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Arrays

Arrays. 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. ElementType. [ ].

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Arrays

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  1. 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. ElementType [ ] id; Brackets Name of Type of indicate array list values in variable being list defined Array variable definition styles • Without initialization int [] a; int a[];

  4. Nonnegative integer expression specifying the number of elements in the array ElementType id ElementType [n]; = new [ ] Reference to a new array of n elements Array variable definition styles • With initialization

  5. c - … value 0 0 0 0 0 Example • Definitions char[] c; int[] value = new int[10]; • Causes • Array object variable c is un-initialized • Array object variable v references a new ten element list of integers • Each of the integers is default initialized to 0

  6. Basic terminology • List is composed of elements • Elements in a list have a common name • 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

  7. 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 • 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

  8. Consider 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(); 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(); 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(); 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(); 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(); 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(); 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(); 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(); 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(); 8 is displayed Suppose 3 is extracted

  9. 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

  10. Today’s demotivators

  11. vertex vertex vertex p[0] p[0] p[0] p[0] p[0] p[0] p[0] p[1] p[1] p[1] p[1] p[1] p[1] p[1] p[2] p[2] p[2] p[2] p[2] p[2] p[2] null null null p p p p p p p Point: (4, 4) Point: (4, 4) Point: (4, 4) Point: (1, 0) Point: (0, 0) Point: (1, 0) Point: (1, 0) Point: (1, 0) Point: (1, 0) Point: (1, 1) Point: (1, 2) Point: (1, 1) Point: (1, 2) Point: (2, 2) Point: (2, 2) Point: (2, 2) Point: (2, 2) Point: (2, 2) 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]; p[2] = vertex; 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]; p[2] = vertex;

  12. id references an array of n elements. id[0] has value exp0, id[1] has value exp1, and so on. Each expiis an expression that evaluates to type ElementType Explicit initialization • Syntax ElementType id exp , exp , ... exp [] = { } ; 0 1 -1 n

  13. Explicit initialization • Example String[] puppy = { “pika“, “arlo“, “schuyler", “nikki" }; int[] unit = { 1 }; • Equivalent to String[] puppy = new String[4]; puppy[0] = “pika"; puppy[1] = “arlo"; puppy[2] = “schuyler"; puppy[3] = “nikki"; int[] unit = new int[1]; unit[0] = 1;

  14. Array members • Member length • Size of the array for (int i = 0; i < puppy.length; ++i) { System.out.println(puppy[i]); }

  15. u[0] u[0] u[0] u[1] u[1] u[1] u u u Point: (0, 0) Point: (0, 0) Point: (0, 0) Point: (1, 1) Point: (1, 1) Point: (1, 1) v v Point: (4, 30) v[0] v[0] v[1] 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] = new Point(4, 30); Point[] u = { new Point(0, 0), new Point(1, 1)}; Point[] v = u.clone(); v[1] = new Point(4, 30);

  16. Making a deep copy • Example Point[] w = new Point[u.length]; for (int i = 0; i < u.length; ++i) { w[i] = (Point) u[i].clone(); }

  17. Making a deep copy

  18. Review of last time • 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]);

  19. Array - length = 5 - data = + … 1 2 3 4 5 1 2 3 4 5 How Java represents arrays • Consider int[] a = { 1, 2, 3, 4, 5 }; a

  20. c d b null a 1 0 2 0 3 0 4 0 5 0 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; int[] a; int[] b = null; int[] c = new int[5]; int[] d = { 1, 2, 3, 4, 5 }; a = c; d = c; -

  21. Searching for a value System.out.println("Enter search value (number): "); int key = stdin.nextInt(); int i; for (i = 0; i < data.length; ++i) { if (key == data[i]) { break; } } if (i != data.length) { System.out.println(key + " is the " + i + "-th element"); } else { System.out.println(key + " is not in the list"); } ++i System.out.println("Enter search value (number): "); int key = stdin.nextInt(); int i; if (key == data[i]) { break; if (i != data.length) { System.out.println(key + " is the " + i + "-th element"); } i = 0 i < data.length

  22. 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]; } }

  23. 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[] 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() throws IOException { ... // 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) { ... }

  24. ArrayTools.java method putList() 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);

  25. 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; }

  26. 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);

  27. Demo.java public class Demo { // main(): application entry point publicstaticvoidmain(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(numbers); System.out.println(""); System.out.println("Your list in reverse"); ArrayTools.putList(numbers); System.out.println(); } }

