CS212 Programming II Arrays Dick Steflik Abstract Data

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 storage retrieve(A, i) – return v at position i in A store(A, I, v) – store v at position i in A destroy(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); )

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 4 th 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) = 100 C 16 base 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; { char name[16]; date. Of. Birth; } student; date pearl. Harbor. Day; // 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 { { char name[10]; short age; int children; float salary; char beard; date dob; } u; }; typedef struct human 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 2 x 2 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

cont. int a[2][2] 0 x 100000 0, 0 0 x 100004 0, 1 0 x 100008 1, 0 0 x 10000 C 1, 1 0123 This storage arrangement is known as: Row Major Order a[m][n] ) SMF = base addr + (dim(n) * element size * indexm ) + (element size * indexn ) ex. a[1][1] addr = 100000 + (2 * 4 * 1) + (4 * 1) = 100000 + 8 + 4 = 0 x 10000 C

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 one dimensional array where: // an array of struct index represents the exponent #define MAXSIZE 10 and the stored value is the typedef struct { corresponding coefficient real coeff; OR 2 x 8 + 4 x 2 + 1 int expnt; } term poly 1[MAXSIZE]; term poly 2[MAXSIZE]; 0 1 2 3 4 5 6 7 8 9 1 4 2 term poly 3[MAXSIZE];

Identity Matrix • Only has values on the major diagonal 0 1 v 0 0 2 0 AMF[m][n] if (m == n) 1 0 2 0 v 0 0 v 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