Lecture 1 Data Structures

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Lecture 1Data Structures

• Shafay Shamail
• September 05, 2006

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Introduction

• Course outline
• Rules and regulations
• Course contents
• Grading

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• Rules
• Conventions
• Good Programming Practices

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Data Types

• Simple (basic)
• char, int, float, double
• Modifiers
• signed, unsigned
• Qualifiers
• static, const, volatile, void
• Structured (derived)
• Arrays, structures, unions, classes
• Advanced (composite)
• List, queues, stacks, trees, graphs

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Abstract Data Type (ADT)

• Abstraction
• Separating data from implementation
• Generalization
• ADT
• A collection of related data items together with
  basic operations between them and operations to
  be performed on them

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Arrays

• Definition
• Collection of items of same type in contiguous
  memory
• ADT
• Collection of data items/elements
• A fixed size sequence (ordered set) of elements,
  all of the same type
• Basic operations
• Direct access to each element in the array so
  that values can be retrived from or stored in
  this element

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Structures

• Definition
• Collection of items of same or different types in
  contiguous memory
• ADT
• Collection of data elements
• A fixed-size sequence (ordered set) of elements,
  not necessarily of the same type. The elements
  are called members or fields.
• Basic operations
• Direct access to each member of the structure so
  that values can be retrieved or stored in this
  member

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Strings

• Definition
• Collection of characters in contiguous memory
• A special form of array
• ADT
• Collection of data elements
• A finite sequence of characters drawn from some
  given character set
• Basic operations
• Input, output, compare, copy, insert, replace,
  length, concatenate, find, delete

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Sequences

• S lts0, s1, s2, , sn-1gt
• S is of length n
• len(S) n
• first(S) s0
• last(S) Sn-1
• len(nilseq) 0
• first(nilseq) not defined
• last(nilseq) not defined

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Sequences

• abstract typedef ltlttpgtgt stp1
• An ADT of a sequence spt1 of arbitrary length
  consisting of elements of same type tp
• abstract typedef lttp0, tp1, , tpn-1gt stp2
• ADT stp2, whose values are sequences of fixed
  length, and of elements of specific type
• abstract typedef ltlttp, ngtgt stp3
• ADT stp3, a sequence of fixed length n, all of
  same type tp elements

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Sequences

• abstract typedef ltltintgtgt seq1
• Sequence of integers of any length
• abstract typedef ltint, char, floatgt seq2
• Sequence of length 3, consisting of int, char,
  float
• abstract typedef ltltint, 10gtgt seq3
• Sequence of 10 integers
• abstract typedef ltlt , 2gtgt seq4
• Arbitrary sequence of length 2 (pair)

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Sequences

• Two sequences are equal if each element of the
  first is equal to the corresponding element of
  the second
• A subsequence is a contiguous portion of a
  sequence
• If S is a sequence then sub(S, i, j) consists of
  j elements starting at location i within S
• Concatenation U ST
• All elements of S followed by all elements of T
• Place (S, i, x)
• Insert x after position i, or at first position
  if i-1, and shift all remaining elements to
  right by one position
• place (S, i, x) sub(S, 0, i-1) ltxgt sub(S,
  i1, len(S)-(i1))
• Delete
• S-ltxgt Sequence S without all occurrences of S
• delete(S, i) delete element at position I
• sub(S, 0, i) sub(S, i1, len(S)-(i1))

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ADT RATIONAL

• / value definition /
• abstract typedef ltinteger, integergt RATIONAL
• condition RATIONAL1 ! 0
• / operator definition /
• abstract RATIONAL makerational(a,b)
• Int a,b
• precondition b ! 0
• postcondition makerational0 a
• makerational1 b
• abstract RATIONAL add(a, b)
• RATIONAL a, b
• postcondition add1 a1b1
• add0 a0b1 b0a1
• abstract RATIONAL mult(a, b)
• RATIONAL a, b
• postcondition mult0 a0b0

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ADT STRING

• / value definition /
• abstract typedef ltltchargtgt STRING
• / operator definition /
• abstract length (s)
• STRING s
• postcondition length len(s)
• abstract STRING concat(s1, s2)
• STRING s1, s2
• postcondition concat s1s2
• abstract STRING substr(s, i, j)
• STRING s
• int i, j
• precondition 0 lt i lt len(s)
• 0 lt j lt len(s) - i
• postcondition substr sub(s, i, j)

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ADT ARRAY

• / value definition /
• abstract typedef ltlteltype, ubgtgt ARRTYPE(ub,
  eltype)
• / operator definition /
• abstract eltype extract(a, i)
• ARRTYPE(ub, eltype) a
• int i
• precondition 0 lt i lt ub
• postcondition extract ai
• abstract store(a, i, elt)
• ARRTYPE(ub, eltype) a
• int i
• eltype elt
• precondition 0 lt i lt ub
• postcondition ai elti