  28. ArrayTools.java method sequentialSearch() publicstaticintsequentialSearch(int[]data,int key){ for (int i = 0; i < data.length; ++i) { if (data[i] == key) { return i; } } return -1; } • Consider int[] score = {6,9,82,11,29,85,11,28, 91}; int i1 = sequentialSearch(score,11); int i2 = sequentialSearch(score,30);

  29. Yale vs. Harvard • Web references: http://www.harvardsucks.org/, http://www.yaledailynews.com/article.asp?AID=27506

  30. 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

  31. 0 1 2 3 4 5 6 7 8 9 v ‘Q' 'W' ‘E' 'R' 'T' 'Y' 'U' 'I' 'O' 'P' 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

  32. 0 1 2 3 4 5 6 7 8 9 v ‘Q' 'W' ‘E' 'R' 'T' 'Y' 'U' 'I' 'O' 'P' 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

  33. 0 1 2 3 4 5 6 7 8 9 v 'E' 'W' 'Q' 'R' 'T' 'Y' 'U' 'I' 'O' 'P' 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

  34. 0 1 2 3 4 5 6 7 8 9 v 'E' 'W' 'Q' 'R' 'T' 'Y' 'U' 'I' 'O' 'P' 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

  35. 0 1 2 3 4 5 6 7 8 9 v 'E' 'I' 'Q' 'R' 'T' 'Y' 'U' 'W' 'O' 'P' 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

  36. 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; } }

  37. 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; } // spotisnowcorrect,swap elementsv[spot]andv[i]

  38. Quick survey • How are we doing with arrays? • Very well • With some review, I’ll be good • Not really • Not at all

  39. April Fools Day Jokes Privacy policy • From time to time, in order to improve Google Gulp's usefulness for our users, Google Gulp will send packets of data related to your usage of this product from a wireless transmitter embedded in the base of your Google Gulp bottle to the GulpPlex™, a heavily guarded, massively parallel server farm whose location is known only to Eric Schmidt, who carries its GPS coordinates on a 64-bit-encrypted smart card locked in a stainless-steel briefcase handcuffed to his right wrist. No personally identifiable information of any kind related to your consumption of Google Gulp or any other current or future Google Foods product will ever be given, sold, bartered, auctioned off, tossed into a late-night poker pot, or otherwise transferred in any way to any untrustworthy third party, ever, we swear. See our Privacy Policy. http://www.google.com/googlegulp/ (or do a Google search for ‘gulp’)

  40. Google Maps…

  41. Binary search • Given a list, find a specific element in the list • List MUST be sorted! • Each time it iterates through, it cuts the list in half • A binary search is MUCH faster than a sequential search

  42. 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 ("Searching for 0: " + ArrayTools.binarySearch(numbers, 0)); System.out.println ("Searching for 1: " + ArrayTools.binarySearch(numbers, 1)); System.out.println ("Searching for 4: " + ArrayTools.binarySearch(numbers, 4)); System.out.println ("Searching for 5: " + ArrayTools.binarySearch(numbers, 5)); System.out.println ("Searching for 6: " + ArrayTools.binarySearch(numbers, 6)); System.out.println ("Searching for 10: " + ArrayTools.binarySearch(numbers, 10)); System.out.println ("Searching for 11: " + ArrayTools.binarySearch(numbers, 11)); } }

  43. Binary search use demo…

  44. 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; } }

  45. key 14 returns: 6 i j m Binary search, take 1 public static int binarySearch (int[] data, int key) { int i = 0; int j = data.length-1; int i = 0; int j = data.length-1; while ( i < j ) { int m = (i+j)/2; if ( key > data[m] ) { i = m+1; } else { j = m; } } 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; } if ( key == data[i] ) { return i; } else { return -1; } data 5 6 0 4 7 6 5 7 9 6

  46. key 15 returns: -1 i j m Binary search, take 2 public static int binarySearch (int[] data, int key) { int i = 0; int j = data.length-1; int i = 0; int j = data.length-1; while ( i < j ) { int m = (i+j)/2; if ( key > data[m] ) { i = m+1; } else { j = m; } } 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; } if ( key == data[i] ) { return i; } else { return -1; } data 5 0 7 6 4 7 9

  47. Binary search • A somewhat alternative view of what a binary search does…

  48. 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 log2n iterations! • Where n is the size of the array

  49. Binary search vs. sequential search • Assume the array has n elements • Sequential search can take (in the worst-case) n iterations to find the element • Binary search can take (in the worst case) log2n 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

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