CS-212 Programming II

Arrays

Dick Steflik

Abstract Data Type

• A collection of pairs <index,value> where index is an ordered set of integers and the values are of some data type that is constant for the array.

• not all languages require the index to be continuous or contiguous or start at 0 or 1.

• In C, arrays are zero based and are contiguous from 0 to size-1 and can contain any simple or aggregate data type

ADT (cont.)

• Pascal allows discontinous indicies– A(2:5, 10:20, 26) other index values are

undefined and take up no memory

• Perl allows indicies that are not integers but are literal values (called an associative array)– A[tom] , A[dick], A[harry]

ADT (cont.)

• Static arrays – arrays allocated at compile time

• Dynamic arrays – arrays allocated by the storage management system at program run time– most embedded systems that run without an

OS don’t have dynamic storage allocation

ADT Operations

• Basic operations:create(A) – allocates storageretrieve(A,i) – return v at position i in A store(A,I,v) – store v at position i in Adestroy(A) – deallocate storage associated with A

create

• static storage : int a[10]; //40 bytes char word[25]; //25 bytes– allocated as part of the program space by the

compiler.– &a is equivalent to a and is the address of a[0]

– once allocated cannot be deallocated, will always take up program space

• can be initialized by compiler using an initializer (ex. int A[5] = (0,0,0,0,0); )

create

• Dynamic : storage is allocated at run-time using malloc, cmalloc or realloc #define SIZE 10 int * myarray; myarray = (int *) malloc (SIZE*sizeof(int)); makes an array of 10 integers named myarray

• cmalloc works same way but initializes array to 0– initialization to anything else requires a loop

• realloc will resize a previously allocated array to bigger or smaller

• since this happens at run time, time is expended

store

• done the same way for both static and dynamic arrays by using the assignment operator (=)

a[5] = 9;

retrieve

• retrieving a value from some position in an array is done the same way for both static and dynamic arrays using the array position implicitly. x[3] ; //the value of the 4th element of x

• can be used this way in any assignment, arithmetic/logical operation or as an argument in a function call

destroy

• destruction of a statically allocated array happens when the program is done

• destruction of dynamically allocated arrays is done using the free(arrayname) function, this returns the storage to the storage management system for subsequent allocation for something else.

• forgetting to deallocate unneeded storage is called a “memory leak” and can cause a program to terminate abnormally (crash/hang)

memory• remember, a computer’s memory is really an

array of bytes (indicies 0 to size-1)• every time an array access (retrieve or store) is

done the machine must make a calculation to see where in memory the desired location is: ex int a[5]; a[3]=2; to calculate the address of a[3] address=base address+(index*element size) = 100016 + (3*4) = 100C16base address is assigned by compiler for static and by SMS for dynamic and

kept track of in a system table for run time

Structures• Allows us to create an aggregate data

type: typedef struct { char name[10]; int age; } person; person tom; - tom takes up 14 bytes of storage; 10 for name and the next 4 for age

Structures

• Structures can be embedded within one another:

typedef struct

{ int month;

int date;

int year;

} date;

typedef struct

{ char name[16];

date dateOfBirth;

} student;

date pearlHarborDay; // 12 bytes of storage

student typical; // 28 bytes of storage

student class[30]; // 840 bytes of storage

Unions• A union is like a structure but the fields don’t

always have to have the same definition

typedef struct sextype

{ enum tag (female, male) sex;

union {

int children;

char beard;

} u;

};

typedef struct human

{ char name[10];

short age;

float salary;

date dob;

sextype sexinfo;

};

The compiler will always reserve the maximum number bytes for the union; i.e.

even though sextype for women is 4 bytes and only one byte for men the compiler will always reserve 4.

Self-Referential Structures

• Structure that refers to an item of the same type.

• used for dynamic data structures like lists and trees.

typedef struct

{ int key;

node * next;

} node;

Array Mapping Functions

• Used by the compiler to help calculate the effective address of an array element in memory

• Takes into account: base address the dimension the element size

2 dimensional arrays

• int a[2][2] can be visualized as a 2x2 square matrix but is really an array of two elements where each element is an array of two ints

0

0 1

1

0

1

0 1

0 1

cont.

0x100000

0x100004

0x100008

0x10000C

0,0

0,1

1,0

1,1

int a[2][2]

This storage arrangement is known as:

Row Major Order

0 1 2 3

SMF = base addr + (dim(n) * element size * indexm ) + (element size * indexn )

a[m][n])

ex. a[1][1]

addr = 100000 + (2 * 4 * 1) + (4 * 1)

= 100000 + 8 + 4 = 0x10000C

Sparse Arrays

• arrays where many or most of the elements will have the value zero (or possibly the same value)

• examples: high order polynomials, bit mapped graphics, linear algebra ( diagional matricies(identity matrix, tridiagonal, banded), triangular matrices, )

Polynomial representation

// an array of struct

#define MAXSIZE 10

typedef struct {

real coeff;

int expnt;} term

term poly1[MAXSIZE];

term poly2[MAXSIZE];

term poly3[MAXSIZE];

one dimensional array where:

index represents the exponent

and the stored value is the

corresponding coefficient

0 1 2 3 4 5 6 7 8 9

2x8 + 4x2 + 1

241

OR

Identity Matrix• Only has values on the major diagonal

v0 0

v 0 0

0 0 v

0 1 2

0

1

2

AMF[m][n]

if (m == n)

return v

else return 0

map it on top of a one dimensional array of three elements

v v v AMF[m][n]

if ( m == n ) return A[m] else return 0