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Week # 2: Arrays
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 representationo Linear (Arrays/linked lists)o Non-linear (Trees/graphs)
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)
A collection of data elements in which all elements are of the same data type, hence homogeneous data
o 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
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
All elements in the array must have the same data type
Index:
Value: 5 10 18 30 45 50 60 65 70 80
0 1 2 3 4 5 6 7 8 9
Index:
Value: 5.5 10.2 18.5 45.6 60.5
0 1 2 43
Index:
Value: ‘A’ 10.2 55 ‘X’ 60.5
0 1 2 43
Not an array
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 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 ];
Array_name[index] For example, in Java
System.out.println(data[4]) will display 0
data[3] = 99 will replace -3 with 99
Array_name[index] For example, in Java
System.out.println(data[4]) will display 0
data[3] = 99 will replace -3 with 99
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
To declare an array follow the type with (empty) []sint[] grade; //orint 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
• Calculating the value to store in each array element– Initialize elements of 10-element array to even integers
InitArray.java
Line 10Declare array as an array of ints
Line 12Create 10 ints for array
Line 16Use array index to assign array value
Summing the elements of an array◦ Array elements can represent a series of values
We can sum these values
Histogram.java
Line 9Declare array with initializer list
Line 19For each array element, print associated number of asterisks
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] + 102. data[3] = data[3] + 10
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
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
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 ]
InitArray.java
Line 16Declare array1 with six initializers in two sublists
Line 17Declare array2 with six initializers in three sublists
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◦ Finding elements in large amounts of data
Determine whether array contains value matching key value
◦ Linear searching◦ Binary searching
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
LinearSearch.java
Line 11Declare array of ints
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
LinearSearch.java
Line 61 Invoked when user presses Enter
Line 68Invoke method linearSearch, using array and search key as arguments
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)
Declae array of ints
BinarySearch.java
Line 14Declare array of ints
BinarySearch.java
Lines 48-51Allocate 15 ints for array and populate array with even ints
Line 56Invoked when user presses Enter
BinarySearch.javaLine 65Invoke method binarySearch, using array and search key as arguments
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
BinarySearch.java
Line 128Display an asterisk next to middle element
SortingSorting
Motivation Generally, to arrange a list of elements in some order
List of numbers 10 20 50 30 40 60 25 (Unsorted list) 10 20 25 30 40 50 60 (Sorted list,
ascending) 60 50 40 30 25 20 10 (Sorted list,
descending) List of alphabets
P A K I S T A N (Unsorted list) A A I K N P S T (Sorted list, ascending) T S P N K I A A (Sorted list, descending)
Sorting AlgorithmsSorting AlgorithmsSorting AlgorithmsSorting Algorithms
1. Bubble Sort
2. Selection Sort
There are few more sorting algorithms; you can find them in a book on data structures and algorithms (or on the Web)
Bubble Sort Algorithm: Bubble Sort Algorithm: InformalInformalBubble Sort Algorithm: Bubble Sort Algorithm: InformalInformal Repeatedly compare the elements at
consecutive locations in a given list, and do the following until the elements are in required order:
If elements are not in the required order, swap them (change their position)
Otherwise do nothing
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Bubble Sort in Action: Bubble Sort in Action: Phase 1Phase 1
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Bubble Sort in Action: Bubble Sort in Action: Phase 2Phase 2
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Bubble Sort in Action: Bubble Sort in Action: Phase 3Phase 3
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Bubble Sort in Action: Bubble Sort in Action: Phase 4Phase 4
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Bubble Sort in Action: Bubble Sort in Action: Phase 5Phase 5
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Bubble Sort in Action: Bubble Sort in Action: Phase 6Phase 6
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Bubble Sort in Action: Bubble Sort in Action: Phase 7Phase 7
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Bubble Sort in Action: Bubble Sort in Action: Phase 8Phase 8
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Bubble Sort Algorithm in Bubble Sort Algorithm in JavaJava
Bubble Sort Algorithm in Bubble Sort Algorithm in JavaJava void bubbleSort(int List[])
{ int temp; int size = List.length; for (i = 0; i < size - 1; i++) {
for (j = 0; j < size – (i + 1); j++) { if (List[j] > List[j+1]) { //swap
temp = List[j];List[j] = List[j+1];List[j+1] = temp;
} }
}}
