Arrays Week 2

Data Structures Data structure Types of data structures 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 Static (or fixed sized) data structures (Arrays) Dynamic data structures (Linked lists) Based on representation Linear (Arrays/linked lists) Non-linear (Trees/graphs)

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 Array is one of the most common structured data types Saves a lot of programming effort (cf. 1000 variable names)

What is an Array? A collection of data elements in which all elements are of the same data type, hence homogeneous data An array of students’ marks An array of students’ names 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

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

Homogeneity Index: 1 2 3 4 5 6 7 8 9 All elements in the array must have the same data type 5 10 18 30 45 50 60 65 70 80 Value: Value: 1 2 4 3 5.5 10.2 18.5 45.6 60.5 Index: 1 2 4 3 Index: Value: ‘A’ 10.2 55 ‘X’ 60.5 Not an array

Contiguous Memory Array elements are stored at contiguous memory locations No empty segment in between values (3 & 5 are empty – not allowed) Index: 1 2 3 4 5 6 7 8 9 Value: 5 10 18 30 45 50 60 65 70 80 1 2 3 4 5 6 7 8 9 Index: Value: 5 10 18 45 60 65 70 80

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 ];

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

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

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

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

Examples Using Arrays (Cont.) Calculating the value to store in each array element creates a 10-element array and assigns to each element one of the even integers from 2 to 20 (2, 4, 6, …, 20).

Examples Using Arrays (Cont.)

Examples Using Arrays (Cont.) Output:

Examples Using Arrays (Cont.) Summing the elements of an array Array elements can represent a series of values We can sum these values

22-Feb-19 Computer Science Department

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? data[5]  + 10 data[3] = data[3] + 10

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) 5 10 18 30 45 50 60 65 70 80 Col 0 Col 1 Col 2 Col 3 Row 0 20 25 60 40 Row 1 30 15 70 90

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

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

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

Multidimensional arrays (Cont.)

Multidimensional arrays (Cont.)

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

Searching Arrays: Linear Search and Binary Search (Cont.) 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

Linear Search

Linear Search(Cont.) Output: Key 34 found at index: 6

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)

Binary Search (Cont.)

Binary Search (Cont.) Output: Key 14's position: 6

Binary Search Example