Arrays Chapter 8 Spring 2006 CS 101 Aaron Bloomfield 1 Introduction to arrays 2 Background Programmer often need the ability to represent a group of values as a list List may be one-dimensional or multidimensional Java provides arrays and the collection classes The Vector class is an example of a collection class Consider arrays first 3 Example Definitions char[] c; int[] value = new int[10]; Causes Array object variable c is un-initialized Array object variable value references a new ten element list of integers Each of the integers is default initialized to 0 c value 0 0 0 0 … 0 4 An array example int[] v = new int[10]; int i = 7; int j = 2; int k = 4; v[0] = 1; v[i] = 5; v[j] = v[i] + 3; v[j+1] = v[i] + v[0]; v[v[j]] = 12; System.out.println(v[2]); v[k] = stdin.nextInt(); v 8 is displayed Suppose 3 is extracted 0 1 0 0 8 0 6 0 3 0 0 0 5 12 0 0 v[0] v[1] v[2] v[3] v[4] v[5] v[6] v[7] v[8] v[9] 5 Array variable definition styles Without initialization ElementType [ ] id; Brackets Name of Type of list values in indicate array variable being list defined int [] a; int a[]; 6 Array variable definition styles With initialization Nonnegative integer expression specifying the number of elements in the array ElementType [ ] id = new ElementType [n]; A new array of n elements 7 Where we’ve seen arrays public static void main (String[] args) Thus, the main() method takes in a String array as the parameter Note that you can also define it as: public static void main (String args[]) or public static void main (String[] foobar) 8 Basic terminology List is composed of elements Elements in a list have a common name Example: a[3] = 5; The common name is ‘a’ The list as a whole is referenced through the common name List elements are of the same type — the base type Elements of a list are referenced by subscripting (indexing) the common name 9 Java array features Subscripts are denoted as expressions within brackets: [ ] Base (element) type can be any type Size of array can be specified at run time This is different that pure C! (for the most part, at least) Index type is integer and the index range must be 0 ... n-1 Where n is the number of elements Just like Strings indexing! Automatic bounds checking Ensures any reference to an array element is valid Data field length specifies the number of elements in the list Array is an object Has features common to all other objects More on this later… 10 Consider Segment int[] b = new int[100]; b[-1] = 0; b[100] = 0; Causes Array variable to reference a new list of 100 integers Each element is initialized to 0 Two exceptions to be thrown -1 is not a valid index – too small 100 is not a valid index – too large IndexOutOfBoundsException 11 Consider Point[] p = new Point[3]; p[0] = new Point(0, 0); p[1] = new Point(1, 1); p[2] = new Point(2, 2); p[0].setX(1); p[1].setY(p[2].getY()); Point vertex = new Point(4,4); p[1] = p[0]; vertex p[2] = vertex; p p[0] p[1] p[2] null null null Point: (1, (0, 0) Point: (4, 4) Point: (1, 2) 1) Point: (2, 2) 12 New 2005 demotivatiors! 13 Explicit initialization Syntax id references an array of n elements. id[0] has value exp0, id[1] has value exp1, and so on. ElementType [] id = { exp0 , exp1 , ... expn-1 } ; Each expi is an expression that evaluates to type ElementType 15 Explicit initialization Example String[] puppy = { “pika”, “mila”, “arlo”, “nikki” }; int[] unit = { 1 }; Equivalent to String[] puppy = new String[4]; puppy[0] = “pika"; puppy[1] = “mila"; puppy[2] = “arlo"; puppy[3] = “nikki"; int[] unit = new int[1]; unit[0] = 1; 16 Array members Member length Size of the array for (int i = 0; i < puppy.length; ++i) { System.out.println(puppy[i]); } 17 Array members Member clone() Produces a shallow copy Point[] u = { new Point(0, 0), new Point(1, 1)}; Point[] v = u.clone(); v[1] = new Point(4, 30); u[0] u[1] u Point: (0, 0) v Point: (1, 1) Point: (4, 30) 18 v[0] v[1] Array members Member clone() Produces a shallow copy Point[] u = { new Point(0, 0), new Point(1, 1)}; Point[] v = u.clone(); v[1].setX(10); u[0] u[1] u Point: (0, 0) (1, 1)1) Point: (10, v 19 v[0] v[1] Making a deep copy We want to copy the array and all the objects each element of the array references This is called a deep copy Example Point[] w = new Point[u.length]; for (int i = 0; i < u.length; ++i) { w[i] = (Point) u[i].clone(); } 20 Making a deep copy u[0] u[1] u[2] u Point: (0, 0) w[0] w[1] Point: (2, 1) Point: (2, 2) Point: (2, 1) Point: (2, 2) w[2] w Point: (0, 0) 21 Review of arrays Creating an array: int[] foo = new int[10]; Accessing an array: foo[3] = 7; System.out.print (foo[1]); Creating an array: String[] bar = new String[10]; Accessing an array: bar[3] = “qux”; System.out.println (bar[1]); 22 How Java represents arrays Consider int[] a = { 1, 2, 3, 4, 5 }; Array - length = 5 a - data = 1 1 2 2 3 4 3 5 4 5 +… 23 More about how Java represents Arrays Consider int[] a; int[] b = null; int[] c = new int[5]; int[] d = { 1, 2, 3, 4, 5 }; a = c; d = c; a - b null c 0 0 0 0 0 d 1 2 3 4 5 24 What do these pictures mean? Light beer Dandy lions Assaulted peanut Eggplant Dr. Pepper Pool table Tap dancers Card shark King of pop I Pod Gator aide Knight mare Hole milk 25 ArrayTools 26 ArrayTools.java We want to create a series of general utility methods to be used for arrays We will put these into an ArrayTools class 27 ArrayTools.java – outline public class ArrayTools { // class constant private static final int MAX_LIST_SIZE = 1000; // sequentialSearch(): examine unsorted list for key public static int sequentialSearch(int[] data, int key) { ... // putList (): prints list to screen public static void putList(int[] data) { ... // getList(): extract and return up to MAX_LIST_SIZE values public static int[] getList() { ... // reverse(): reverses the order of the element values public static void reverse(int[] list) { ... // binarySearch(): examine sorted list for a key public static int binarySearch(char[] data, char key) { ... } 28 ArrayTools.java method putList() To print the array: public static void putList(int[] data) { for (int i = 0; i < data.length; ++i) { System.out.println(data[i]); } } Consider int[] score = { 6, 9, 82, 11, 29, 85, 11, 28, 91 }; putList(score); 29 ArrayTools.java method getList() public static int[] getList() { Scanner stdin = new Scanner (System.in); int[] buffer = new int[MAX_LIST_SIZE]; int listSize = 0; for (int i = 0; (i < MAX_LIST_SIZE) && stdin.hasNext(); ++i) { buffer[i] = stdin.nextInt(); ++listSize; } int[] data = new int[listSize]; for (int i = 0; i < listSize; ++i) { data[i] = buffer[i]; } return data; } 30 ArrayTools.java method reverse() public static void reverse(int[] data) { int[] clone = data.clone(); for ( int i = 0; i < clone.length; ++i ) { data[i] = clone[clone.length-1-i]; } } Consider int[] foo = { 1, 2, 3, 4, 5 }; reverse (foo); putList (foo); 31 Demo.java public class Demo { // main(): application entry point public static void main(String[] args) { System.out.println (""); System.out.println ("Enter list of integers:"); int[] numbers = ArrayTools.getList (); System.out.println (""); System.out.println ("Your list"); ArrayTools.putList (numbers); ArrayTools.reverse System.out.println System.out.println ArrayTools.putList System.out.println (numbers); (""); ("Your list in reverse"); (numbers); (); } } 32 ArrayTools demo… ArrayDemo.java 34 … main (String args[]) 36 Consider that main() method again public static void main (String args[]) How does one pass in a parameter to the main method? public class MainParameters { public static void main (String args[]) { System.out.println ("Number of paramters to “ + "main(): " + args.length); if ( args.length > 0 ) { for ( int i = 0; i < args.length; i++ ) System.out.println ("parameter " + i + ": '" + args[i] + "'"); } } 37 } Program Demo MainParameters.java Via JCreator Via the command line 38 Basic array searching 39 Searching for a value System.out.println("Enter search value (number): "); int key = stdin.nextInt(); int i; for (i i = 0 0; i < data.length data.length; ++i ++i) { if (key == data[i]) { break; } } 0 1 2 data 4 9 5 key 5 i 0 1 2 if (i != data.length) { System.out.println(key + " is the " + i + "-th element"); } else { System.out.println(key + " is not in the list");40 } Searching for the minimum value Segment int minimumSoFar = sample[0]; for (int i = 1; i < sample.length; ++i) { if (sample[i] < minimumSoFar) { minimumSoFar = sample[i]; } } 41 ArrayTools.java method sequentialSearch() public static int sequentialSearch(int[] data, int key) { for (int i = 0; i < data.length; ++i) { if (data[i] == key) { return i; } } key 11 return -1; } data 0 1 2 3 4 5 6 7 8 6 9 82 11 29 85 11 29 91 Consider int[] score = { 6, 9, 82, 11, 29, 85, 11, 28, 91 }; int i1 = sequentialSearch(score, 11); 42 int i2 = sequentialSearch(score, 30); Today’s demotivators 43 Sorting 44 Sorting Problem Arranging elements so that they are ordered according to some desired scheme Standard is non-decreasing order Why don't we say increasing order? Major tasks Comparisons of elements Updates or element movement 45 Selection sorting Algorithm basis On iteration i, a selection sorting method: Finds the element containing the ith smallest value of its list v and exchanges that element with v[i] Example – iteration 0 Swaps smallest element with v[0] This results in smallest element being in the correct place for a sorted result v 0 1 2 3 4 5 6 ‘Q' 'E' 'W' ‘E' 'Q' 'R' 'T' 'Y' 'U' 7 'I' 8 9 'O' 'P' 46 Selection sorting Algorithm basis On iteration i, a selection sorting method: Finds the element containing the ith smallest value of its list v and exchanges that element with v[i] Example – iteration 1 Swaps second smallest element with v[1] This results in second smallest element being in the correct place for a sorted result v 0 1 2 3 4 5 6 7 8 9 'E' 'W' 'I' 'Q' 'R' 'T' 'Y' 'U' 'I' 'W' 'O' 'P' 47 Selection sorting Algorithm basis On iteration i, a selection sorting method: Finds the element containing the ith smallest value of its list v and exchanges that element with v[i] Example – iteration 2 Swaps third smallest element with v[2] This results in third smallest element being in the correct place for a sorted result 0 v 'E' 1 'I' 2 3 4 5 6 7 8 9 'Q' ‘O' 'R' 'T' 'Y' 'U' 'W' 'O' ‘Q' 'P' 48 Selection sorting Algorithm basis On iteration i, a selection sorting method: Finds the element containing the ith smallest value of its list v and exchanges that element with v[i] Example – iteration 3 Swaps fourth smallest element with v[3] This results in fourth smallest element being in the correct place for a sorted result 0 v 'E' 1 'I' 2 3 4 5 6 7 8 9 ‘O' 'R' ‘P' 'T' 'Y' 'U' 'W' ‘Q' 'P' ‘R' 49 Selection sorting Algorithm basis On iteration i, a selection sorting method: Finds the element containing the ith smallest value of its list v and exchanges that element with v[i] Example – iteration 4 Swaps fifth smallest element with v[4] This results in fifth smallest element being in the correct place for a sorted result 0 v 'E' 1 'I' 2 3 4 5 6 7 8 9 ‘O' ‘P' 'T' ‘Q' 'Y' 'U' 'W' ‘Q' ‘T' ‘R' 50 ArrayTools.java selection sorting public static void selectionSort(int[] v) { for (int i = 0; i < v.length-1; ++i) { // find the location of the ith smallest element int spot = i; for (int j = i+1; j < v.length; ++j) { if (v[j] < v[spot]) { // is current location ok? // update spot to index of smaller element spot = j; } } // spot is now correct, so swap elements int rmbr = v[i]; v[i] = v[spot]; v[spot] = rmbr; } } 51 Iteration i // find the location of the ith smallest element int spot = i; for (int j = i+1; j < v.length; ++j) { if (v[j] < v[spot]) // is spot ok? // update spot with index of smaller element spot = j; } // spot is now correct, swap elements v[spot] and v[i] 52 From Dubai 53 Binary search 54 Binary search Given a list, find a specific element in the list List MUST be sorted! Each time it iterates through, it cuts the search space in half A binary search is MUCH faster than a sequential search 55 Binary search use The ‘BS’ in BSDemo is for Binary Search, mind you public class BSDemo { public static void main(String[] args) { int[] numbers = { 9, 3, 1, 8, 4, 6, 10, 2 }; System.out.println ("The original list of