Structured Data Types

1
Structured Data Types
2
Date Types

• We have seen various data types
• Integer, Real, Character, Logical
• All these types define data values of different
  kinds
• 128, 4500, 1, 0 (Integer)
• 0.5E19, 28.0, 0.214141E2 (Real)
• hari,maithoo,cs101, fortran (character strings)
• .True., .False. (logical)
• The Data types define, besides values,
• operations, relations and intrinsic functions
• A summary given here - refer to books/manuals for
  details

3
Numerical Data Types

• Constants 127, - 456, 12.76, 56.7 E 10, -
  0.12E-23
• Note decimal points in mantissa but not in
  exponent
• no commas allowed 12,23,600
• Operations ,,/,-
• Relations gt,lt,gt,lt,,/
• Intrinsic Functions
• Real, Nint,Int, Abs, Mod, Exp,Log, Sign, Sin,
  Cos, Sinh,Cosh,

4
Character Data Types

• Constants ABabDf, Fortran, CS101
• Note capital and small letters distinguished
• Operations //, (nm)
• Relations equality operators, , /
• Other comparison operators lt , lt, gt, gt
• ASCII encoding 8 bit encoding of characters
• A is 65, B is 66, etc
• a is 97, b is 98 etc

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Lexicographic Ordering

• Collating Sequence order in which characters
  occur in
• ASCII set
• Relation over individual characters based upon
  the collating sequence order
• eg. A lt E, Z lt a, d lt s
• How to compare strings?
• Dictionary ordering (Lexicographic ordering)
• eg. AAA lt AAB, AAA lt AAAA,
• AAAA lt AB
• Intrinsic Functions Trim, Len,

6
Logical Data Types

• Constants .true., .false.
• Operations .not., .and.,.or.,.equiv,
• .nequiv.

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Structured Data

• All these data types (except character) are
  atomic
• values are simple and non composite
• scalar data types
• Many real life entities are organized (or
  structured) collections of simpler data values
• students, accounts, employees (records with
  constituent items)
• pack of cards, tables, vectors, matrices
• queues, stacks, graphs
• Referring to the constituent data values rather
  than the whole
• results in loss of abstraction and clarity
• cumbersome

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Structured Data Types

• Modern PL enable design of rich set of structured
  data types to represent structured data
• They provide constructs using which complex and
  structured data types can be built from scalar
  types
• A PL provides
• fixed primitive types for representation of
  simple data value
• constructs for building organized collection from
  primitive types
• hence called user defined data types

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Single Dimensional Arrays

• Array is one of the simplest and most often used
  structure
• Examples Vectors, list of students ordered by
  roll
• numbers, array of cars
  in a parking lot
• Array data type is provided to represent such
  data
• Typical array values are
• (32, 45, 67, 100, 780) - integer array
• (4.50, 345.0E10, 28.25E-12) - real array
• (Fortran, Pascal, C, C, ADA) - character array
• (.true., .false., .true., .false., .false.,
  .true., .true.)
• logical array

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Properties of Arrays

• All entries in an array are values of identical
  types
• The data values are of some type, called the base
  type
• An array can contain one or more number of
  entries
• Every entry is associated with an index
• By default, the index of the first entry is 1,
  that of second 2, etc
• The number of entries is called the size or
  length of the array
• Any entry can be accessed directly by indicating
  its index hence called random access data
  structure
• Arrays are called single dimensional

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Example

• Let MARKS be an array (32,24,49,20,0)
• base type of MARKS is integer
• size or length of the array is 5
• MARKS(5) is 0 while MARKS(2) is 24
• Let Planets (Venus, Earth, Mars, Saturn,
  Uranus, Neptune, Pluto)
• base type is character
• length is 7
• Planets(4) is Saturn

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Array Declarations

• Program Variables can store array values like any
  other basic values
• Typical declarations
• Integer, Dimension(5) Marks
• Character(len8), Dimension(7) Planets
• base type and length mentioned in declarations
• The index of these arrays, also called as
  subscripts, start from 1 and end in the number
  specified
• The subscripts can start anywhere and end
  anywhere they should be specified then
• Integer, Dimension(-810) Students
• specifies the subscripts of Students to range
  from -8 to 10

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Array References

• Arrays can be referred in statements either as a
  whole or individually
• Individual array elements are like any other
  variable of the base type
• They can appear anywhere where the variables can
  appear, eg.
• Students(2) 5
• Marks(5) Students(2) 10
• Students(i) Student(i1)
• Passed(j) .TRUE.
• Planets(k) Jupiter
• if (Students(i) gt 0) then
• Type matching same as variables of the base type

