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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 allocationo Static (or fixed sized) data structures (Arrays)o Dynamic data structures (Linked lists)
Based on representationo Linear (Arrays/linked lists)o 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
o Array is one of the most common structured data typeso 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
datao An array of students’ markso An array of students’ nameso 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
All elements in the array must have the same data type
Index:
Value: 5 10 18 30 45 50 60 65 70 800 1 2 3 4 5 6 7 8 9
Index:
Value:
5.5 10.2 18.5 45.6 60.50 1 2 43
Index:Value: ‘A’ 10.2 55 ‘X’ 60.5
0 1 2 43
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:
Value: 5 10 18 30 45 50 60 65 70 80
0 1 2 3 4 5 6 7 8 9
Index:
Value: 5 10 18 45 60 65 70 80
0 1 2 3 4 5 6 7 8 9
Declaring and Creating ArraysDeclaring 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 tooString 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 commasint 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) []sint[] 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
– Initialize elements of 10-element array to even integers
Examples Using Arrays (Cont.)
InitArray.java
Line 10Declare array as an array of ints
Line 12Create 10 ints for array
Line 16Use array index to assign array value
Examples Using Arrays (Cont.) Summing the elements of an array
Array elements can represent a series of values We can sum these values
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
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
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.)
a[ 1 ][ 0 ] a[ 1 ][ 1 ] a[ 1 ][ 2 ] a[ 1 ][ 3 ]
Row 0
Row 1
Row 2
Column 0 Column 1 Column 2 Column 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 ]
Multidimensional arrays (Cont.)
InitArray.java
Line 16Declare array1 with six initializers in two sublists
Line 17Declare array2 with six initializers in three sublists
Multidimensional arrays (Cont.)
InitArray.java
Line 34array[row].length returns number of columns associated with row subscript
Line 35Use double-bracket notation to access two-dimensional array values
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
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
Linear Search(Cont.)LinearSearch.javaLines 39-42Allocate 100 ints for array and populate array with even ints
Line 50Loop through array
Lines 53-54If array element at index matches search key, return index
Linear Search(Cont.)
LinearSearch.java
Line 61 Invoked when user presses Enter
Line 68Invoke method linearSearch, using array and search key as arguments
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.)BinarySearch.java
Lines 48-51Allocate 15 ints for array and populate array with even ints
Line 56Invoked when user presses Enter
Binary Search (Cont.)
BinarySearch.javaLine 65Invoke method binarySearch, using array and search key as arguments
Binary Search (Cont.)BinarySearch.javaLines 93-94If search key matches middle array element, return element indexLines 97-98If search key is less than middle array element, repeat search on first array halfLines 101-102If search key is greater than middle array element, repeat search on second array halfLines 112-137Method build-Output displays array contents being searched