numbers:"); ArrayTools.putList(numbers); System.out.println(); ArrayTools.selectionSort(numbers); System.out.println ("The sorted list of numbers:"); ArrayTools.putList(numbers); System.out.println(); System.out.println System.out.println System.out.println System.out.println System.out.println System.out.println System.out.println ("Searching ("Searching ("Searching ("Searching ("Searching ("Searching ("Searching for for for for for for for 0: " + ArrayTools.binarySearch(numbers, 0)); 1: " + ArrayTools.binarySearch(numbers, 1)); 4: " + ArrayTools.binarySearch(numbers, 4)); 5: " + ArrayTools.binarySearch(numbers, 5)); 6: " + ArrayTools.binarySearch(numbers, 6)); 10: " + ArrayTools.binarySearch(numbers, 10)); 11: " + ArrayTools.binarySearch(numbers, 11)); } } 56 Binary search use demo… BSDemo.java 57 Chapter 2: Computer bugs 58 Binary search public static int binarySearch (int[] data, int key) { int i = 0; // left endpoint of search interval int j = data.length-1; // right endpoint of search interval while ( i < j ) { int m = (i+j)/2; if ( key > data[m] ) { i = m+1; } else { j = m; } } if ( key == data[i] ) { return i; } else { return -1; } 59 } Binary search, take 1 public static int binarySearch (int[] data, int key) { int i = 0; int j = data.length-1; data i while ( i < j ) { int m = (i+j)/2; if ( key > data[m] ) { i = m+1; } else { j = m; } } if ( key == data[i] ) { return i; } else { return -1; } key returns: a0 a1 a2 a3 a4 a5 a6 a7 a8 a9 2 4 6 8 10 12 14 16 18 20 0 5 6 m 4 7 6 5 j 9 7 6 14 6 60 Binary search But what if the element is not in the list? 61 Binary search, take 2 public static int binarySearch (int[] data, int key) { int i = 0; int j = data.length-1; data i while ( i < j ) { int m = (i+j)/2; if ( key > data[m] ) { i = m+1; } else { j = m; } } if ( key == data[i] ) { return i; } else { return -1; } key returns: a0 a1 a2 a3 a4 a5 a6 a7 a8 a9 2 4 6 8 10 12 14 16 18 20 0 5 7 m 4 7 6 j 9 7 15 -1 62 Binary search A somewhat alternative view of what a binary search does… 63 How long does a binary search take? Given a array of 64 elements 1st iteration cuts the array to 32 2nd iteration cuts the array to 16 3rd to 8 4th to 4 5th to 2 6th to 1 Given a array of 1024 elements 1st iteration cuts the array to 512 ... 10th iteration cuts the list to 1 element Thus, the binary search takes log2 n iterations! Where n is the size of the array 64 Binary search vs. sequential search Assume the array has n elements Sequential search takes n iterations to find the element Binary search takes log2 n iterations to find the element Consider a list of 1 million elements Binary search takes about 20 iterations Sequential search takes 1,000,000 iterations Consider a list of 1 trillion elements Binary search takes about 40 iterations Sequential search takes 1,000,000,000,000 iterations 65 Multi-dimensional arrays 67 Multidimensional arrays Many problems require information be organized as a twodimensional or multidimensional list Examples Matrices Graphical animation Economic forecast models Map representation Time studies of population change Microprocessor design 68 Example Segment int[][] m = new int[3][]; m[0] = new int[4]; m[1] = new int[4]; m[2] = new int[4]; Produces m[0] m m[1] m[2] m[2][0] m 0 m[0][0] 0 m[0][1] When an array is created, each value is initialized! 0 m[0][2] 0 m[0][3] m[2][1] m[2][2] m[2][3] 0 0 0 0 0 0 0 0 m[1][0] m[1][1] m[1][2] m[1][3] 69 Example Alternative int[][] m = new int[3][4]; Produces m[0] m[1] m[2] m[2][0] m 0 m[0][0] 0 m[0][1] 0 m[0][2] 0 m[0][3] m[2][1] m[2][2] m[2][3] 0 0 0 0 0 0 0 0 m[1][0] m[1][1] m[1][2] m[1][3] 70 Multidimensional array visualization A multi-dimensional array declaration (either one): int[][] m = new int[3][4]; How we visualize it: 0 0 0 0 0 0 0 0 0 0 0 0 or 0 0 0 0 0 0 0 0 0 0 0 0 71 Example Segment for (int c = 0; c < m.length; ++c) { for (int r = 0; r < m[c].length; ++r) { System.out.print("Enter a value: "); m[c][r] = stdin.nextInt(); } } 0 0 0 0 0 0 0 0 0 0 0 0 72 Rows by columns or columns by rows? Consider int[][] m = new int[3][4]; Is that 3 rows by 4 columns or 3 columns