1. ARRAYS 1 Week 2

2. Data Structures  Data structure  A particular way of storing and organising data in a computer so that it can be used efficiently  Types of data structures  Based on memory allocation o Static (or fixed sized) data structures (Arrays) o Dynamic data structures (Linked lists)  Based on representation o Linear(Arrays/linked lists) o Non-linear(Trees/graphs)

3. Array: motivation  You want to store 5 numbers in a computer  Define 5 variables, e.g. num1, num2,..., num5  What, if you want to store 1000 numbers?  Defining 1000 variables is a pity!  Requires much programming effort  Any better solution?  Yes, some structured data type o Array is one of the most common structured data types o Saves a lot of programming effort (cf. 1000 variable names)

4. What is an Array?  A collection of data elements in which  all elements are of the same data type, hence homogeneous data o An array of students’ marks o An array of students’ names o An array of objects (OOP perspective!)  elements (or their references) are stored at contiguous/ consecutive memory locations  Array is a static data structure  An array cannot grow or shrink during program execution – its size is fixed

5. Basic concepts  Array name (data)  Index/subscript (0...9)  The slots are numbered sequentially starting at zero (Java, C++)  If there are N slots in an array, the index will be 0 through N-1  Array length = N = 10  Array size = N x Size of an element = 40  Direct access to an element

6. Homogeneity  All elements in the array must have the same data type Index: Value: 5101830455060657080 01234 5678 9 Index: Value: 5.510.218.545.660.5 0124 3 Index: Value: ‘A’10.255‘X’ 60.5 0124 3 Not an array

7. Contiguous Memory  Array elements are stored at contiguous memory locations  No empty segment in between values (3 & 5 are empty – not allowed) Index: Value: 5101830455060657080 01234 5678 9 Index: Value: 510184560657080 01234 5678 9

8. Declaring and Creating Arrays Declaring and Creating arrays ◦ Arrays are objects that occupy memory ◦ Created dynamically with keyword new int c[] = new int[ 12 ];  Equivalent to int c[]; // declare array variable c = new int[ 12 ]; // create array  We can create arrays of objects too String b[] = new String[ 100 ];

9. Using Arrays  Array_name[index]  For example, in Java  System.out.println(data[4]) will display 0  data[3] = 99 will replace -3 with 99

10. Using Arrays  Array_name[index]  For example, in Java  System.out.println(data[4]) will display 0  data[3] = 99 will replace -3 with 99

11. Using Arrays  Using an array initializer  Use initializer list Items enclosed in braces ( {} ) Items in list separated by commas int n[] = { 10, 20, 30, 40, 50 }; Creates a five-element array Index values of 0, 1, 2, 3, 4  Do not need keyword new

12. Using Arrays (Cont.)  To declare an array follow the type with (empty) []s int[] grade; //or int grade[]; //both declare an int array  In Java arrays are objects so must be created with the new keyword  To create an array of ten integers: int[] grade = new int[10]; Note that the array size has to be specified, although it can be specified with a variable at run-time

13. Examples Using Arrays (Cont.) Calculating the value to store in each array element –Initialize elements of 10-element array to even integers

14. Examples Using Arrays (Cont.) InitArray.java Line 10 Declare array as an array of int s Line 12 Create 10 int s for array Line 16 Use array index to assign array value

15. Examples Using Arrays (Cont.)

16.  Summing the elements of an array  Array elements can represent a series of values We can sum these values

17. Some more concepts  data[ -1 ] always illegal  data[ 10 ] illegal (10 > upper bound)  data[ 1.5 ] always illegal  data[ 0 ] always OK  data[ 9 ] OK  Q. What will be the output of? 1. data[5] + 10 2. data[3] = data[3] + 10

18. Array’s Dimensionality  One dimensional (just a linear list)  e.g.,  Only one subscript is required to access an individual element  Two dimensional (matrix/table)  e.g., 2 x 4 matrix (2 rows, 4 columns) 5101830455060657080 Col 0Col 1Col 2Col 3 Row 020256040 Row 130157090

