Cat \ 4\ java Cat public class Cat{ public static void main(string[] elephants){ String result = ""; for(int i = 0; i < elephants.length; i++){ result = result + elephants[i]; System.out.println(result);

19 This is the output at my terminal java Cat mfrydr@jack:~$ java Cat mfrydr@jack:~$ java Cat \"4\" "4" mfrydr@jack:~$ java Cat "4" 5 45

20 class UselessObject{ int evennumber; int oddnumber; public UselessObject(){ evennumber = 6; oddnumber = 1; public int getsum(){ return evennumber + oddnumber; public void incrementall(int step){ if(step%2 == 0){ evennumber = evennumber + step; oddnumber = oddnumber + step;

21 What is printed when we run ObjectExercise? public class ObjectExercise{ public static void main(string[] args){ UselessObject a = new UselessObject(); UselessObject b = new UselessObject(); a.evennumber = -4; b.incrementall(4); System.out.println(a.getSum() - b.getsum());