by 4 rows? 0 0 0 0 0 0 0 0 0 0 0 0 or 0 0 0 0 0 0 0 0 0 0 0 0 The answer is that it can be either As long as you are consistent with your column/row 73 placement Rows by columns or columns by rows? This makes it 3 columns by 4 rows: for (int c = 0; c < m.length; ++c) for (int r = 0; r < m[c].length; ++r) { System.out.print("Enter a value: "); m[c][r] = stdin.nextInt(); } This makes it 3 rows by 4 columns: for (int c = 0; c < m.length; ++c) for (int r = 0; r < m[c].length; ++r) { System.out.print("Enter a value: "); m[r][c] = stdin.nextInt(); } 74 Example Segment String[][] s[0] = new s[1] = new s[2] = new s[3] = new Produces s[0] s = new String[4][]; String[2]; String[2]; String[4]; String[3]; s[1] s[2] s[3] null null null s[3][0] s[3][1] s[3][2] s null null null null s[2][0] s[2][1] s[2][2] s[2][3] null null s[0][0] s[0][1] null null 75 s[1][0] s[1][1] Multidimensional array visualization Segment String[][] s[0] = new s[1] = new s[2] = new s[3] = new Produces s = new String[4][]; String[2]; String[2]; String[4]; String[3]; 0 0 0 0 0 0 0 0 0 0 or 0 0 0 0 0 0 0 0 0 0 0 Called a “ragged” array 0 76 Explicit Initialization Segment int c[][] = {{1, 2}, {3, 4}, {5, 6}, {7, 8, 9}}; Produces c[0] c[1] c[2] 7 c[3] 8 9 c[3][0] c[3][1] c[3][2] c 5 6 c[2][0] c[2][1] 1 2 c[0][0] c[0][1] 3 4 c[1][0] c[1][1] 77 Matrices A two-dimensional array is sometimes known as a matrix because it resembles that mathematical concept A matrix a with m rows and n columns is represented mathematically in the following manner a1 1 a 1 2 a 1 n a2 1 a 2 2 a 2 n am 1 a m 2 a m n 78 Matrix addition Definition C = A + B cij = aij + bij cij is sum of the elements in the same row and column of A and B 79 Matrix addition public static double[][] add(double[][] a, double[][] b) { // determine number of rows in solution int m = a.length; // determine number of columns in solution int n = a[0].length; // create the array to hold the sum double[][] c = new double[m][n]; // compute the matrix sum row by row for (int i = 0; i < m; ++i) { // produce the current row for (int j = 0; j < n; ++j) { c[i][j] = a[i][j] + b[i][j]; } } return c; } 80 Homework J8 You will be creating a Universe class The Universe class contains a 2-D array In each spot will be a Location object (from a previous HW) Lab 10 is going to be a Map class Will print out the 2-D Universe via text 81 Alien Song AlienSong.mpg 82 Vector class This is also the review for the third midterm 83 Limitations of arrays You can’t change their size once created This can be a big problem! So we will create a new class that will operate like an array: We can store and get elements by index number It will automatically increase in size as needed And other fancy features… Let’s call the class Vector As we are basically writing the java.util.Vector class 84 Properties of our Vector class It needs to have an array to hold the values As our internal array will often be bigger than the number of elements in the Vector, we need a size as well More on what this means in a slide or two… Not much else… 85 Methods in our Vector class Insert and remove elements into the Vector Get an element from the Vector Find the length Print it out to the screen What happens when the array field is full, and we want to add an element? We will need to increase the size of the array So we need a method to do that as well 86 Our first take on our Vector class public class Vector { private Object array[]; private int size = 0; Vector() { array = new Object[100]; } Vector(int length) { array = new Object[length]; } } What does this mean? We’ll see that a bit later… But briefly, it means the array can store any object 87 Adding an element to our Vector public void add (Object o) { array[size++] = o; } Pretty easy! But what if the array is full? We need a way to increase the capacity of the array 88 Increasing the Vector’s array’s capacity private void increaseCapacity() { int oldSize = array.length; Object newArray[] = new Object[2*oldSize]; for ( int i = 0; i < oldSize; i++ ) newArray[i] = array[i]; array = newArray; } And our new