19. Multidimensional arrays  Multidimensional arrays  Tables with rows and columns Two-dimensional array Declaring two-dimensional array b[2][2] int b[][] = { { 1, 2 }, { 3, 4 } }; 1 and 2 initialize b[0][0] and b[0][1] 3 and 4 initialize b[1][0] and b[1][1] int b[][] = { { 1, 2 }, { 3, 4, 5 } }; row 0 contains elements 1 and 2 row 1 contains elements 3, 4 and 5

20. Multidimensional arrays (Cont.)  Creating multidimensional arrays  Can be allocated dynamically 3 -by- 4 array int b[][]; b = new int[ 3 ][ 4 ]; Rows can have different number of columns int b[][]; b = new int[ 2 ][ ]; // allocate rows b[ 0 ] = new int[ 5 ]; // allocate row 0 b[ 1 ] = new int[ 3 ]; // allocate row 1

21. Multidimensional arrays (Cont.) a[ 1 ][ 0 ]a[ 1 ][ 1 ]a[ 1 ][ 2 ]a[ 1 ][ 3 ] Row 0 Row 1 Row 2 Column 0Column 1Column 2Column 3 Row index Array name Column index a[ 0 ][ 0 ]a[ 0 ][ 1 ]a[ 0 ][ 2 ]a[ 0 ][ 3 ] a[ 2 ][ 0 ]a[ 2 ][ 1 ]a[ 2 ][ 2 ]a[ 2 ][ 3 ]

22. Multidimensional arrays (Cont.) InitArray.jav a Line 16 Declare array1 with six initializers in two sublists Line 17 Declare array2 with six initializers in three sublists

23. Multidimensional arrays (Cont.) InitArray.java Line 34 array[row].leng th returns number of columns associated with row subscript Line 35 Use double-bracket notation to access two- dimensional array values

24. Searching Arrays: Linear Search and Binary Search  Searching  Finding elements in large amounts of data Determine whether array contains value matching key value  Linear searching  Binary searching

25. Searching Arrays: Linear Search and Binary Search (Cont.)  Linear search  Compare each array element with search key If search key found, return element index If search key not found, return –1 (invalid index)  Works best for small or unsorted arrays  Inefficient for larger arrays

26. Linear Search LinearSearch.java Line 11 Declare array of int s

27. Linear Search(Cont.) LinearSearch.java Lines 39-42 Allocate 100 int s for array and populate array with even int s Line 50 Loop through array Lines 53-54 If array element at index matches search key, return index

28. Linear Search(Cont.) LinearSearch.java Line 61 Invoked when user presses Enter Line 68 Invoke method linearSearch, using array and search key as arguments

29. Binary Search  Binary search ◦ Efficient for large, sorted arrays ◦ Eliminates half of the elements in search through each pass  Compare middle array element to search key  If element equals key  Return array index  If element is less than key  Repeat search on first half of array  If element is greater then key  Repeat search on second half of array  Continue search until  element equals search key (success)  Search contains one element not equal to key (failure)

30. Binary Search (Cont.) Declae array of int s BinarySearch.java Line 14 Declare array of int s

31. Binary Search (Cont.) BinarySearch.java Lines 48-51 Allocate 15 int s for array and populate array with even int s Line 56 Invoked when user presses Enter

32. Binary Search (Cont.) BinarySearch.java Line 65 Invoke method binarySearch, using array and search key as arguments

33. Binary Search (Cont.) BinarySearch.java Lines 93-94 If search key matches middle array element, return element index Lines 97-98 If search key is less than middle array element, repeat search on first array half Lines 101-102 If search key is greater than middle array element, repeat search on second array half Lines 112-137 Method build- Output displays array contents being searched

34. Binary Search (Cont.) BinarySearch.java Line 128 Display an asterisk next to middle element

35. Binary Search (Cont.)