Arrays

ARRAYS
 The Array is the most commonly used Data Structure.
 An array is a collection of data elements that are of the same type (e.g.,
a collection of integers, collection of characters, collection of doubles).
OR
 Array is a data structure that represents a collection of the same types
of data.
 The values held in an array are called array elements
 An array stores multiple values of the same type – the element type
 The element type can be a primitive type or an object reference
 Therefore, we can create an array of integers, an array of characters, an
array of String objects, an array of Coin objects, etc.
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Array Applications
 Given a list of test scores, determine the maximum and minimum scores.
 Read in a list of student names and rearrange them in alphabetical order
(sorting).
 Given the height measurements of students in a class, output the names of
those students who are taller than average.
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Array Declaration
 Syntax:
<type> <arrayName>[<array_size>]
Ex. int Ar[10];
 The array elements are all values of the type <type>.
 The size of the array is indicated by <array_size>, the number
of elements in the array.
 <array_size> must be an int constant or a constant expression.
Note that an array can have multiple dimensions.
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Array Declaration
// array of 10 uninitialized ints
int Ar[10];
0 1 2 3 4 5 6 7 8 9
Ar -- -- -- -- -- -- -- -- -- --
0 1 2 3 4 5
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Subscripting
 Declare an array of 10 integers:
int Ar[10]; // array of 10 ints
 To access an individual element we must apply a subscript to array named
Ar.
 A subscript is a bracketed expression.
 The expression in the brackets is known as the index.
 First element of array has index 0.
Ar[0]
 Second element of array has index 1, and so on.
Ar[1], Ar[2], Ar[3],…
 Last element has an index one less than the size of the array.
Ar[9]
 Incorrect indexing is a common error.
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Subscripting
// array of 10 uninitialized ints
int Ar[10];
Ar[3] = 1;
int x = Ar[3];
0 1 2 3 4 5 6 7 8 9
Ar -- -- -- 1 -- -- -- -- -- --
Ar[0] Ar[1] Ar[2] Ar[3] Ar[4] Ar[5] Ar[6] Ar[7] Ar[8] Ar[9]
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Subscripting Example
#include <stdio.h>
int main ()
{
int n[10]; /* n is an array of 10 integers */
int i,j;
/* initialize elements of array n to 0 */
for ( i = 0; i < 10; i++ )
{
n[ i ] = i + 100; /* set element at location i to i + 100 */
}
/* output each array element's value */
for (j = 0; j < 10; j++ )
{
printf("Element[%d] = %dn", j, n[j] );
}
return 0;
}
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Multidimensional Arrays
 An array can have many dimensions – if it has more than one dimension, it
is called a multidimensional array
 Each dimension subdivides the previous one into the specified number of
elements
 Each dimension has its own length constant
 Because each dimension is an array of array references, the arrays within
one dimension can be of different lengths
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Multidimensional Arrays
2 Dimensional 3 Dimensional
Multiple dimensions get difficult to visualize graphically.
•
double Coord[100][100][100];
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Processing Multi-dimensional Arrays
The key to processing all cells of a multi-dimensional array is nested
loops.
[0] [1] [2] [3]
[0]
[1]
[2]
10 11 12 13
14 15 16 17
18 19 20 21
22 23 24 25
26 27 28 29
[3]
[4]
for (int row=0; row!=5; row++) {
for (int col=0; col!=4; col++) {
System.out.println( myArray[row][col] );
}
}
for (int col=0; col!=4; col++) {
for (int row=0; row!=5; row++) {
System.out.println( myArray[row][col] );
}
}
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Two-Dimensional Arrays
• A one-dimensional array stores a list of elements
• A two-dimensional array can be thought of as a table of
elements, with rows and columns
two
dimensions
one
dimension
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Two-Dimensional Arrays [Cont…]
A two-dimensional array consists of a certain number of rows and columns:
const int NUMROWS = 3;
const int NUMCOLS = 7;
int Array[NUMROWS][NUMCOLS];
0 1 2 3 4 5 6
0 4 18 9 3 -4 6 0
1 12 45 74 15 0 98 0
2 84 87 75 67 81 85 79
Array[2][5] 3rd value in 6th column
Array[0][4] 1st value in 5th column
The declaration must specify the number of rows and the number of columns,
and both must be constants.
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Address calculation using column
and row major ordering
 In computing, row-major order and column-major order describe methods
for storing multidimensional arrays in linear memory.
 By following standard matrix notation, rows are numbered by the first index
of a two-dimensional array and columns by the second index.
 Array layout is critical for correctly passing arrays between programs
written in different languages. It is also important for performance when
traversing an array because accessing array elements that are contiguous in
memory is usually faster than accessing elements which are not, due
to caching.
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Row-major order  In row-major storage, a multidimensional array in linear memory is
organized such that rows are stored one after the other. It is the
approach used by the C programming language, among others.
 For example, consider this 2×3 array:
1 2 3
4 5 6
 An array declared in C as
int A[2][3] = { {1, 2, 3}, {4, 5, 6} };
is laid out contiguously in linear memory as:
1 2 3 4 5 6
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Row-major order[Cont…]
 To traverse this array in the order in which it is laid out in memory, one
would use the following nested loop:
for (row = 0; row < 2; row++)
for (column = 0; column < 3; column++)
printf("%dn", A[row][column]);
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Column-major order
 Column-major order is a similar method of flattening arrays
onto linear memory, but the columns are listed in sequence.
 The scientific programming languages Fortran and Julia, the
matrix-oriented languages MATLAB and Octave, use column-major
ordering. The array
1 2 3
4 5 6
 if stored contiguously in linear memory with column-major
order looks like the following:
1 4 2 5 3 6
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THANK YOU….. !!!
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