add() method: public void add (Object o) { if ( size == array.length ) increaseCapacity(); array[size++] = o; } 89 Methods can be private as well Notice that the increaseCapacity() method is called only by the add() method when necessary It’s not ever going to be called by whomever is using our Vector Thus, we will make it private That means that only other Vector methods can call it 90 Removing an element from a Vector public Object remove (int which) { Object ret = array[which]; for ( int i = which; i < array.length-1; i++ ) array[i] = array[i+1]; array[array.length-1] = null; size--; return ret; } 91 Miscellaneous other methods public int size() { return size; } public Object get (int which) { return array[which]; } 92 Our toString() method public String toString() { String ret = "["; for ( int i = 0; i < size; i++ ) { ret += array[i]; if ( i != size-1 ) ret += ", "; } ret += "]"; return ret; } 93 Using our Vector This code is in a separate class called VectorUsage public static void main (String[] args) { Vector v = new Vector(); for ( int i = 12; i < 30; i++ ) { v.add (String.valueOf(i)); } System.out.println (v); System.out.println (v.size()); String s = (String) v.get(5); System.out.println (s); v.remove (5); System.out.println (v); v.remove (5); System.out.println (v); } 94 Program Demo VectorUsage.java 95 The “real” Vector class Java provides a Vector class In java.util It contains all of the methods shown 96 Program Demo VectorUsage.java But using java.util.Vector 97 What about those errors? When compiled with java.util.Vector, we see: Note: C:\...\VectorUsage.java uses unchecked or unsafe operations. Note: Recompile with -Xlint:unchecked for details. You can ignore these They deal with generics, which you will see in future courses The program was still compiled 98 More on using the Vector class To add a Location object l to the end of a Vector v v.add(l); To get the Location object at the end of the Vector v Location l = (Location) v.get(v.size()-1); To remove a Location object from the end of a Vector v Location l = (Location) v.remove(v.size()-1); This both removes the object from the Vector and stores the removed value into l 99 Very unofficial demotivators 100 Wrapper classes 102 But what about adding variables? The add method takes an Object as a parameter public void add (Object o) { Although we haven’t seen it yet, this means you can add any object you want to the vector Primitive types (i.e. variables) are not objects How can they be added? The solution: wrapper classes! 103 The Integer wrapper class This is how you add an int variable to a Vector: int x = 5; Integer i = new Integer(x); vector.add (i); //… Integer j = (Integer) v.get(0); int y = j.intValue(); Pretty annoying syntax – we’ll see how to get around it in a bit… 104 More on wrapper classes All the primitive types have wrapper classes Usually, the names are just the capitalized version of the type I.e. Double for double, Byte for byte, etc. Two exceptions: int and char int has Integer char has Character 105 More on wrapper classes Consider this code: int x = 5; vector.add (x); //… int y = vector.get(0); Does this code work? It shouldn’t As we are adding a variable (not an object) to a vector But it does work! Why? 106 Auto-boxing Java 1.5 will automatically “wrap” a primitive value into it’s wrapper class when needed And automatically “unwrap” a wrapper object into the primitive value So Java translates the previous code into the following: int x = 5; vector.add (new Integer(x)); //… int y = ((Integer)vector.get(0)).intValue(); This is called autoboxing And auto-unboxing (unauto-boxing?) This does not work in Java 1.4 or before 107 More on auto-boxing Consider the following code: Double d = 7.5; Double e = 6.5; Double f = d + e; System.println (f); This is doing a lot of auto-boxing (and auto-unboxing): Double d = new Double(7.5); Double e = new Double(6.5); Double f = newDouble(d.doubleValue() + e.doubleValue()); System.println (f); 108 A solution to commenting your code The commentator: http://www.cenqua.com/commentator/ 109