C Class

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Chapter 2
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C Class

• A class name
• Data members
• Member functions
• Levels of program access
• Public section of a class can be accessed by
  anyone
• Private section of a class can only be accessed
  by member functions and friends of that class
• Protected section of a class can only be
  accessed by member functions and friends of that
  class, and by member functions and friends of
  derived classes

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Definition of the C class Rectangle
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Program 2.2 Implementation of operations on
Rectangle

• // In the source file Rectangle.C
• include Rectangle.h
• // The prefix Rectangle identifies
  GetHeight() and GetWidth() as member functions
  belong to class Rectangle. It is required because
  the member functions are implemented outside
  their class definition
• int RectangleGetHeight() return h
• int RectangleGetWidth() return w

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Constructor and Destructor

• Constructor is a member function which
  initializes data members of an object.
• Adv all class objects are well-defined as soon
  as they are created.
• Must have the same name of the class
• Must not specify a return type or a return value
• Destructor is a member fucntion which deletes
  data members immediately before the object
  disappears.
• Must be named identical to the name of the class
  prefixed with a tilde .
• It is invoked automatically when a class object
  goes out of scope or when a class object is
  deleted.

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Constructors for Rectangle

• Rectangle r(1, 3, 6, 6)
• Rectangle s new Rectangle(0, 0, 3, 4)

Rectangle t
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Operator Overloading

• C can distinguish the operator when
  comparing two floating point numbers and two
  integers. But what if you want to compare two
  Rectangles?

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Array

• Is it necessary to define an array as an ADT?
• C array requires the index set to be a set of
  consecutive integers starting at 0
• C does not check an array index to ensure that
  it belongs to the range for which the array is
  defined.

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ADT 2.1 GeneralArray
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ADT 2.2 Polynomial
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Polynomial Representations

• Representation 1
• private
• int degree // degree MaxDegree
• float coef MaxDegree 1
• Representation 2
• private
• int degree
• float coef
• PolynomialPolynomial(int d)
• degree d
• coef new float degree1

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Polynomial Representation 3

• class Polynomial // forward delcaration
• class term
• friend Polynomial
• private
• float coef // coefficient
• int exp // exponent
• private
• static term termArrayMaxTerms
• static int free
• int Start, Finish
• term Polynomial termArrayMaxTerms
• Int Polynomialfree 0 // location of next
  free location in temArray

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Representation 3 for two Polynomials

• Represent the following two polynomials
• A(x) 2x1000 1
• B(x) x4 10x3 3x2 1

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Polynomial Addition
O(mn)
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Adding a new Term
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Disadvantages of Representing Polynomials by
Arrays

• What should we do when free is going to exceed
  MaxTerms?
• Either quit or reused the space of unused
  polynomials. But costly.
• If use a single array of terms for each
  polynomial, it may alleviate the above issue but
  it penalizes the performance of the program due
  to the need of knowing the size of a polynomial
  beforehand.

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Sparse Matrices
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ADT 2.3 SparseMatrix
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Sparse Matrix Representation

• Use triple ltrow, column, valuegt
• Store triples row by row
• For all triples within a row, their column
  indices are in ascending order.
• Must know the number of rows and columns and the
  number of nonzero elements

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Sparse Matrix Representation (Cont.)

• class SparseMatrix // forward declaration
• class MatrixTerm
• friend class SparseMatrix
• private
• int row, col, value
• In class SparseMatrix
• private
• int Rows, Cols, Terms
• MatrixTerm smArrayMaxTerms

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Transposing A Matrix

• Intuitive way
• for (each row i)
• take element (i, j, value) and store it in (j,
  i, value) of the transpose
• More efficient way
• for (all elements in column j)
• place element (i, j, value) in position (j, i,
  value)

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Transposing a Matrix
O(termscolumns)
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Fast Matrix Transpose

• The O(termscolumns) time gt O(rowscolumns2)
  when terms is the order of rowscolumns
• A better transpose function
• It first computes how many terms in each columns
  of matrix a before transposing to matrix b. Then
  it determines where is the starting point of each
  row for matrix b. Finally it moves each term from
  a to b.

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O(columns)
O(terms)
O(columns-1)
O(terms)
O(row column)
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Matrix Multiplication

• Definition Given A and B, where A is mxn and B
  is nxp, the product matrix Result has dimension
  mxp. Its ij element is
• for 0 i lt m and 0 j lt p.

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Matrix Multiplication
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Representation of Arrays

• Multidimensional arrays are usually implemented
  by one dimensional array via either row major
  order or column major order.
• Example One dimensional array

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Two Dimensional Array Row Major Order
Col 0
Col 1
Col 2
Col u2 - 1
Row 0
X
X
X
X
X
X
X
X
Row 1
Row u1 - 1
X
X
X
X
u2 elements
u2 elements
Row u1 - 1
Row 0
Row 1
Row i
i u2 element
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Generalizing Array Representation

• The address indexing of Array Ai1i2,,in is
  
• a i1 u2 u3 un
• i2 u3 u4 un
• i3 u4 u5 un
• in-1 un
• in
• a

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String

• Usually string is represented as a character
  array.
• General string operations include comparison,
  string concatenation, copy, insertion, string
  matching, printing, etc.

H
e
l
l
o
W
o
r
l
d
\0
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String Matching The Knuth-Morris-Pratt Algorithm

• Definition If p p0p1pn-1 is a pattern, then
  its failure function, f, is defined as
• If a partial match is found such that si-j si-1
  p0p1pj-1 and si ? pj then matching may be
  resumed by comparing si and pf(j1)1 if j ? 0.
  If j 0, then we may continue by comparing si1
  and p0.

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Fast Matching Example

• Suppose exists a string s and a pattern pat
  abcabcacab, lets try to match pattern pat in
  string s.
• j 0 1 2 3 4 5 6 7
  8 9
• pat a b c a b c a c
  a b
• f -1 -1 -1 0 1 2 3 -1
  0 1
• s - a b c a ? ? . .
  . ?
• pat a b c a b c a c
  a b
• a b c a b c a c
  a b

j 4, pf(j-1)1 p1
New start matching point
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