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Whole array references

• The whole array variable can also appear on both
  rhs and lhs, eg.
• Planets (/ Mars,Earth,Pluto,Neptune,Venus,Jupite
  r /)
• Marks Students
• These are whole array assignments the types of
  both lhs and rhs should match
• Types of two array valued expressions match
  provided
• they evaluate to arrays
• of the same size and base type
• subscript ranges may be different
• The same constant value can be assigned to all
  elements of an array
• Passed .FALSE.
• All the array entries are assigned the value
  false useful for initialization

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Array Initialization

• Arrays can be initialized at declarations, eg.
• integer, dimension(10) a (/
  0,1,2,3,4,5,6,7,8,9 /)
• initializes array a to (0,1,2,3,4,5,6,7,8,9)
• Implied do loop (Shorthand notation for loops)
  can be used for initialization, eg.
• a (/ (2i, i1,10) /) ! i must be declared
  before use
• a (/ (i,i, i 1,10,2) /)
• a is 1,1,3,3,5,5,7,7,9,9

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Reading/Writing of Arrays

• Arrays may be read or printed as a whole, eg.
• read , a
• print , a
• Values input/output on a single line
• Implied do loops may also be used, eg.
• read , (a(i), i 1,n)
• values of a(1) to a(n), read on one line

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Array Sections

• Arrays can be referred as a whole, per entry or
  even in parts
• Parts of the arrays can be referred using
  sections, eg
• Given an array Ex declared as follows
• integer dimension(100), Ex
• Ex(8892) - part of the array
• Ex(8),Ex(10),...,Ex(88)
• Ex(1050) - references Ex(10),Ex(11),...,Ex(50)
• Ex(285) - refer to Ex(28),Ex(33),...,Ex(98)
• Ex(282) - null array
• Ex(1100) - whole section, referred directly as
  Ex itself

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Array Bounds

• Every array has bounds - lower and upper bounds
• The above array Ex has 1 as lower bound and 100
  as upper bound
• Ex(i) is defined provided 1 lt i lt 100
• Any reference to Ex(-25) or Ex(111) is illegal
  and may produce unknown results
• A reference is illegal or not can be detected,in
  general, at run-time only
• Ex(j) exceeds bound or not depends on value of j
  - not known at compile time
• Fortran compiler provides the option of detecting
  (at run-time) of array index exceeding bounds
• If this option is on, it inserts code, which can
  produce run-time errors
• If off, you have the responsibility for illegal
  references

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Operations on Arrays

• Array assignments involve expressions involving
  whole arrays
• Operations are defined over arrays depending upon
  the base type
• Operations are lifted' from the base type
• arithmetic operations over real and integer
  arrays
• logical operations over logical arrays
• Operations apply point wise' to the array
  entries
• Arrays involved should be of the same size

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Example

• integer, dimension(50) A, B
• integer, dimension(51100) C
• read , A, B ! reads 100 values (A
  followed by B)
• C 2A B 5 ! C(i) 2A(i)
  B(50i) 5
• operation is applied to corresponding elements
  in parallel
• similar to component wise vector addition
• other arithmetic operations (except ) applied
  similarly
• scalar operation performed on each element

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Relational Operators

• whole array or array sections can be compared
  using relational operator
• As usual, type and size constraints need to
  respected
• Comparison to scalars also possible
• Example
• integer, dimension(50) a, b
• logical, dimension(50) c
• c (a lt b) .and. ( a gt a(1))
• ! c(i) is .true. iff a(i) lt b(i) and
  a(i) gt a(1), 1lti lt50
• similarly for other relational operators

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Intrinsic Functions

• Many intrinsic functions available for arrays
• Lifting' of Intrinsic functions of base type to
  arrays
• functions of integers and reals can be applied to
  integer or real arrays
• functions applied pointwise - to all elements
  separately
• size(a) number of elements in array a
• maxval(a) and minval(a)
• maximum and minimum value in integer or real
  array a

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Intrinsic Functions (contd.)

• sum(a), product(a)
• sum or product of elements of integer or real
  array a
• dot_product(a,b)
• dot product of two vectors of same size
• Array operations and intrinsic functions makes
  program more readable
• More efficient also, as operations can be done in
  parallel