1. Chapter 6
Part 1

2. Array Implementation 1D Array … 1 2 k-1 k n M Memory Base Address… 1 2
k-1 k n M
1D Array
Memory
Base Address
Address(list[k]) = address(list[1]) + (k-1) * element_size
Generalization:
Address(list[k]) = address(list[lower_bound]) + (k - lower_bound) * element_size
Example: Array A with following information:
10 elements
Element size = 10 bytes
Base address = 1500
Lower bound = 0
Address( A[5]) = ?
Address( A[5]) = *10 = 1550

3. 2D Arrays 1) Row Major Order 2) Column Major Order
2 common ways for mapping 2D arrays to 1D:
1) Row Major Order
2) Column Major Order
Ex: Would be stored as 3, 4, 7, 6, 2, 5, 1, 3, 8
Ex: Would be stored as 3, 6, 1, 4, 2, 3, 7, 5, 8

4. 2D Array - Row Major Order
In general: address of an element =
base address + element size * number of elements that precede it.
2D Array - Row Major Order 1 2
j-1 j n …
i-1 i m
. . .

5. 2D Array - Row Major Order
In general: address of an element =
base address + element size * number of elements that precede it.
2D Array - Row Major Order 1 2
j-1 j n …
i-1 i m
. . .

6. 2D Array - Row Major Order
In general: address of an element =
base address + element size * number of elements that precede it.
2D Array - Row Major Order 1 2
j-1 j n …
i-1 i m
. . .
Address(a[i,j]) = address(a[1,1]) + ((((number of rows above i)* (row size)) + (number of elements left j)) * element size)
= address(a[1,1]) + ((((i-1)* n) + (j-1)) * element_size)
Generalization:
Address(a[i,j]) = address(a[row_lb,col_lb]) + ((((i-row_lb)* n) + (j-col_lb)) * element_size)

7. 2D Array - Row Major Order
In general: address of an element =
base address + element size * number of elements that precede it.
2D Array - Row Major Order 1 2
j-1 j n …
i-1 i m
. . .
Example: Array A with following information:
15 rows and 5 columns
Element size = 10 bytes
Base address = 1000
Row lower bound =column lower bound = 0
Address( A[2,3]) = ?
Address( A[2,3]) = (((2-0)*5) + (3-0)) *10 = 1130

8. 2D Array - Column Major Order
In general: address of an element =
base address + element size * number of elements that precede it.
2D Array - Column Major Order 1 2
j-1 j n …
i-1 i m
. . .

9. 2D Array - Column Major Order
In general: address of an element =
base address + element size * number of elements that precede it.
2D Array - Column Major Order 1 2
j-1 j n …
i-1 i m
. . .

10. 2D Array - Column Major Order
In general: address of an element =
base address + element size * number of elements that precede it.
2D Array - Column Major Order 1 2
j-1 j n …
i-1 i m
. . .
Address(a[i,j]) = address(a[1,1]) + ((((number of columns left j)* (col size)) + (number of elements above i)) * element size)
= address(a[1,1]) + ((((j-1)* m) + (i-1)) * element_size)
Generalization:
Address(a[i,j]) = address(a[row_lb,col_lb]) + ((((j-col_lb)* m) + (i-row_lb)) * element_size)

11. 2D Array - Column Major Order
In general: address of an element =
base address + element size * number of elements that precede it.
2D Array - Column Major Order 1 2
j-1 j n …
i-1 i m
. . .
Example: Array A with following information:
15 rows and 5 columns
Element size = 10 bytes
Base address = 1000
Row lower bound =column lower bound = 0
Address( A[2,3]) = ?
Address( A[2,3]) = (((3-0)*15) + (2-0)) *10 = 1470

12. Address relative to the beginning of the record
Records
Record
Array
Used when a collection of data is heterogeneous.
All the data values have the same type.
Different fields are not processed in the same way.
Processed in the same way.
Number of components is fixed.
Fixed or variable.
Field names are static.
Subscripts are dynamic.
Faster access.
Slower access.
Compile-time descriptor
Record
Name
Type
Offset
. . .
Address
Field 1
Address relative to the beginning of the record
Field n

13. Example: Employee record
Compile-time descriptor
Example: Employee record
Field Name
Field Type
Field Size
Name
String
20 bytes
Salary
Double
8 bytes
Year
Integer
4 bytes
Record
Name
Type = String
Offset = 0
Salary
Type = double
Offset = 0+20 = 20
Year
Type = integer
Offset = = 28
Base Address
Field 1
Field 2
Address (Name) = base address + 0
Address (Salary) = base address + 20
Address (Year) = base address + 28
Field 3
Base Address
Name
Salary
Year M
20 bytes
8 bytes
4 bytes 20 28
Memory
Relative address = offset

14. Union
A union is a type that may store different type values at different times during execution.

15. Variant Records A single record type with several variants.
Specification:
In Pascal:
type PayType=(Salaried, Hourly);
var Employee:record
ID : integer;
Dept: array[1..3] of char;
Age : integer;
case PayClass : PayType of
Salaried:(MonthlyRate:real;
StartDate :integer);
Hourly :(HourRate:real;
Reg :integer;
Overtime:integer)
end
Common part
Variant part

16. In C: (use the ‘union’ keyword)
typedef enum {Salaried,Hourly} PayType;
typedef struct {
int ID;
char Dept[3];
int Age;
PayType PayClass;
PayVariant pay;
} EmployeeRecord;
EmployeeRecord Employee;
float MonthlyRate;
int StartDate;
} SalariedType ;
float HourRate;
int Reg, Overtime;
} HourlyType ;
typedef union {
SalariedType sal_type;
HourlyType hour_type;
} PayVariant ;
Common part
Variant part

17. Implementation: