Data Structures

Arrays

Arrays

• An array is a homogeneous aggregate of data elements in which an individual element is identified by its position in the aggregate relative to the first element.

A [ ][ ][ ][ G ][ … ][ ][ ] A[G] -> Access the Gth element of the array.

• The operation that selects a component from the array is called scripting or indexing.

Array_Name[ Subscript_Value ]

• Selection operation can be though as a mapping from the array name and a set of subscript values to an element of the aggregate.

Arrays: Stack Representation

Arrays: Array Descriptor

Array Descriptor in Stack

Arrays: L-Value (L-Address)

• Let us assume that the 1st element of the array “A” begins at location .

L-Value(A[ N ]) = + ( N – LB ) * EL-Value(A[ N ]) = – LB * E + N * E K = – LB * E and is a constant value.L-Value(A[ N ]) = K + N * EWhen E = 1 and LB = 0, then:L-Value(A[ N ]) = + N

• B: Array[ 3 … 10 ] of INT

= 100 L-Value(B[ 4 ]) = 100 – 3 + 4 = 101LB = 3 E = 1LB ≤ N ≤ UB

Arrays: Virtual Origin (VO)

• So far we know:

L-Value(A[ N ]) = ( – LB * E) + ( N * E )

• And for A[ 0 ]:

L-Value(A[ 0 ]) = ( – LB * E) + ( 0 * E )

• Sometimes the lower bound of the array could be greater than zero. This address is called the virtual origin.

Arrays: Finding the Virtual Origin

1. On creation of vector storage, allocate “N” ( UB – LB + 1) components of the vector of size E and the descriptor of size “D”.

2. Compute the Virtual Origin:VO = – LB * E

Example: VO = 100 – 3 * 1 = 97

3. On accessing an array component (assuming LB N UB):L-Value(A[ N ]) = VO + N * E

Arrays: Finding the Virtual Origin

• Example:

A[ 3 … N]

Assuming: = 100

E = 1VO = 97 (See previous slide, step 2)

L-Value(A[ 4 ]) = VO + N * E

= 97 + 4 * 1

= 101

Arrays: Multidimensional Arrays

• Ordering:Example: M = 3, 4, 7, 6, 2, 5, 1, 3, 8

• Row major order:

M:

• Column major order:

M:

3 4 7

6 2 5

1 3 8

3 6 1

4 2 3

7 5 8

Arrays: Multidimensional Arrays

• Storage• Location of A[ N , J ] is given by:

L-Value( A[ N , J ] ) = + ( N – LB1 ) * S + ( J – LB2 ) * E

= Base Address

S = Length of a Row ( UB2 – LB2 + 1) * E

VO = – LB1 * S – LB2 * E

• Example:L-Value( A[ N , J ]) = VO + N * S + J * E

L-Value( A[ 2 , 3 ]) = ( 2 * row length) + 3

Arrays: Multidimensional Arrays

• Slices– Slices of a 2 dimensional array (matrix) are treated as an array.

• L-Value( A[ N , J ] ) = VO + N * 3 + J * 1VO = – LB1 * S – LB2 * E = – 4Assuming that a = 100:VO = 96L-Value( A[ 2 , 2 ] ) = VO + N * 3 + 2 * 1

= 96 + 2 * 3 + 2 * 1= 96 + 6 + 2= 104

DESCRIPTOR

VO – 4

LB1 1

UB1 4

MULTIPLIER 3

LB2 1

UB2 3

MULTIPLIER 1

Data Structures

Dynamic Arrays

Dynamic Arrays

A[ ] ≡

A[ ] ≡

A[ ][ ] [ ] ≡

x

Dynamic Arrays

New int [100]

int finalMark – allocating space in memory

(a way to access that memory location)

finalMark[ ] = new int [100]

int marks[ ][ ] = new int [3][2]

Dynamic Arrays (Continued)

finalMark

pointer arithmetic

Dynamic Arrays (Continued)

List [3]

List [2]List [1]List [0]

1000 1008 1016P

P + K ≡ &List[K] (pointer arithmetic)

AR

xy

AR

x

y

ARRAY DESCRIPTION

DESCRIPTOR

DESCRIPTOR

DESCRIPTOR

1000i x 8

Data Structures

Records

• A record is a heterogeneous data structure composed of a fixed number of components of different types

• The record elements are referenced by names (identifiers)• Records were introduced by COBOL

Example: 01 Employee – Name

02 Employee – Name

05 First Name Picture is x(20)

05 Middle Name Picture is x(10)

05 Last Name Picture is x(20)

02 Hourly Rate Picture is 99v99

Name Hourly Rate

First Middle Last

Let us assume we have a record structure called employee with 4 fields

(ID, AGE, SALARY, DEPT)

To address a component of the array, the selector operator “.” is used.

Example: Employee.ID;

Employee.DEPT;

int int int int

ID

AGE

SALARY

DEPT

Record Example

L-Address (value) (R.I.)

L-Address (R.I.) = α + ∑ (size of R.J.)

We need a record descriptor

I = 1

J = 1

Field J

R.I. Field

α

Record DescriptionRECORD

NAME

TYPE

.

.

.

OFFSET

TYPE

NAME

TYPE

OFFSET

NAME

TYPE

OFFSET

During Execution Time{{

{

FIELD 1

FIELD 2

FIELD N

RECORD

NAME

TYPE

OFFSET

NAME

TYPE

OFFSET

NAME

TYPE

OFFSET

α

L-value (R.I) = α + KI

OFFSET

A

ID AGE DEPT SALARY

Record Description (Continued)

ARRAY DESCRIPTOR

Y

X

UB – Upper Bound

LB – Lower Bound

RECORD DESCRIPTOR

β

A[I].ID

AR

α

A[I]

DESCRIPTOR

UB LB

{

(offset is the same for each element) → use one record descriptor

(displacement)